12. IN the next place, from what has been now proved, our great author

has deduced this farther consequence, no less surprizing than elegant;

that each of the particles, out of which the bodies of the sun and

planets are framed, exert their power of gravitation by the same law,

and in the same proportion to the distance, as the great bodies which

they compose. For this purpose he first demonstrates, that if a globe

were compounded of particles, which will attract the particles of any

other body reciprocally in the duplicate proportion of their distances,

the whole globe will attract the same in the reciprocal duplicate

proportion of their distances from the center of the globe; provided

the globe be of uniform density throughout[251]. And from this our

author deduces the reverse, that if a globe acts upon distant bodies by

the law just now specified, and the power of the globe is derived from

its being composed of attractive particles; each of those particles

will attract after the same proportion[252]. The manner of deducing

this is not set down at large by our author, but is as follows. The

globe is supposed to act upon the particles of a body without it

constantly in the reciprocal duplicate proportion of their distances

from its center; and therefore at the same distance from the globe, on

which side soever the body be placed, the globe will act equally upon

it. Now because, if the particles, of which the globe is composed,

acted upon those without in the reciprocal duplicate proportion of

their distances, the whole globe would act upon them in the same manner

as it does; therefore, if the particles of the globe have not all of

them that property, some must act stronger than in that proportion,

while others act weaker: and if this be the condition of the globe,

it is plain, that when the body attracted is in such a situation

in respect of the globe, that the greater number of the strongest

particles are nearest to it, the body will be more forcibly attracted;

than when by turning the globe about, the greater quantity of weak

particles should be nearest, though the distance of the body should

remain the same from the center of the globe. Which is contrary to what

was at first remarked, that the globe on all sides of it acts with the

same strength at the same distance. Whence it appears, that no other

constitution of the globe can agree to it.

13. FROM these propositions it is farther collected, that if all

the particles of one globe attract all the particles of another in

the proportion so often mentioned, the attracting globe will act

upon the other in the same proportion to the distance between the

center of the globe which attracts, and the center of that which is

attracted[253]: and farther, that this proportion holds true, though

either or both the globes be composed of dissimilar parts, some rarer

and some more dense; provided only, that all the parts in the same

globe equally distant from the center be homogeneous[254]. And also,

if both the globes attract each other[255]. All which place it beyond

contradiction, that this proportion obtains with as much exactness

near and contiguous to the surface of attracting globes, as at greater

distances from them.

14. THUS our author, without the pompous pretence of explaining the

cause of gravity, has made one very important step toward it, by

shewing that this power in the great bodies of the universe, is derived

from the same power being lodged in every particle of the matter which

composes them: and consequently, that this property is no less than

universal to all matter whatever, though the power be too minute to

produce any visible effects on the small bodies, wherewith we converse,

by their action on each other[256]. In the fixed stars indeed we have

no particular proof that they have this power; for we find no apperance

to demonstrate that they either act, or are acted upon by it. But

since this power is found to belong to all bodies, whereon we can make

observation; and we see that it is not to be altered by any change in

the form of bodies, but always accompanies them in every shape without

diminution, remaining ever proportional to the quantity of solid matter

in each; such a power must without doubt belong universally to all

matter.

15. THIS therefore is the universal law of matter; which recommends

it self no less for its great plainness and simplicity, than for the

surprizing discoveries it leads us to. By this principle we learn the

different weight, which the same body will have upon the surfaces

of the sun and of diverse planets; and by the same we can judge of

the composition of those celestial bodies, and know the density of

each; which is formed of the most compact, and which of the most rare

substance. Let the adversaries of this philosophy reflect here, whether

loading this principle with the appellation of an occult quality, or

perpetual miracle, or any other reproachful name, be sufficient to

dissuade us from cultivating it; since this quality, which they call

occult, leads to the knowledge of such things, that it would have

been reputed no less than madness for any one, before they had been

discovered, even to have conjectured that our faculties should ever

have reached so far.

16. SEE how all this naturally follows from the foregoing principles

in those planets, which have satellites moving about them. By the

times, in which these satellites perform their revolutions, compared

with their distances from their respective primary, the proportion

between the power, with which one primary attracts his satellites, and

the force with which any other attracts his will be known; and the

proportion of the power with which any planet attracts its secondary,

to the power with which it attracts a body at its surface is found,

by comparing the distance of the secondary planet from the center of

the primary, to the distance of the primary planet’s surface from the

same: and from hence is deduced the proportion between the power of

gravity upon the surface of one planet, to the gravity upon the surface

of another. By the like method of comparing the periodical time of a

primary planet about the sun, with the revolution of a satellite about

its primary, may be found the proportion of gravity, or of the weight

of any body upon the surface of the sun, to the gravity, or to the

weight of the same body upon the surface of the planet, which carries

about the satellite.

17. BY these kinds of computation it is found, that the weight of the

same body upon the surface of the sun will be about 23 times as great,

as here upon the surface of the earth; about 10⅗ times as great, as

upon the surface of Jupiter; and near 19 times as great, as upon the

surface of Saturn[257].

18. THE quantity of matter, which composes each of these bodies, is

proportional to the power it has upon a body at a given distance. By

this means it is found, that the sun contains 1067 times as much matter

as Jupiter; Jupiter 158⅔ times as much as the earth, and 2-5/6 times as

much as Saturn[258]. The diameter of the sun is about 92 times, that of

Jupiter about 9 times, and that of Saturn about 7 times the diameter of

the earth.

19. BY making a comparison between the quantity of matter in these

bodies and their magnitudes, to be found from their diameters, their

respective densities are readily deduced; the density of every body

being measured by the quantity of matter contained under the same bulk,

as has been above remarked[259]. Thus the earth is found 4¼ times

more dense than Jupiter; Saturn has between ⅔ and ¾ of the density of

Jupiter; but the sun has one fourth part only of the density of the

earth[260]. From which this observation is drawn by our author; that

the sun is rarified by its great heat, and that of the three planets

named, the more dense is nearer the sun than the more rare; as was

highly reasonable to expect, the densest bodies requiring the greatest

heat to agitate and put their parts in motion; as on the contrary, the

planets which are more rare, would be rendered unfit for their office,

by the intense heat to which the denser are exposed. Thus the waters

of our seas, if removed to the distance of Saturn from the sun, would

remain perpetually frozen; and if as near the sun as Mercury, would

constantly boil[261].

20. THE densities of the three planets Mercury, Venus, and Mars, which

have no satellites, cannot be expresly assigned; but from what is

found in the others, it is very probable, that they also are of such

different degrees of density, that universally the planet which is

nearest to the sun, is formed of the most compact substance.

~CHAP~. VI.

Of the FLUID PARTS of the PLANETS.

THIS globe, that we inhabit, is composed of two parts; the solid earth,

which affords us a foundation to dwell upon; and the seas and other

waters, that furnish rains and vapours necessary to render the earth

fruitful, and productive of what is requisite for the support of life.

And that the moon, though but a secondary planet, is composed in like

manner, is generally thought, from the different degrees of light

which appear on its surface; the parts of that planet, which reflect a

dim light, being supposed to be fluid, and to imbibe the sun’s rays,

while the solid parts reflect them more copiously. Some indeed do not

allow this to be a conclusive argument: but whether we can distinguish

the fluid part of the moon’s surface from the rest or not; yet it is

most probable that there are two such different parts, and with still

greater reason we may ascribe the like to the other primary planets,

which yet more nearly resemble our earth. The earth is also encompassed

by another fluid the air, and we have before remarked, that probably

the rest of the planets are surrounded by the like. These fluid parts

in particular engage our author’s attention, both by reason of some

remarkable appearances peculiar to them, and likewise of some effects

they have upon the whole bodies to which they belong.

2. FLUIDS have been already treated of in general, with respect to the

effect they have upon solid bodies moving in them[262]; now we must

consider them in reference to the operation of the power of gravity

upon them. By this power they are rendered weighty, like all other

bodies, in proportion to the quantity of matter, which is contained

in them. And in any quantity of a fluid the upper parts press upon

the lower as much, as any solid body would press on another, whereon

it should lie. But there is an effect of the pressure of fluids on

the bottom of the vessel, wherein they are contained, which I shall

particularly explain. The force supported by the bottom of such a

vessel is not simply the weight of the quantity of the fluid in the

vessel, but is equal to the weight of that quantity of the fluid, which

would be contained in a vessel of the same bottom and of equal width

throughout, when this vessel is filled up to the same height, as that

to which the vessel proposed is filled. Suppose water were contained

in the vessel A B C D (in fig. 109.) filled up to E F. Here it is

evident, that if a part of the bottom, as G H, which is directly under

any part of the space E F, be considered separately; it will appear

at once, that this part sustains the weight of as much of the fluid,

as stands perpendicularly over it up to the height of E F; that is,

the two perpendiculars G I and H K being drawn, the part G H of the

bottom will sustain the whole weight of the fluid included between

these two perpendiculars. Again, I say, every other part of the bottom

equally broad with this, will sustain as great a pressure. Let the

part L M be of the same breadth with G H. Here the perpendiculars

L O and M N being drawn, the quantity of water contained between

these perpendiculars is not so great, as that contained between the

perpendiculars G I and H K; yet, I say, the pressure on L M will be

equal to that on G H. This will appear by the following considerations.

It is evident, that if the part of the vessel between O and N were

removed, the water would immediately flow out, and the surface E F

would subside; for all parts of the water being equally heavy, it must

soon form itself to a level surface, if the form of the vessel, which

contains it, does not prevent. Therefore since the water is prevented

from rising by the side N O of the vessel, it is manifest, that it must

press against N O with some degree of force. In other words, the water

between the perpendiculars L O and M N endeavours to extend itself with

a certain degree of force; or more correctly, the ambient water presses

upon this, and endeavours to force this pillar or column of water into

a greater length. But since this column of water is sustained between

N O and L M, each of these parts of the vessel will be equally pressed

against by the power, wherewith this column endeavours to extend.

Consequently L M bears this force over and above the weight of the

column of water between L O and M N. To know what this expansive force

is, let the part O N of the vessel be removed, and the perpendiculars

L O and M N be prolonged; then by means of some pipe fixed over N O

let water be filled between these perpendiculars up to P Q an equal

height with E F. Here the water between the perpendiculars L P and M Q

is of an equal height with the highest part of the water in the vessel;

therefore the water in the vessel cannot by its pressure force it

up higher, nor can the water in this column subside; because, if it

should, it would raise the water in the vessel to a greater height than

itself. But it follows from hence, that the weight of water contained

between P O and Q N is a just balance to the force, wherewith the

column between L O and M N endeavours to extend. So the part L M of

the bottom, which sustains both this force and the weight of the water

between L O and M N, is pressed upon by a force equal to the united

weight of the water between L O and M N, and the weight of the water

between P O and Q N; that is, it is pressed on by a force equal to the

weight of all the water contained between L P and M Q. And this weight

is equal to that of the water contained between G I and H K, which is

the weight sustained by the part G H of the bottom. Now this being

true of every part of the bottom B C, it is evident, that if another

vessel R S T V be formed with a bottom R V equal to the bottom B C, and

be throughout its whole height of one and the same breadth; when this

vessel is filled with water to the same height, as the vessel A B C D

is filled, the bottoms of these two vessels shall be pressed upon with

equal force. If the vessel be broader at the top than at the bottom,

it is evident, that the bottom will bear the pressure of so much of

the fluid, as is perpendicularly over it, and the sides of the vessel

will support the rest. This property of fluids is a corollary from a

proposition of our author[263]; from whence also he deduces the effects

of the pressure of fluids on bodies resting in them. These are, that

any body heavier than a fluid will sink to the bottom of the vessel,

wherein the fluid is contained, and in the fluid will weigh as much as

its own weight exceeds the weight of an equal quantity of the fluid;

any body uncompressible of the same density with the fluid, will rest

any where in the fluid without suffering the least change either in

its place or figure from the pressure of such a fluid, but will remain

as undisturbed as the parts of the fluid themselves; but every body

of less density than the fluid will swim on its surface, a part only

being received within the fluid. Which part will be equal in bulk to

a quantity of the fluid, whose weight is equal to the weight of the

whole body; for by this means the parts of the fluid under the body

will suffer as great a pressure as any other parts of the fluid as much

below the surface as these.

3. IN the next place, in relation to the air, we have above made

mention, that the air surrounding the earth being an elastic fluid,

the power of gravity will have this effect on it, to make the lower

parts near the surface of the earth more compact and compressed

together by the weight of the air incumbent, than the higher parts,

which are pressed upon by a less quantity of the air, and therefore

sustain a less weight[264]. It has been also observed, that our author

has laid down a rule for computing the exact degree of density in

the air at all heights from the earth[265]. But there is a farther

effect from the air’s being compressed by the power of gravity, which

he has distinctly considered. The air being elastic and in a state

of compression, any tremulous body will propagate its motion to the

air, and excite therein vibrations, which will spread from the body

that occasions them to a great distance. This is the efficient cause

of sound: for that sensation is produced by the air, which, as it

vibrates, strikes against the organ of hearing. As this subject was

extremely difficult, so our great author’s success is surprizing.

4. OUR author’s doctrine upon this head I shall endeavour to explain

somewhat at large. But preliminary thereto must be shewn, what he has

delivered in general of pressure propagated through fluids; and also

what he has set down relating to that wave-like motion, which appears

upon the surface of water, when agitated by throwing any thing into it,

or by the reciprocal motion of the finger, &c.

5. CONCERNING the first, it is proved, that pressure is spread

through fluids, not only right forward in a streight line, but also

laterally, with almost the same ease and force. Of which a very obvious

exemplification by experiment is proposed: that is, to agitate the

surface of water by the reciprocal motion of the finger forwards and

backwards only; for though the finger have no circular motion given

it, yet the waves excited in the water will diffuse themselves on each

hand of the direction of the motion, and soon surround the finger. Nor

is what we observe in sounds unlike to this, which do not proceed in

straight lines only, but are heard though a mountain intervene, and

when they enter a room in any part of it, they spread themselves into

every corner; not by reflection from the walls, as some have imagined,

but as far as the sense can judge, directly from the place where they

enter.

6. HOW the waves are excited in the surface of stagnant water, may be

thus conceived. Suppose in any place, the water raised above the rest

in form of a small hillock; that water will immediately subside, and

raise the circumambient water above the level of the parts more remote,

to which the motion cannot be communicated under longer time. And

again, the water in subsiding will acquire, like all falling bodies, a

force, which will carry it below the level surface, till at length the

pressure of the ambient water prevailing, it will rise again, and even

with a force like to that wherewith it descended, which will carry it

again above the level. But in the mean time the ambient water before

raised will subside, as this did, sinking below the level; and in so

doing, will not only raise the water, which first subsided, but also

the water next without itself. So that now beside the first hillock, we

shall have a ring investing it, at some distance raised above the plain

surface likewise; and between them the water will be sunk below the

rest of the surface. After this, the first hillock, and the new made

annular rising, will descend; raising the water between them, which

was before depressed, and likewise the adjacent part of the surface

without. Thus will these annular waves be successively spread more

and more. For, as the hillock subsiding produces one ring, and that

ring subsiding raises again the hillock, and a second ring; so the

hillock and second ring subsiding together raise the first ring, and

a third; then this first and third ring subsiding together raise the

first hillock, the second ring, and a fourth; and so on continually,

till the motion by degrees ceases. Now it is demonstrated, that these

rings ascend and descend in the manner of a pendulum; descending with

a motion continually accelerated, till they become even with the plain

surface of the fluid, which is half the space they descend; and then

being retarded again by the same degrees as those, whereby they were

accelerated, till they are depressed below the plain surface, as much

as they were before raised above it: and that this augmentation and

diminution of their velocity proceeds by the same degrees, as that of

a pendulum vibrating in a cycloid, and whose length should be a fourth

part of the distance between any two adjacent waves: and farther, that

a new ring is produced every time a pendulum, whose length is four

times the former, that is, equal to the interval between the summits of

two waves, makes one oscillation or swing[266].

7. THIS now opens the way for understanding the motion consequent upon

the tremors of the air, excited by the vibrations of sonorous bodies:

which we must conceive to be performed in the following manner.

8. LET A, B, C, D, E, F, G, H (in fig. 110.) represent a series of

the particles of the air, at equal distances from each other. I K L

a musical chord, which I shall use for the tremulous and sonorous

body, to make the conception as simple as may be. Suppose this chord

stretched upon the points I and L, and forcibly drawn into the

situation I K L, so that it become contiguous to the particle A in its

middle point K: and let the chord from this situation begin to recoil,

pressing against the particle A, which will thereby be put into motion

towards B: but the particles A, B, C being equidistant, the elastic

power, by which B avoids A, is equal to, and balanced by the power, by

which it avoids C; therefore the elastic force, by which B is repelled

from A, will not put B into any degree of motion, till A is by the

motion of the chord brought nearer to B, than B is to C: but as soon as

that is done, the particle B will be moved towards C; and being made

to approach C, will in the next place move that; which will upon that

advance, put D likewise into motion, and so on: therefore the particle

A being moved by the chord, the following particles of the air B, C, D,

&c. will successively be moved. Farther, if the point K of the chord

moves forward with an accelerated velocity, so that the particle A

shall move against B with an advancing pace, and gain ground of it,

approaching nearer and nearer continually; A by approaching will press

more upon B, and give it a greater velocity likewise, by reason that as

the distance between the particles diminishes, the elastic power, by

which they fly each other, increases. Hence the particle B, as well as

A, will have its motion gradually accelerated, and by that means will

more and more approach to C. And from the same cause C will more and

more approach D; and so of the rest. Suppose now, since the agitation

of these particles has been shewn to be successive, and to follow one

another, that E be the remotest particle moved, while the chord is

moving from its curve situation I K L into that of a streight line, as

I k L; and F the first which remains unaffected, though just upon the

point of being put into motion. Then shall the particles A, B, C, D,

E, F, G, when the point K is moved into k, have acquired the rangement

represented by the adjacent points _a, b, c, d, e, f, g_: in which _a_

is nearer to _b_ than _b_ to _c_, and _b_ nearer to _c_ than _c_ to

_d_, and _c_ nearer to _d_ than _d_ to _e_ and _d_ nearer to _e_ than

_e_ to _f_, and lastly _e_ nearer to _f_ than _f_ to _g_.

9. BUT now the chord having recovered its rectilinear situation I k L,

the following motion will be changed, for the point K, which before

advanced with a motion more and more accelerated, though by the force

it has acquired it will go on to move the same way as before, till it

has advanced near as far forwards, as it was at first drawn backwards;

yet the motion of it will henceforth be gradually lessened. The effect

of which upon the particles _a, b, c, d, e, f, g_ will be, that by the

time the chord has made its utmost advance, and is upon the return,

these particles will be put into a contrary rangement; so that _f_

shall be nearer to _g_, than _e_ to _f_, and _e_ nearer to _f_ than _d_

to _e_; and the like of the rest, till you come to the first particles

_a_, _b_, whose distance will then be nearly or quite what it was at

first. All which will appear as follows. The present distance between

_a_ and _b_ is such, that the elastic power, by which _a_ repels _b_,

is strong enough to maintain that distance, though a advance with the

velocity, with which the string resumes its rectilinear figure; and

the motion of the particle _a_ being afterwards slower, the present

elasticity between _a_ and _b_ will be more than sufficient to preserve

the distance between them. Therefore while it accelerates _b_ it will

retard _a_. The distance _b c_ will still diminish, till _b_ come about

as near to _c_, as it is from a at present; for after the distances

_a b_ and _b c_ are become equal, the particle _b_ will continue its

velocity superior to that of _c_ by its own power of inactivity, till

such time as the increase of elasticity between _b_ and _c_ more than

shall be between _a_ and _b_ shall suppress its motion: for as the

power of inactivity in _b_ made a greater elasticity necessary on the

side of a than on the side of _c_ to push _b_ forward, so what motion

_b_ has acquired it will retain by the same power of inactivity, till

it be suppressed by a greater elasticity on the side of _c_, than on

the side of _a_. But as soon as _b_ begins to slacken its pace the

distance of _b_ from c will widen as the distance _a b_ has already

done. Now as _a_ acts on _b_, so will _b_ on _c_, _c_ on _d_, &c. so

that the distances between all the particles _b, c, d, e, f, g_ will

be successively contracted into the distance of _a_ from _b_, and then

dilated again. Now because the time, in which the chord describes

this present half of its vibration, is about equal to that it took up

in describing the former; the particles _a_, _b_ will be as long in

dilating their distance, as before in contracting it, and will return

nearly to their original distance. And farther, the particles _b_, _c_,

which did not begin to approach so soon as _a_, _b_, are now about as

much longer, before they begin to recede; and likewise the particles

_c_, _d_, which began to approach after _b_, _c_, begin to separate

later. Whence it appears that the particles, whose distance began to be

lessened, when that of _a_, _b_ was first enlarged, viz. the particles

_f_, _g,_ should be about their nearest distance, when _a_ and _b_ have

recovered their prime interval. Thus will the particles _a, b, c, d, e,

f, g_ have changed their situation in the manner asserted. But farther,

as the particles _f_, _g_ or F, G gradually approach each other, they

will move by degrees the succeeding particles to as great a length, as

the particles A, B did by a like approach. So that, when the chord has

made its greatest advance, being arrived into the situation I ϰ L, the

particles moved by it will have the rangement noted by the points α, β,

γ, δ, ε, ζ, η, θ, λ, μ, ν, χ. Where α, β are at the original distance

of the particles in the line A H; ζ, η are the nearest of all, and the

distance ν χ is equal to that between α and β.

10. BY this time the chord I ϰ L begins to return, and the distance

between the particles α and β being enlarged to its original magnitude,

α has lost all that force it had acquired by its motion, being now at

rest; and therefore will return with the chord, making the distance

between α and β greater than the natural; for β will not return so

soon, because its motion forward is not yet quite suppressed, the

distance β γ not being already enlarged to its prime dimension: but the

recess of α, by diminishing the pressure upon β by its elasticity, will

occasion the motion of β to be stopt in a little time by the action of

γ, and then shall β begin to return: at which time the distance between

γ and δ shall by the superior action of δ above β be enlarged to the

dimension of the distance β γ, and therefore soon after to that of α β.

Thus it appears, that each of these particles goes on to move forward,

till its distance from the preceding one be equal to its original

distance; the whole chain α, β, γ, δ, ε, ζ, η, having an undulating

motion forward, which is stopt gradually by the excess of the expansive

power of the preceding parts above that of the hinder. Thus are these

parts successively stopt, as before they were moved; so that when the

chord has regained its rectilinear situation, the expansion of the

parts of the air will have advanced so far, that the interval between

ζ η, which at present is most contracted, will then be restored to its

natural size: the distances between η and θ, θ and λ, λ and μ, μ and ν,

ν and χ, being successively contracted into the present distance of ζ

from η, and again enlarged; so that the same effect shall be produced

upon the parts beyond ζ η, by the enlargement of the distance between

those two particles, as was occasioned upon the particles α, β, γ, δ,

ε, ζ, η, θ, λ, μ, ν, χ, by the enlargement of the distance α β to its

natural extent. And therefore the motion in the air will be extended

half as much farther as at present, and the distance between ν and χ

contracted into that, which is at present between ζ and η, all the

particles of the air in motion taking the rangement expressed in figure

111. by the points α, β, γ, δ, ε, ζ, η, θ, λ, μ, ν, χ, ϰ, ρ, σ, τ, φ

wherein the particles from α to χ have their distances from each other

gradually diminished, the distances between the particles ν, χ being

contracted the most from the natural distance between those particles,

and the distance between α, β as much augmented, and the distance

between the middle particles ζ, η becoming equal to the natural. The

particles π, ρ, ω τ, φ which follow χ, have their distances gradually

greater and greater, the particles ν, χ, π, ρ, σ, τ, φ being ranged

like the particles _a, b, c, d, e, f, g_, or like the particles ζ,

η, θ, λ, μ, ν, χ in the former figure. Here it will be understood,

by what has been before explained, that the particles ζ, η being at

their natural distance from each other, the particle ζ is at rest, the

particles ε, δ, λ, β, ϰ between them and the string being in motion

backward, and the rest of the particles η, θ, λ, μ, ν, χ, π, ρ, σ, τ

in motion forward: each of the particles between η and χ moving faster

than that, which immediately follows it; but of the particles from χ

to φ, on the contrary, those behind moving on faster than those, which

precede.

11. BUT now the string having recovered its rectilinear figure, though

it shall go on recoiling, till it return near to its first situation

I K L, yet there will be a change in its motion; so that whereas it

returned from the situation I ϰ L with an accelerated motion, its

motion shall from hence be retarded again by the same degrees, as

accelerated before. The effect of which change upon the particles of

the air will be this. As by the accelerated motion of the chord α

contiguous to it moved faster than β, γ, so as to make the interval α

β greater than the interval β γ, and from thence β was made likewise

to move faster than γ, and the distance between β and γ rendered

greater than the distance between γ and δ, and so of the rest; now the

motion of α being diminished, β shall overtake it, and the distance

between α and β be reduced into that, which is at present between β

and γ, the interval between β and γ being inlarged into the present

distance between α and β; but when the interval β γ is increased to

that, which is at present between α and β γ the distance between γ

and δ shall be enlarged to the present distance between γ and β,

and the distance between δ and ι inlarged into the present distance

between γ and δ; and the same of the rest. But the chord more and more

slackening its pace, the distance between α and β shall be more and

more diminished; and in consequence of that the distance between β and

γ shall be again contracted, first into its present dimension, and

afterwards into a narrower space; while the interval γ δ shall dilate

into that at present between α and β, and as soon as it is so much

enlarged, it shall contract again. Thus by the reciprocal expansion

and contraction of the air between α and ζ, by that time the chord is

got into the situation I K L, the interval ζ η shall be expanded into

the present distance between α and β; and by that time likewise the

present distance of α from β will be contracted into their natural

interval: for this distance will be about the same time in contracting

it self, as has been taken up in its dilatation; seeing the string will

be as long in returning from its rectilinear figure, as it has been in

recovering it from its situation I ϰ L. This is the change which will

be made in the particles between α and ζ. As for those between ζ and

χ, because each preceding particle advances faster than that, which

immediately follows it, their distances will successively be dilated

into that, which is at present between ζ and η. And as soon as any two

particles are arrived at their natural distance, the hindermost of them

shall be stopt, and immediately after return, the distances between

the returning particles being greater than the natural. And this

dilatation of these distances shall extend so far, by that time the

chord is returned into its first situation I K L, that the particles ι

χ shall be removed to their natural distance. But the dilatation of ν

χ shall contract the interval τ φ into that at present between ν and

χ, and the contraction of the distance between those two particles τ

and φ will agitate a part of the air beyond; so that when the chord is

returned into the situation I K L, having made an intire vibration, the

moved particles of the air will take the rangement expressed by the

points, _l, m, n, o, p, q, r, s, t, u, w, x, y, z_, 1, 2, 3, 4, 5, 6,

7, 8: in which _l m_, are at the natural distance of the particles, the

distance _m n_ greater than _l m_ and _n o_ greater than _m n_, and so

on, till you come to _q r_, the widest of all: and then the distances

gradually diminish not only to the natural distance, as _w x_, but till

they are contracted as much as χ τ was before; which falls out in the

points 2, 3, from whence the distances augment again, till you come to

the part of the air untouched.

12. THIS is the motion, into which the air is put, while the chord

makes one vibration, and the whole length of air thus agitated in

the time of one vibration of the chord our author calls the length

of one pulse. When the chord goes on to make another vibration, it

will not only continue to agitate the air at present in motion, but

spread the pulsation of the air as much farther, and by the same

degrees, as before. For when the chord returns into its rectilinear

situation I _k_ L, _l m_ shall be brought into its most contracted

state, _q r_ now in the state of greatest dilatation shall be reduced

to its natural distance, the points _w_, _x_ now at their natural

distance shall be at their greatest distance, the points 2, 3 now most

contracted enlarged to their natural distance, and the points 7, 8

reduced to their most contracted state: and the contraction of them

will carry the agitation of the air as far beyond them, as that motion

was carried from the chord, when it first moved out of the situation

I K L into its rectilinear figure. When the chord is got into the

situation I ϰ L, _l m_ shall recover its natural dimensions, _q r_ be

reduced to its state of greatest contraction, _w x_ brought to its

natural dimension, the distance 2 3 enlarged to the utmost, and the

points 7, 8 shall have recovered their natural distance; and by thus

recovering themselves they shall agitate the air to as great a length

beyond them, as it was moved beyond the chord, when it first came into

the situation I ϰ L. When the chord is returned back again into its

rectilinear situation, _l m_ shall be in its utmost dilatation, _q r_

restored again to its natural distance, _w x_ reduced into its state of

greatest contraction, 2 3 shall recover its natural dimension, and 7 8

be in its state of greatest dilatation. By which means the air shall be

moved as far beyond the points 7, 8, as it was moved beyond the chord,

when it before made its return back to its rectilinear situation; for

the particles 7, 8 have been changed from their state of rest and

their natural distance into a state of contraction, and then have

proceeded to the recovery of their natural distance, and after that to

a dilatation of it, in the same manner as the particles contiguous to

the chord were agitated before. In the last place, when the chord is

returned into the situation I K L, the particles of air from _l_ to δ

shall acquire their present rangement, and the motion of the air be

extended as much farther. And the like will happen after every compleat

vibration of the string.

13. CONCERNING this motion of sound, our author shews how to compute

the velocity thereof, or in what time it will reach to any proposed

distance from the sonorous body. For this he requires to know the

height of air, having the same density with the parts here at the

surface of the earth, which we breath, that would be equivalent in

weight to the whole incumbent atmosphere. This is to be found by the

barometer, or common weatherglass. In that instrument quicksilver is

included in a hollow glass cane firmly closed at the top. The bottom is

open, but immerged into quicksilver contained in a vessel open to the

air. Care is taken when the lower end of the cane is immerged, that the

whole cane be full of quicksilver, and that no air insinuate itself.

When the instrument is thus fixed, the quicksilver in the cane being

higher than that in the vessel, if the top of the cane were open, the

fluid would soon sink out of the glass cane, till it came to a level

with that in the vessel. But the top of the cane being closed up, so

that the air, which has free liberty to press on the quicksilver in

the vessel, cannot bear at all on that, which is within the cane, the

quicksilver in the cane will be suspended to such a height, as to

balance the pressure of the air on the quicksilver in the vessel. Here

it is evident, that the weight of the quicksilver in the glass cane is

equivalent to the pressure of so much of the air, as is perpendicularly

over the hollow of the cane; for if the cane be opened that the air may

enter, there will be no farther use of the quicksilver to sustain the

pressure of the air without; for the quicksilver in the cane, as has

already been observed, will then subside to a level with that without.

Hence therefore if the proportion between the density of quicksilver

and of the air we breath be known, we may know what height of such air

would form a column equal in weight to the column of quicksilver within

the glass cane. When the quicksilver is sustained in the barometer

at the height of 30 inches, the height of such a column of air will

be about 29725 feet; for in this case the air has about 1/870 of the

density of water, and the density of quicksilver exceeds that of water

about 13⅔ times, so that the density of quicksilver exceeds that of the

air about 11890 times; and so many times 30 inches make 29725 feet. Now

Sir ~ISAAC NEWTON~ determines, that while a pendulum of the length of

this column should make one vibration or swing, the space, which any

sound will have moved, shall bear to this length the same proportion,

as the circumference of a circle bears to the diameter thereof;

that is, about the proportion of 355 to 113[267]. Only our author

here considers singly the gradual progress of sound in the air from

particle to particle in the manner we have explained, without taking

into consideration the magnitude of those particles. And though there

requires time for the motion to be propagated from one particle to

another, yet it is communicated to the whole of the same particle in an

instant: therefore whatever proportion the thickness of these particles

bears to their distance from each other, in the same proportion will

the motion of sound be swifter. Again the air we breath is not simply

composed of the elastic part, by which sound is conveyed, but partly of

vapours, which are of a different nature; and in the computation of the

motion of sound we ought to find the height of a column of this pure

air only, whose weight should be equal to the weight of the quicksilver

in the cane of the barometer, and this pure air being a part only of

that we breath, the column of this pure air will be higher than 29725

feet. On both these accounts the motion of sound is found to be about

1142 feet in one second of time, or near 13 miles in a minute, whereas

by the computation proposed above, it should move but 979 feet in one

second.

14. WE may observe here, that from these demonstrations of our author

it follows, that all sounds whether acute or grave move equally swift,

and that sound is swiftest, when the quicksilver stands highest in the

barometer.

15. THUS much of the appearances, which are caused in these fluids from

their gravitation toward the earth. They also gravitate toward the

moon; for in the last chapter it has been proved, that the gravitation

between the earth and moon is mutual, and that this gravitation of

the whole bodies arises from that power acting in all their parts; so

that every particle of the moon gravitates toward the earth, and every

particle of the earth toward the moon. But this gravitation of these

fluids toward the moon produces no sensible effect, except only in the

sea, where it causes the tides.

16. THAT the tides depend upon the influence of the moon has been the

receiv’d opinion of all antiquity; nor is there indeed the least shadow

of reason to suppose otherwise, considering how steadily they accompany

the moon’s course. Though how the moon caused them, and by what

principle it was enabled to produce so distinguish’d an appearance,

was a secret left for this philosophy to unfold: which teaches, that

the moon is not here alone concerned, but that the sun likewise has a

considerable share in their production; though they have been generally

ascribed to the other luminary, because its effect is greatest, and by

that means the tides more immediately suit themselves to its motion;

the sun discovering its influence more by enlarging or restraining the

moon’s power, than by any distinct effects. Our author finds the power

of the moon to bear to the power of the sun about the proportion of

4½ to 1. This he deduces from the observations made at the mouth of

the river Avon, three miles from Bristol, by Captain STURMEY, and at

Plymouth by Mr. COLEPRESSE, of the height to which the water is raised

in the conjunction and opposition of the luminaries, compared with the

elevation of it, when the moon is in either quarter; the first being

caused by the united actions of the sun and moon, and the other by the

difference of them, as shall hereafter be shewn.

17. THAT the sun should have a like effect on the sea, as the moon, is

very manifest; since the sun likewise attracts every single particle,

of which this earth is composed. And in both luminaries since the power

of gravity is reciprocally in the duplicate proportion of the distance,

they will not draw all the parts of the waters in the same manner;

but must act upon the nearest parts stronger, than upon the remotest,

producing by this inequality an irregular motion. We shall now attempt

to shew how the actions of the sun and moon on the waters, by being

combined together, produce all the appearances observed in the tides.

18. TO begin therefore, the reader will remember what has been said

above, that if the moon without the sun would have described an orbit

concentrical to the earth, the action of the sun would make the orbit

oval, and bring the moon nearer to the earth at the new and full,

than at the quarters[268]. Now our excellent author observes, that

if instead of one moon, we suppose a ring of moons, contiguous and

occupying the whole orbit of the moon, his demonstration would still

take place, and prove that the parts of this ring in passing from the

quarter to the conjunction or opposition would be accelerated, and be

retarded again in passing from the conjunction or opposition to the

next quarter. And as this effect does not depend on the magnitude of

the bodies, whereof the ring is composed, the same would hold, though

the magnitude of these moons were so far to be diminished, and their

number increased, till they should form a fluid[269]. Now the earth

turns round continually upon its own center, causing thereby the

alternate change of day and night, while by this revolution each part

of the earth is successively brought toward the sun, and carried off

again in the space of 24 hours. And as the sea revolves round along

with the earth itself in this diurnal motion, it will represent in some

sort such a fluid ring.

19. BUT as the water of the sea does not move round with so much

swiftness, as would carry it about the center of the earth in the

circle it now describes, without being supported by the body of the

earth; it will be necessary to consider the water under three distinct

cases. The first case shall suppose the water to move with the degree

of swiftness, required to carry a body round the center of the

earth disingaged from it in a circle at the distance of the earth’s

semidiameter, like another moon. The second case is, that the waters

make but one turn about the axis of the earth in the space of a month,

keeping pace with the moon; so that all parts of the water should

preserve continually the same situation in respect of the moon. The

third case shall be the real one of the waters moving with a velocity

between these two, neither so swift as the first case requires, nor so

slow as the second.

20. IN the first case the waters, like the body which they equalled

in velocity, by the action of the moon would be brought nearer the

center under and opposite to the moon, than in the parts in the middle

between these eastward or westward. That such a body would so alter

its distance by the moon’s action upon it, is clear from what has

been mentioned of the like changes in the moon’s motion caused by

the sun[270]. And computation shews, that the difference between the

greatest and least distance of such a body would not be much above 4½

feet. But in the second case, where all the parts of the water preserve

the same situation continually in respect of the moon, the weight of

those parts under and opposite to the moon will be diminished by the

moon’s action, and the parts in the middle between these will have

their weight increased: this being effected just in the same manner,

as the sun diminishes the attraction of the moon towards the earth in

the conjunction and opposition, but increases that attraction in the

quarters. For as the first of these consequences from the sun’s action

on the moon is occasioned by the moon’s being attracted by the sun in

the conjunction more than the earth, and in the opposition less than

it, and therefore in the common motion of the earth and moon, the moon

is made to advance toward the sun in one case too fast, and in the

other is left as it were behind; so the earth will not have its middle

parts drawn towards the moon so strongly as the nearer parts, and yet

more forcibly than the remotest: and therefore since the earth and

moon move each month round their common center of gravity[271], while

the earth moves round this center, the same effect will be produced,

on the parts of the water nearest to that center or to the moon, as

the moon feels from the sun when in conjunction, and the water on the

contrary side of the earth will be affected by the moon, as the moon is

by the sun, when in opposition[272]; that is, in both cases the weight

of the water, or its propensity towards the center of the earth, will

be diminished. The parts in the middle between these will have their

weight increased, by being pressed towards the center of the earth

through the obliquity of the moon’s action upon them to its action

upon the earth’s center, just as the sun increases the gravitation

of the moon in the quarters from the same cause[273]. But now it is

manifest, that where the weight of the same quantity of water is least,

there it will be accumulated; while the parts, which have the greatest

weight, will subside. Therefore in this case there would be no tide or

alternate rising and falling of the water, but the water would form it

self into an oblong figure, whose axis prolonged would pass through the

moon. By Sir ~ISAAC NEWTON~’s computation the excess of this axis above

the diameters perpendicular to it, that is, the height of the waters

under and opposite to the moon above their height in the middle between

these places eastward or westward caused by the moon, is about 8⅔ feet.

21. THUS the difference of height in this latter supposition is little

short of twice that difference in the preceding. But the case of the

sea is a middle between these two: for a body, which should revolve

round the center of the earth at the distance of a semidiameter without

pressing on the earth’s surface, must perform its period in less than

an hour and half, whereas the earth turns round but once in a day; and

in the case of the waters keeping pace with the moon it should turn

round but once in a month: so that the real motion of the water is

between the motions required in these two cases. Again, if the waters

moved round as swiftly as the first case required, their weight would

be wholly taken off by their motion; for this case supposes the body

to move so, as to be kept revolving in a circle round the earth by

the power of gravity without pressing on the earth at all, so that

its motion just supports its weight. But if the power of gravity had

been only 1/289 part of what it is, the body could have moved thus

without pressing on the earth, and have been as long in moving round,

as the earth it self is. Consequently the motion of the earth takes off

from the weight of the water in the middle between the poles, where

its motion is swiftest, 1/289 part of its weight and no more. Since

therefore in the first case the weight of the waters must be intirely

taken off by their motion, and by the real motion of the earth they

lose only 1/289 part thereof, the motion of the water will so little

diminish their weight, that their figure will much nearer resemble

the case of their keeping pace with the moon than the other. Upon

the whole, if the waters moved with the velocity necessary to carry

a body round the center of the earth at the distance of the earth’s

semidiameter without bearing on its surface, the water would be lowest

under the moon, and rise gradually as it moved on with the earth

eastward, till it came half way toward the place opposite to the moon;

from thence it would subside again, till it came to the opposition,

where it would become as low as at first; afterwards it would rise

again, till it came half way to the place under the moon; and from

hence it would subside, till it came a second time under the moon. But

in case the water kept pace with the moon, it would be highest where

in the other case it is lowest, and lowest where in the other it is

highest; therefore the diurnal motion of the earth being between the

motions of these two cases, it will cause the highest place of the

water to fall between the places of the greatest height in these two

cases. The water as it passes from under the moon shall for some time

rise, but descend again before it arrives half way to the opposite

place, and shall come to its least height before it becomes opposite

to the moon; then it shall rise again, continuing so to do till it has

passed the place opposite to the moon, but subside before it comes

to the middle between the places opposite to and under the moon; and

lastly it shall come to its lowest, before it comes a second time

under the moon. If A (in fig. 112, 113, 114.) represent the moon, B

the center of the earth, the oval C D E F in fig. 112. will represent

the situation of the water in the first case; but if the water kept

pace with the moon, the line C D E F in fig. 113. would represent

the situation of the water; but the line C D E F in fig. 114. will

represent the same in the real motion of the water, as it accompanies

the earth in its diurnal rotation: in all these figures C and E being

the places where the water is lowest, and D and F the places where it

is highest. Pursuant to this determination it is found, that on the

shores, which lie exposed to the open sea, the high water usually falls

out about three hours after the moon has passed the meridian of each

place.

22. LET this suffice in general for explaining the manner, in which the

moon acts upon the seas. It is farther to be noted, that these effects

are greatest, when the moon is over the earth’s equator[274], that

is, when it shines perpendicularly upon the parts of the earth in the

middle between the poles. For if the moon were placed over either of

the poles, it could have no effect upon the water to make it ascend and

descend. So that when the moon declines from the equator toward either

pole, it’s action must be something diminished, and that the more, the

farther it declines. The tides likewise will be greatest, when the moon

is nearest to the earth, it’s action being then the strongest.

23. THUS much of the action of the moon. That the sun should produce

the very same effects, though in a less degree, is too obvious to

require a particular explanation: but as was remarked before, this

action of the sun being weaker than that of the moon, will cause the

tides to follow more nearly the moon’s course, and principally shew it

self by heightening or diminishing the effects of the other luminary.

Which is the occasion, that the highest tides are found about the

conjunction and opposition of the luminaries, being then produced by

their united action, and the weakest tides about the quarters of the

moon; because the moon in this case raising the water where the sun

depresses it, and depressing it where the sun raises it, the stronger

action of the moon is in part retunded and weakened by that of the sun.

Our author computes that the sun will add near two feet to the height

of the water in the first case, and in the other take from it as much.

However the tides in both comply with the same hour of the moon. But at

other times, between the conjunction or opposition and quarters, the

time deviates from that forementioned, towards the hour in which the

sun would make high water, though still it keeps much nearer to the

moon’s hour than to the sun’s.

24. AGAIN the tides have some farther varieties from the situation of

the places where they happen northward or southward. Let _p_ P (in fig.

115.) represent the axis, on which the earth daily revolves, let _h_

_p_ H P represent the figure of the water, and let _n_ B N D be a globe

inscribed within this figure. Suppose the moon to be advanced from the

equator toward the north pole, so that _h_ H the axis of the figure of

the water _p_ A H P E _h_ shall decline towards the north pole N; take

any place G nearer to the north pole than to the south, and from the

center of the earth C draw C G F; then will G F denote the altitude

to which the water is raised by the tide, when the moon is above the

horizon: in the space of twelve hours, the earth having turned half

round its axis, the place G will be removed to _g_; but the axis _h_

H will have kept its place preserving its situation in respect of the

moon, at least will have moved no more than the moon has done in that

time, which it is not necessary here to take into consideration. Now

in this case the height of the water will be equal to _g_ _f_, which

is not so great as G F. But whereas G F is the altitude at high water,

when the moon is above the horizon, _g_ _f_ will be the altitude of the

same, when the moon is under the horizon. The contrary happens toward

the south pole, for K L is less than _k_ _l_. Hence is proved, that

when the moon declines from the equator, in those places, which are on

the same side of the equator as the moon, the tides are greater, when

the moon is above the horizon, than when under it; and the contrary

happens on the other side of the equator.

25. NOW from these principles may be explained all the known

appearances in the tides; only by the assistance of this additional

remark, that the fluctuating motion, which the water has in flowing

and ebbing, is of a durable nature, and would continue for some time,

though the action of the luminaries should cease; for this prevents

the difference between the tide when the moon is above the horizon,

and the tide when the moon is below it from being so great, as the

rule laid down requires. This likewise makes the greatest tides not

exactly upon the new and full moon, but to be a tide or two after; as

at Bristol and Plymouth they are found the third after.

26. THIS doctrine farther shews us, why not only the spring tides fall

out about the new and full moon, and the neap tides about the quarters;

but likewise how it comes to pass, that the greatest spring tides

happen about the equinoxes; because the luminaries are then one of them

over the equator, and the other not far from it. It appears too, why

the neap tides, which accompany these, are the least of all, for the

sun still continuing over the equator continues to have the greatest

power of lessening the moon’s action, and the moon in the quarters

being far removed toward one of the poles, has its power thereby

weakned.

27. MOREOVER the action of the moon being stronger, when near the

earth, than when more remote; if the moon, when new suppose, be at its

nearest distance from the earth, it shall when at the full be farthest

off; whence it is, that two of the very largest spring tides do never

immediately succeed each other.

28. BECAUSE the sun in its passage from the winter solstice to the

summer recedes from the earth, and passing from the summer solstice

to the winter approaches it, and is therefore nearer the earth before

the vernal equinox than after, but nearer after the autumnal equinox

than before; the greatest tides oftner precede the vernal equinox than

follow it, and in the autumnal equinox on the contrary they oftner

follow it than come before it.

29. THE altitude, to which the water is raised in the open ocean,

corresponds very well to the forementioned calculations; for as it was

shewn, that the water in spring tides should rise to the height of 10

or 11 feet, and the neap tides to 6 or 7; accordingly in the Pacific,

Atlantic and Ethiopic oceans in the parts without the tropics, the

water is observed to rise about 6, 9, 12 or 15 feet. In the Pacific

ocean this elevation is said to be greater than in the other, as it

ought to be by reason of the wide extent of that sea. For the same

reason in the Ethiopic ocean between the tropics the ascent of the

water is less than without, by reason of the narrowness of the sea

between the coasts of Africa and the southern parts of America. And

islands in such narrow seas, if far from shore, have less tides than

the coasts. But now in those ports where the water flows in with great

violence upon fords and shoals, the force it acquires by that means

will carry it to a much greater height, so as to make it ascend and

descend to 30, 40 or even 50 feet and more; instances of which we have

at Plymouth, and in the Severn near Chepstow; at St. Michael’s and

Auranches in Normandy; at Cambay and Pegu in the East Indies.

30. AGAIN the tides take a considerable time in passing through long

straits, and shallow places. Thus the tide, which is made on the west

coast of Ireland and on the coast of Spain at the third hour after the

moon’s coming to the meridian, in the ports eastward toward the British

channel falls out later, and as the flood passes up that channel still

later and later, so that the tide takes up full twelve hours in coming

up to London bridge.

31. IN the last place tides may come to the same port from different

seas, and as they may interfere with each other, they will produce

particular effects. Suppose the tide from one sea come to a port at the

third hour after the moon’s passing the meridian of the place, but from

another sea to take up six hours more in its passage. Here one tide

will make high water, when by the other it should be lowest; so that

when the moon is over the equator, and the two tides are equal, there

will be no rising and falling of the water at all; for as much as the

water is carried off by one tide, it will be supplied by the other.

But when the moon declines from the equator, the same way as the port

is situated, we have shewn that of the two tides of the ocean, which

are made each day, that tide, which is made when the moon is above the

horizon, is greater than the other. Therefore in this case, as four

tides come to this port each day the two greatest will come on the

third, and on the ninth hour after the moon’s passing the meridian, and

the two least at the fifteenth and at the twenty first hour. Thus from

the third to the ninth hour more water will be in this port by the two

greatest tides than from the ninth to the fifteenth, or from the twenty

first to the following third hour, where the water is brought by one

great and one small tide; but yet there will be more water brought

by these tides, than what will be found between the two least tides,

that is, between the fifteenth and twenty first hour. Therefore in the

middle between the third and ninth hour, or about the moon’s setting,

the water will be at its greatest height; in the middle between the

ninth and fifteenth, as also between the twenty first and following

third hour it will have its mean height; and be lowest in the middle

between the fifteenth and twenty first hour, that is, at the moon’s

rising. Thus here the water will have but one flood and one ebb each

day. When the moon is on the other side of the equator, the flood will

be turned into ebb, and the ebb into flood; the high water falling

out at the rising of the moon, and the low water at the setting. Now

this is the case of the port of Batsham in the kingdom of Tunquin in

the East Indies; to which port there are two inlets, one between the

continent and the islands which are called the Manillas, and the other

between the continent and Borneo.

32. THE next thing to be considered is the effect, which these fluids

of the planets have upon the solid part of the bodies to which they

belong. And in the first place I shall shew, that it was necessary upon

account of these fluid parts to form the bodies of the planets into a

figure something different from that of a perfect globe. Because the

diurnal rotation, which our earth performs about its axis, and the

like motion we see in some of the other planets, (which is an ample

conviction that they all do the like) will diminish the force, with

which bodies are attracted upon all the parts of their surfaces, except

at the very poles, upon which they turn. Thus a stone or other weighty

substance resting upon the surface of the earth, by the force which it

receives from the motion communicated to it by the earth, if its weight

prevented not, would continue that motion in a straight line from the

point where it received it, and according to the direction, in which it

was given, that is, in a line which touches the surface at that point;

insomuch that it would move off from the earth in the same manner, as

a weight fasten’d to a string and whirled about endeavours continually

to recede from the center of motion, and would forthwith remove it self

to a greater distance from it, if loosed from the string which retains

it. And farther, as the centrifugal force, with which such a weight

presses from the center of its motion, is greater, by how much greater

the velocity is, with which it moves; so such a body, as I have been

supposing to lie on the earth, would recede from it with the greater

force, the greater the velocity is, with which the part of the earth’s

surface it rests upon is moved, that is, the farther distant it is from

the poles. But now the power of gravity is great enough to prevent

bodies in any part of the earth from being carried off from it by this

means; however it is plain that bodies having an effort contrary to

that of gravity, though much weaker than it, their weight, that is,

the degree of force, with which they are pressed to the earth, will

be diminished thereby, and be the more diminished, the greater this

contrary effort is; or in other words, the same body will weigh heavier

at either of the poles, than upon any other part of the earth; and if

any body be removed from the pole towards the equator, it will lose of

its weight more and more, and be lightest of all at the equator, that

is, in the middle between the poles.

33. THIS now is easily applied to the waters of the seas, and shews

that the water under the poles will press more forcibly to the earth,

than at or near the equator: and consequently that which presses

least, must give place, till by ascending it makes room for receiving

a greater quantity, which by its additional weight may place the whole

upon a ballance. To illustrate this more particularly I shall make

use of fig. 116 In which let A C B D be a circle, by whose revolution

about the diameter A B a globe should be formed, representing a globe

of solid earth. Suppose this globe covered on all sides with water to

the same height, suppose that of E A or B F, at which distance the

circle E G F H surrounds the circle A C B D; then it is evident, if the

globe of earth be at rest, the water which surrounds it will rest in

that situation. But if the globe be turned incessantly about its axis

A B, and the water have likewise the same motion, it is also evident,

from what has been explained, that the water between the circles E H

F G and A D B C will remain no longer in the present situation, the

parts of it between H and D, and between G and C being by this rotation

become lighter, than the parts between E and A and between B and F; so

that the water over the poles A and B must of necessity subside, and

the water be accumulated over D and C, till the greater quantity in

these latter places supply the defect of its weight. This would be the

case, were the globe all covered with water. And the same figure of the

surface would also be preserved, if some part of the water adjoining

to the globe in any part of it were turned into solid earth, as is too

evident to need any proof; because the parts of the water remaining

at rest, it is the same thing, whether they continue in the state of

being easily separable, which denominates them fluid, or were to be

consolidated together, so as to make a hard body: and this, though the

water should in some places be thus consolidated, even to the surface

of it. Which shews that the form of the solid part of the earth makes

no alteration in the figure the water will take: and by consequence in

order to the preventing some parts of the earth from being entirely

overflowed, and other parts quite deserted, the solid parts of the

earth must have given them much the same figure, as if the whole earth

were covered on all sides with water.

34. FARTHER, I say, this figure of the earth is the same, as it would

receive, were it entirely a globe of water, provided that water were of

the same density as the substance of the globe. For suppose the globe A

C B D to be liquified, and that the globe E H F G, now entirely water,

by its rotation about its axis should receive such a figure as we have

been describing, and then the globe A C B D should be consolidated

again, the figure of the water would plainly not be altered, by such a

consolidation.

35. BUT from this last observation our author is enabled to determine

the proportion between the axis of the earth drawn from pole to pole,

and the diameter of the equator, upon the supposition that all the

parts of the earth are of equal density; which he does by computing in

the first place the proportion of the centrifugal force of the parts

under the equator to the power of gravity; and then by considering

the earth as a spheroid, made by the revolution of an ellipsis about

its lesser axis, that is, supposing the line M I L K to be an exact

ellipsis, from which it can differ but little, by reason that the

difference between the lesser axis M L and the greater I K is but very

small. From this supposition, and what was proved before, that all the

particles which compose the earth have the attracting power explained

in the preceding chapter, he finds at what distance the parts under the

equator ought to be removed from the center, that the force, with which

they shall be attracted to the center, diminished by their centrifugal

force, shall be sufficient to keep those parts in a ballance with those

which lie under the poles. And upon the supposition of all the parts of

the earth having the same degree of density, the earth’s surface at the

equator must be above 17 miles more distant from the center, than at

the poles[275].

36. AFTER this it is shewn, from the proportion of the equatorial

diameter of the earth to its axis, how the same may be determined of

any other planet, whose density in comparison of the density of the

earth, and the time of its revolution about its axis, are known. And

by the rule delivered for this, it is found, that the diameter of the

equator in Jupiter should bear to its axis about the proportion of 10

to 9[276], and accordingly this planet appears of an oval form to the

astronomers. The most considerable effects of this spheroidical figure

our author takes likewise into consideration; one of which is that

bodies are not equally heavy in all distances from the poles; but near

the equator, where the distance from the center is greatest, they are

lighter than towards the poles: and nearly in this proportion, that

the actual power, by which they are drawn to the center, resulting

from the difference between their absolute gravity and centrifugal

force, is reciprocally as the distance from the center. That this may

not appear to contradict what has before been said of the alteration

of the power of gravity, in proportion to the change of the distance

from the center, it is proper carefully to remark, that our author

has demonstrated three things relating hereto: the first is, that

decrease of the power of gravity as we recede from the center, which

has been fully explained in the last chapter, upon supposition that

the earth and planets are perfect spheres, from which their difference

is by many degrees too little to require notice for the purposes there

intended: the next is, that whether they be perfect spheres, or exactly

such spheroids as have now been mentioned, the power of gravity, as

we descend in the same line to the center, is at all distances as the

distance from the center, the parts of the earth above the body by

drawing the body towards them lessening its gravitation towards the

center[277]; and both these assertions relate to gravity alone: the

third is what we mentioned in this place, that the actual force on

different parts of the surface, with which bodies are drawn to the

center, is in the proportion here assigned[278].

38. THE next effect of this figure of the earth is an obvious

consequence of the former: that pendulums of the same length do not in

different distances from the pole make their vibrations in the same

time; but towards the poles, where the gravity is strongest, they move

quicker than near the equator, where they are less impelled to the

center; and accordingly pendulums, that measure the same time by their

vibrations, must be shorter near the poles than at a greater distance.

Both which deductions are found true in fact; of which our author has

recounted particularly several experiments, in which it was found, that

clocks exactly adjusted to the true measure of time at Paris, when

transported nearer to the equator, became erroneous and moved too slow,

but were reduced to their true motion by contracting their pendulums.

Our author is particular in remarking, how much they lost of their

motion, while the pendulums remained unaltered; and what length the

observers are said to have shortened them, to bring them to time. And

the experiments, which appear to be most carefully made, shew the earth

to be raised in the middle between the poles, as much as our author

found it by his computation[279].

39. THESE experiments on the pendulum our author has been very exact

in examining, inquiring particularly how much the extension of the

rod of the pendulum by the great heats in the torrid zone might make

it necessary to shorten it. For by an experiment made by PICART, and

another made by DE LA HIRE, heat, though not very intense, was found

to increase the length of rods of iron. The experiment of PICART was

made with a rod one foot long, which in winter, at the time of frost,

was found to increase in length by being heated at the fire. In the

experiment of DE LA HIRE a rod of six foot in length was found, when

heated by the summer sun only, to grow to a greater length, than it

had in the aforesaid cold season. From which observations a doubt has

been raised, whether the rod of the pendulums in the aforementioned

experiments was not extended by the heat of those warm climates to all

that excess of length, the observers found themselves obliged to lessen

them by. But the experiments now mentioned shew the contrary. For in

the first of them the rod of a foot long was lengthened no more than

1/9 part of what the pendulum under the equator must be diminished;

and therefore a rod of the length of the pendulum would not have been

extended above ⅓ of that length. In the experiment of DE LA HIRE,

where the heat was less, the rod of six foot long was extended no more

than 3/10 of what the pendulum must be shortened; so that a rod of the

length of the pendulum would not have gained above 3/20 or 1/7 of that

length. And the heat in this latter experiment, though less than in

the former, was yet greater than the rod of a pendulum can ordinarily

contract in the hottest country; for metals receive a great heat when

exposed to the open sun, certainly much greater than that of a human

body. But pendulums are not usually so exposed, and without doubt in

these experiments were kept cool enough to appear so to the touch;

which they would do in the hottest place, if lodged in the shade. Our

author therefore thinks it enough to allow about 1/10 of the difference

observed upon account of the greater warmth of the pendulum.

40. THERE is a third effect, which the water has on the earth by

changing its figure, that is taken notice of by our author; for

the explaining of which we shall first prove, that bodies descend

perpendicularly to the surface of the earth in all places. The manner

of collecting this from observation, is as follows. The surfaces of

all fluids rest parallel to that part of the surface of the sea, which

is in the same place with them, to the figure of which, as has been

particularly shewn, the figure of the whole earth is formed. For if

any hollow vessel, open at the bottom, be immersed into the sea; it

is evident, that the surface of the sea within the vessel will retain

the same figure it had, before the vessel inclosed it; since its

communication with the external water is not cut off by the vessel.

But all the parts of the water being at rest, it is as clear, that if

the bottom of the vessel were closed, the figure of the water could

receive no change thereby, even though the vessel were raised out of

the sea; any more than from the insensible alteration of the power of

gravity, consequent upon the augmentation of the distance from the

center. But now it is clear, that bodies descend in lines perpendicular

to the surfaces of quiescent fluids; for if the power of gravity did

not act perpendicularly to the surface of fluids, bodies which swim on

them could not rest, as they are seen to do; because, if the power of

gravity drew such bodies in a direction oblique to the surface whereon

they lay, they would certainly be put in motion, and be carried to the

side of the vessel, in which the fluid was contained, that way the

action of gravity inclined.

41. HENCE it follows, that as we stand, our bodies are perpendicular

to the surface of the earth. Therefore in going from north to south

our bodies do not keep in a parallel direction. Now in all distances

from the pole the same length gone on the earth will not make the same

change in the position of our bodies, but the nearer we are to the

poles, we must go greater length to cause the same variation herein.

Let M I L K (in fig. 117) represent the figure of the earth, M, L the

poles, I, K two opposite points in the middle between these poles. Let

T V and P O be two arches, T V being most remote from the pole L; draw

T W, V X, P Q, O R, each perpendicular to the surface of the earth,

and let T W, V X meet in Y, and P Q, O R in S. Here it is evident,

that in passing from V to T the position of a man’s body would be

changed by the angle under T Y V, for at V he would stand in the line

Y V continued upward, and at T in the line Y T; but in passing from O

to P the position of his body would be changed by the angle under O

S P. Now I say, if these two angles are equal the arch O P is longer

than T V: for the figure M I L K being oblong, and I K longer than M L,

the figure will be more incurvated toward I than toward L; so that the

lines T W and V X will meet in Y before they are drawn out to so great

a length as the lines P Q and O R must be continued to, before they

will meet in S. Since therefore Y T and Y V are shorter than P S and S

V, T V must be less than O P. If these angles under T Y V and O S P are

each 1/90 part of the angle made by a perpendicular line, they are said

each to contain one degree. And the unequal length of these arches O P

and V T gives occasion to the assertion, that in passing from north to

south the degrees on the earth’s surface are not of an equal length,

but those near the pole longer than those toward the equator. For the

length of the arch on the earth lying between the two perpendiculars,

which make an angle of a degree with each other, is called the length

of a degree on the earth’s surface.

42. THIS figure of the earth has some effect on eclipses. It has been

observed above, that sometimes the nodes of the moon’s orbit lie in a

straight line drawn from the sun to the earth; in which case the moon

will cross the plane of the earth’s motion at the new and full. But

whenever the moon passes near the plane at the full, some part of the

earth will intercept the sun’s light, and the moon shining only with

light borrow’d from the sun, when that light is prevented from falling

on any part of the moon, so much of her body will be darkened. Also

when the moon at the new is near the plane of the earth’s motion, the

inhabitants on some part of the earth will see the moon come under

the sun, and the sun thereby be covered from them either wholly or in

part. Now the figure, which we have shewn to belong to the earth, will

occasion the shadow of the earth on the moon not to be perfectly round,

but cause the diameter from east to west to be somewhat longer than

the diameter from north to south. In eclipse of the sun this figure

of the earth will make some little difference in the place, where the

sun shall appear wholly or in any given part covered. Let A B C D (in

fig. 118.) represent the earth, A C the axis whereon it turns daily,

E the center. Let F A G C represent a perfect globe inscribed within

the earth. Let H I be a line drawn through the centers of the sun and

moon, crossing the surface of the earth in K, and the surface of the

globe inscribed in L. Draw E L, which will be perpendicular to the

surface of the globe in L: and draw likewise K M, so that it shall

be perpendicular to the surface of the earth in K. Now whereas the

eclipse would appear central at L, if the earth were the globe A G C

F, and does really appear so at K; I say, the latitude of the place K

on the real earth is different from the latitude of the place L on the

globe F A G C. What is called the latitude of any place is determined

by the angle which the line perpendicular to the surface of the earth

at that place makes with the axis; the difference between this angle,

and that made by a perpendicular line or square being called the

latitude of each place. But it might here be proved, that the angle

which K M makes with M C is less, than the angle made between L E and

E C: consequently the latitude of the place K is greater, than the

latitude, which the place L would have.

43. THE next effect, which follows from this figure of the earth,

is that gradual change in the distance of the fixed stars from the

equinoctial points, which astronomers observe. But before this can be

explained, it is necessary to say something more particular, than has

yet been done, concerning the manner of the earth’s motion round the

sun.

44. IT has already been said, that the earth turns round each day on

its own axis, while its whole body is carried round the sun once in a

year. How these two motions are joined together may be conceived in

some degree by the motion of a bowl on the ground, where the bowl in

rouling on continually turns upon its axis, and at the same time the

whole body thereof is carried straight on. But to be more express let

A (in fig. 119) represent the sun B C D E four different situations

of the earth in its orbit moving about the sun. In all these let F

G represent the axis, about which the earth daily turns. The points

F, G are called the poles of the earth; and this axis is supposed to

keep always parallel to it self in every situation of the earth; at

least that it would do so, were it not for a minute deviation, the

cause whereof will be explained in what follows. When the earth is in

B, the half H I K will be illuminated by the sun, and the other half

H L K will be in darkness. Now if on the globe any point be taken in

the middle between the poles, this point shall describe by the motion

of the globe the circle M N, half of which is in the enlightened part

of the globe, and half in the dark part. But the earth is supposed to

move round its axis with an equable motion; therefore on this point of

the globe the sun will be seen just half the day, and be invisible the

other half. And the same will happen to every point of this circle, in

all situations of the earth during its whole revolution round the sun.

This circle M N is called the equator, of which we have before made

mention.

45. NOW suppose any other point taken on the surface of the globe

toward the pole F, which in the diurnal revolution of the globe

shall describe the circle O P. Here it appears that more than half

this circle is enlightned by the sun, and consequently that in any

particular point of this circle the sun will be longer seen than

lie hid, that is the day will be longer than the night. Again if we

consider the same circle O P on the globe situated in D the opposite

part of the orbit from B, we shall see, that here in any place of this

circle the night will be as much longer than the day.

46. IN these situations of the globe of earth a line drawn from the

sun to the center of the earth will be obliquely inclined toward the

axis F G. Now suppose, that such a line drawn from the sun to the

center of the earth, when in C or E, would be perpendicular to the

axis F G; in which cases the sun will shine perpendicularly upon the

equator, and consequently the line drawn from the center of the earth

to the sun will cross the equator, as it passes through the surface

of the earth; whereas in all other situations of the globe this line

will pass through the surface of the globe at a distance from the

equator either northward or southward. Now in both these cases half the

circle O P will be in the light, and half in the dark; and therefore

to every place in this circle the day will be equal to the night. Thus

it appears, that in these two opposite situations of the earth the

day is equal to the night in all parts of the globe; but in all other

situations this equality will only be found in places situated in the

very middle between the poles, that is, on the equator.

47. THE times, wherein this universal equality between the day and

night happens, are called the equinoxes. Now it has been long observed

by astronomers, that after the earth hath set out from either equinox,

suppose from E (which will be the spring equinox, if F be the north

pole) the same equinox shall again return a little before the earth has

made a compleat revolution round the sun. This return of the equinox

preceding the intire revolution of the earth is called the precession

of the equinox, and is caused by the protuberant figure of the earth.

49. SINCE the sun shines perpendicularly upon the equator, when the

line drawn from the sun to the center of the earth is perpendicular to

the earth’s axis, in this case the plane, which should cut through

the earth at the equator, may be extended to pass through the sun;

but it will not do so in any other position of the earth. Now let us

consider the prominent part of the earth about the equator, as a solid

ring moving with the earth round the sun. At the time of the equinoxes,

this ring will have the same kind of situation in respect of the sun,

as the orbit of the moon has, when the line of the nodes is directed

to the sun; and at all other times will resemble the moon’s orbit in

other situations. Consequently this ring, which otherwise would keep

throughout its motion parallel to it self, will receive some change in

its position from the action of the sun upon it, except only at the

time of the equinox. The manner of this change may be understood as

follows. Let A B C D (in fig. 120) represent this ring, E the center of

the earth, S the sun, A F C G a circle described in the plane of the

earth’s motion to the center E. Here A and C are the two points, in

which the earth’s equator crosses the plane of the earth’s motion; and

the time of the equinox falls out, when the straight line A C continued

would pass through the sun. Now let us recollect what was said above

concerning the moon, when her orbit was in the same situation with this

ring. From thence it will be understood, if a body were supposed to

be moving in any part of this circle A B C D, what effect the action

of the sun on the body would have toward changing the position of the

line A C. In particular H I being drawn perpendicular to S E, if the

body be in any part of this circle between A and H, or between C and I,

the line A C would be so turned, that the point A shall move toward

B, and the point C toward D; but if it were in any other part of the

circle, either between H and C, or between I and A, the line A C would

be turned the contrary way. Hence it follows, that as this solid ring

turns round the center of the earth, the parts of this ring between A

and H, and between C and I, are so influenced by the sun, that they

will endeavour, so to change the situation of the line A C as to cause

the point A to move toward B, and the point C to move toward D; but all

the parts of the ring between H and C, and between I and A, will have

the opposite tendency, and dispose the line A C to move the contrary

way. And since these last named parts are larger than the other, they

will prevail over the other, so that by the action of the sun upon this

ring, the line A C will be so turned, that A shall continually be more

and more moving toward D, and C toward B. Thus no sooner shall the sun

in its visible motion have departed from A, but the motion of the line

A C shall hasten its meeting with C, and from thence the motion of this

line shall again hasten the sun’s second conjunction with A; for as

this line so turns, that A is continually moving toward D, so the sun’s

visible motion is the same way as from S toward T.

49. THE moon will have on this ring the like effect as the sun, and

operate on it more strongly, in the same proportion as its force on

the sea exceeded that of the sun on the same. But the effect of the

action of both luminaries will be greatly diminished by reason of this

ring’s being connected to the rest of the earth; for by this means the

sun and moon have not only this ring to move, but likewise the whole

globe of the earth, upon whose spherical part they have no immediate

influence. Beside the effect is also rendred less, by reason that the

prominent part of the earth is not collected all under the equator,

but spreads gradually from thence toward both poles. Upon the whole,

though the sun alone carries the nodes of the moon through an intire

revolution in about 19 years, the united force of both luminaries on

the prominent parts of the earth will hardly carry round the equinox in

a less space of time than 26000 years.

50. TO this motion of the equinox we must add another consequence of

this action of the sun and moon upon the elevated parts of the earth,

that this annular part of the earth about the equator, and consequently

the earth’s axis, will twice a year and twice a month change its

inclination to the plane of the earth’s motion, and be again restored,

just as the inclination of the moon’s orbit by the action of the sun

is annually twice diminished, and as often recovers its original

magnitude. But this change is very insensible.

51. I SHALL now finish the present chapter with our great author’s

inquiry into the figure of the secondary planets, particularly of our

moon, upon the figure of which its fluid parts will have an influence.

The moon turns always the same side towards the earth, and consequently

revolves but once round its axis in the space of an entire month; for

a spectator placed without the circle, in which the moon moves, would

in that time observe all the parts of the moon successively to pass

once before his view and no more, that is, that the whole globe of the

moon has turned once round. Now the great slowness of this motion will

render the centrifugal force of the parts of the waters very weak, so

that the figure of the moon cannot, as in the earth, be much affected

by this revolution upon its axis: but the figure of those waters are

made different from spherical by another cause, viz. the action of

the earth upon them; by which they will be reduced to an oblong oval

form, whose axis prolonged would pass through the earth; for the same

reason, as we have above observed, that the waters of the earth would

take the like figure, if they had moved so slowly, as to keep pace with

the moon. And the solid part of the moon must correspond with this

figure of the fluid part: but this elevation of the parts of the moon

is nothing near so great as is the protuberance of the earth at the

equator, for it will not exceed 93 english feet.

52. The waters of the moon will have no tide, except what will arise

from the motion of the moon round the earth. For the conversion of the

moon about her axis is equable, whereby the inequality in the motion

round the earth discovers to us at some times small parts of the moon’s

surface towards the east or west, which at other times lie hid; and

as the axis, whereon the moon turns, is oblique to her motion round

the earth, sometimes small parts of her surface toward the north, and

sometimes the like toward the south are visible, which at other times

are out of sight. These appearances make what is called the libration

of the moon, discovered by HEVELIUS. But now as the axis of the oval

figure of the waters will he pointed towards the earth, there must

arise from hence some fluctuation in them; and beside, by the change of

the moon’s distance from the earth, they will not always have the very

same height.

[Illustration]

[Illustration]

~BOOK III~.

~CHAP~ I.

Concerning the cause of COLOURS inherent in the LIGHT.

AFTER this view which has been taken of Sir ISAAC NEWTON’S mathematical

principles of philosophy, and the use he has made of them, in

explaining the system of the world, &c. the course of my design directs

us to turn our eyes to that other philosophical work, his treatise of

Optics, in which we shall find our great author’s inimitable genius

discovering it self no less, than in the former; nay perhaps even

more, since this work gives as many instances of his singular force

of reasoning, and of his unbounded invention, though unassisted in

great measure by those rules and general precepts, which facilitate

the invention of mathematical theorems. Nor yet is this work inferior

to the other in usefulness; for as that has made known to us one great

principle in nature, by which the celestial motions are continued, and

by which the frame of each globe is preserved; so does this point out

to us another principle no less universal, upon which depends all those

operations in the smaller parts of matter, for whose sake the greater

frame of the universe is erected; all those immense globes, with which

the whole heavens are filled, being without doubt only design’d as so

many convenient apartments for carrying on the more noble operations of

nature in vegetation and animal life. Which single consideration gives

abundant proof of the excellency of our author’s choice, in applying

himself carefully to examine the action between light and bodies, so

necessary in all the varieties of these productions, that none of them

can be successfully promoted without the concurrence of heat in a

greater or less degree.

2. ’TIS true, our author has not made so full a discovery of the

principle, by which this mutual action between light and bodies is

caused; as he has in relation to the power, by which the planets are

kept in their courses: yet he has led us to the very entrance upon it,

and pointed out the path so plainly which must be followed to reach it;

that one may be bold to say, whenever mankind shall be blessed with

this improvement of their knowledge, it will be derived so directly

from the principles laid down by our author in this book, that the

greatest share of the praise due to the discovery will belong to him.

3. IN speaking of the progress our author has made, I shall distinctly

pursue three things, the two first relating to the colours of natural

bodies: for in the first head shall be shewn, how those colours are

derived from the properties of the light itself; and in the second upon

what properties of the bodies they depend: but the third head of my

discourse shall treat of the action of bodies upon light in refracting,

reflecting, and inflecting it.

4. THE first of these, which shall be the business of the present

chapter, is contained in this one proposition: that the sun’s direct

light is not uniform in respect of colour, not being disposed in every

part of it to excite the idea of whiteness, which the whole raises; but

on the contrary is a composition of different kinds of rays, one sort

of which if alone would give the sense of red, another of orange, a

third of yellow, a fourth of green, a fifth of light blue, a sixth of

indigo, and a seventh of a violet purple; that all these rays together

by the mixture of their sensations impress upon the organ of sight

the sense of whiteness, though each ray always imprints there its own

colour; and all the difference between the colours of bodies when

viewed in open day light arises from this, that coloured bodies do not

reflect all the sorts of rays falling upon them in equal plenty, but

some sorts much more copiously than others; the body appearing of that

colour, of which the light coming from it is most composed.

5. THAT the light of the sun is compounded, as has been said, is proved

by refracting it with a prism. By a prism I here mean a glass or other

body of a triangular form, such as is represented in fig. 121. But

before we proceed to the illustration of the proposition we have just

now laid down, it will be necessary to spend a few words in explaining

what is meant by the refraction of light; as the design of our present

labour is to give some notion of the subject, we are engaged in, to

such as are not versed in the mathematics.

6. IT is well known, that when a ray of light passing through the air

falls obliquely upon the surface of any transparent body, suppose water

or glass, and enters it, the ray will not pass on in that body in the

same line it described through the air, but be turned off from the

surface, so as to be less inclined to it after passing it, than before.

Let A B C D (in fig. 122.) represent a portion of water, or glass, A

B the surface of it, upon which the ray of light E F falls obliquely;

this ray shall not go right on in the course delineated by the line

F G, but be turned off from the surface A B into the line F H, less

inclined to the surface A B than the line E F is, in which the ray is

incident upon that surface.

7. ON the other hand, when the light passes out of any such body into

the air, it is inflected the contrary way, being after its emergence

rendred more oblique to the surface it passes through, than before.

Thus the ray F H, when it goes out of the surface C D, will be turned

up towards that surface, going out into the air in the line H I.

8. THIS turning of the light out of its way, as it passes from one

transparent body into another is called its refraction. Both these

cases may be tried by an easy experiment with a bason and water. For

the first case set an empty bason in the sunshine or near a candle,

making a mark upon the bottom at the extremity of the shadow cast

by the brim of the bason, then by pouring water into the bason you

will observe the shadow to shrink, and leave the bottom of the bason

enlightned to a good distance from the mark. Let A B C (in fig. 123.)

denote the empty bason, E A D the light shining over the brim of it,

so that all the part A B D be shaded. Then a mark being made at D, if

water be poured into the bason (as in fig. 124.) to F G, you shall

observe the light, which before went on to D, now to come much short of

the mark D, falling on the bottom in the point H, and leaving the mark

D a good way within the enlightened part; which shews that the ray E A,

when it enters the water at I, goes no longer straight forwards, but is

at that place incurvated, and made to go nearer the perpendicular. The

other case may be tryed by putting any small body into an empty bason,

placed lower than your eye, and then receding from the bason, till you

can but just see the body over the brim. After which, if the bason be

filled with water, you shall presently observe the body to be visible,

though you go farther off from the bason. Let A B C (in fig. 125.)

denote the bason as before, D the body in it, E the place of your eye,

when the body is seen just over the edge A, while the bason is empty.

If it be then filled with water, you will observe the body still to be

visible, though you take your eye farther off. Suppose you see the body

in this case just over the brim A, when your eye is at F, it is plain

that the rays of light, which come from the body to your eye have not

come straight on, but are bent at A, being turned downwards, and more

inclined to the surface of the water, between A and your eye at F, than

they are between A and the body D.

9. THIS we hope is sufficient to make all our readers apprehend,

what the writers of optics mean, when they mention the refraction

of the light, or speak of the rays of light being refracted. We

shall therefore now go on to prove the assertion advanced in the

forementioned proposition, in relation to the different kinds of

colours, that the direct light of the sun exhibits to our sense: which

may be done in the following manner.

10. IF a room be darkened, and the sun permitted to shine into it

through a small hole in the window shutter, and be made immediately to

fall upon a glass prism, the beam of light shall in passing through

such a prism be parted into rays, which exhibit all the forementioned

colours. In this manner if A B (in fig. 126) represent the window

shutter; C the hole in it; D E F the prism; Z Y a beam of light coming

from the sun, which passes through the hole, and falls upon the prism

at Y, and if the prism were removed would go on to X, but in entring

the surface B F of the glass it shall be turned off, as has been

explained, into the course Y W falling upon the second surface of the

prism D F in W, going out of which into the air it shall be again

farther inflected. Let the light now, after it has passed the prism, be

received upon a sheet of paper held at a proper distance, and it shall

paint upon the paper the picture, image, or spectrum L M of an oblong

figure, whose length shall much exceed its breadth; though the figure

shall not be oval, the ends L and M being semicircular and the sides

straight. But now this figure will be variegated with colours in this

manner. From the extremity M to some length, suppose to the line _n

o_, it shall be of an intense red; from _n o_ to _p q_ it shall be an

orange; from _p q_ to _r s_ it shall be yellow; from thence to _t u_ it

shall be green; from thence to _w x_ blue; from thence to _y z_ indigo;

and from thence to the end violet.

11. THUS it appears that the sun’s white light by its passage through

the prism, is so changed as now to be divided into rays, which exhibit

all these several colours. The question is, whether the rays while

in the sun’s beam before this refraction possessed these properties

distinctly; so that some part of that beam would without the rest have

given a red colour, and another part alone have given an..orange,

&c. That this is possible to be the case, appears from hence; that if

a convex glass be placed between the paper and the prism, which may

collect all the rays proceeding out of the prism into its focus, as a

burning glass does the sun’s direct rays; and if that focus fall upon

the paper, the spot formed by such a glass upon the paper shall appear

white, just like the sun’s direct light.

[Illustration]

The rest remaining as before, let P Q. (in fig. 127.) be the convex

glass, causing the rays to meet upon the paper H G I K in the point N,

I say that point or rather spot of light shall appear white, without

the least tincture of any colour. But it is evident that into this

spot are now gathered all those rays, which before when separate gave

all those different colours; which shews that whiteness may be made by

mixing those colours: especially if we consider, it can be proved that

the glass P Q does not alter the colour of the rays which pass through

it. Which is done thus: if the paper be made to approach the glass P

Q, the colours will manifest themselves as far as the magnitude of the

spectrum, which the paper receives, will permit. Suppose it in the

situation _h g i k_, and that it then receive the spectrum _l m_, this

spectrum shall be much smaller, than if the glass P Q were removed,

and therefore the colours cannot be so much separated; but yet the

extremity _m_ shall manifestly appear red, and the other extremity _l_

shall be blue; and these colours as well as the intermediate ones shall

discover themselves more perfectly, the farther the paper is removed

from N, that is, the larger the spectrum is: the same thing happens,

if the paper be removed farther off from P Q than N. Suppose into the

position θ γ η ϰ, the spectrum λ μ painted upon it shall again discover

its colours, and that more distinctly, the farther the paper is

removed, but only in an inverted order: for as before, when the paper

was nearer the convex glass, than at N, the upper part of the image was

blue, and the under red; now the upper part shall be red, and the under

blue: because the rays cross at N.

12. NAY farther that the whiteness at the focus N, is made by the union

of the colours may be proved without removing the paper out of the

focus, by intercepting with any opake body part of the light near the

glass; for if the under part, that is the red, or more properly the

red-making rays, as they are styled by our author, are intercepted,

the spot shall take a bluish hue; and if more of the inferior rays are

cut off, so that neither the red-making nor orange-making rays, and if

you please the yellow-making rays likewise, shall fall upon the spot;

then shall the spot incline more and more to the remaining colours.

In like manner if you cut off the upper part of the rays, that is the

violet coloured or indigo-making rays, the spot shall turn reddish, and

become, more so, the more of those opposite colours are intercepted.

13. THIS I think abundantly proves that whiteness may be produced by a

mixture of all the colours of the spectrum. At least there is but one

way of evading the present arguments, which is, by asserting that the

rays of light after passing the prism have no different properties to

exhibit this or the other colour, but are in that respect perfectly

homogeneal, so that the rays which pass to the under and red part of

the image do not differ in any properties whatever from those, which

go to the upper and violet part of it; but that the colours of the

spectrum are produced only by some new modifications of the rays, made

at their incidence upon the paper by the different terminations of

light and shadow: if indeed this assertion can be allowed any place,

after what has been said; for it seems to be sufficiently obviated

by the latter part of the preceding experiment, that by intercepting

the inferior part of the light, which comes from the prism, the white

spot shall receive a bluish cast, and by stopping the upper part the

spot shall turn red, and in both cases recover its colour, when the

intercepted light is permitted to pass again; though in all these

trials there is the like termination of light and shadow. However our

author has contrived some experiments expresly to shew the absurdity of

this supposition; all which he has explained and enlarged upon in so

distinct and expressive a manner, that it would be wholly unnecessary

to repeat them in this place[280]. I shall only mention that of them,

which may be tried in the experiment before us. If you draw upon

the paper H G I K, and through the spot N, the straight line _w x_

parallel to the horizon, and then if the paper be much inclined into

the situation _r s v t_ the line _w x_ still remaining parallel to

the horizon, the spot N shall lose its whiteness and receive a blue

tincture; but if it be inclined as much the contrary way, the same

spot shall exchange its white colour for a reddish dye. All which can

never be accounted for by any difference in the termination of the

light and shadow, which here is none at all; but are easily explained

by supposing the upper part of the rays, whenever they enter the eye,

disposed to give the sensation of the dark colours blue, indigo and

violet; and that the under part is fitted to produce the bright colours

yellow, orange and red: for when the paper is in the situation _r s t

u_, it is plain that the upper part of the light falls more directly

upon it, than the under part, and therefore those rays will be most

plentifully reflected from it; and by their abounding in the reflected

light will cause it to incline to their colour. Just so when the paper

is inclined the contrary way, it will receive the inferior rays most

directly, and therefore ting the light it reflects with their colour.

14. IT is now to be proved that these dispositions of the rays of

light to produce some one colour and some another, which manifest

themselves after their being refracted, are not wrought by any action

of the prism upon them, but are originally inherent in those rays; and

that the prism only affords each species an occasion of shewing its

distinct quality by separating them one from another, which before,

while they were blended together in the direct beam of the sun’s light,

lay conceal’d. But that this is so, will be proved, if it can be shewn

that no prism has any power upon the rays, which after their passage

through one prism are rendered uncompounded and contain in them but one

colour, either to divide that colour into several, as the sun’s light

is divided, or so much as to change it into any other colour. This will

be proved by the following experiment[281]. The same thing remaining,

as in the first experiment, let another prism N O (in fig. 128.) be

placed either immediately, or at some distance after the first, in a

perpendicular posture, so that it shall refract the rays issuing from

the first sideways. Now if this prism could divide the light falling

upon it into coloured rays, as the first has done, it would divide the

spectrum breadthwise into colours, as before it was divided lengthwise;

but no such thing is observed. If L M were the spectrum, which the

first prism D E F would paint upon the paper H G I K; P Q lying in an

oblique posture shall be the spectrum projected by the second, and

shall be divided lengthwise into colours corresponding to the colours

of the spectrum L M, and occasioned like them by the refraction of the

first prism, but its breadth shall receive no such division; on the

contrary each colour shall be uniform from side to side, as much as in

the spectrum L M, which proves the whole assertion.

15. THE same is yet much farther confirmed by another experiment.

Our author teaches that the colours of the spectrum L M in the first

experiment are yet compounded, though not so much as in the sun’s

direct light. He shews therefore how, by placing the prism at a

distance from the hole, and by the use of a convex glass, to separate

the colours of the spectrum, and make them uncompounded to any degree

of exactness[282]. And he shews when this is done sufficiently, if

you make a small hole in the paper whereon the spectrum is received,

through which any one sort of rays may pass, and then let that coloured

ray fall so upon a prism, as to be refracted by it, it shall in no case

whatever change its colour; but shall always retain it perfectly as at

first, however it be refracted[283].

16. NOR yet will these colours after this full separation of them

suffer any change by reflection from bodies of different colours; on

the other hand they make all bodies placed in these colours appear of

the colour which falls upon them[284]: for minium in red light will

appear as in open day light; but in yellow light will appear yellow;

and which is more extraordinary, in green light will appear green, in

blue, blue; and in the violet-purple coloured light will appear of a

purple colour; in like manner verdigrease, or blue bise, will put on

the appearance of that colour, in which it is placed; so that neither

bise placed in the red light shall be able to give that light the least

blue tincture, or any other different from red; nor shall minium in

the indigo or violet light exhibit the least appearance of red, or any

other colour distinct from that it is placed in. The only difference

is, that each of these bodies appears most luminous and bright in the

colour, which corresponds with that it exhibits in the day light, and

dimmed in the colours most remote from that; that is, though minium and

bise placed in blue light shall both appear blue, yet the bise shall

appear of a bright blue, and the minium of a dusky and obscure blue:

but if minium and bise be compared together in red light, the minium

shall afford a brisk red, the bise a duller colour, though of the same

species.

17. AND this not only proves the immutability of all these simple

and uncompounded colours; but likewise unfolds the whole mystery,

why bodies appear in open day-light of such different colours, it

consisting in nothing more than this, that whereas the white light of

the day is composed of all sorts of colours, some bodies reflect the

rays of one sort in greater abundance than the rays of any other[285].

Though it appears by the fore-cited experiment, that almost all these

bodies reflect some portion of the rays of every colour, and give the

sense of particular colours only by the predominancy of some sorts of

rays above the rest. And what has before been explained of composing

white by mingling all the colours of the spectrum together shews

clearly, that nothing more is required to make bodies look white,

than a power to reflect indifferently rays of every colour. But this

will more fully appear by the following method: if near the coloured

spectrum in our first experiment a piece of white paper be so held, as

to be illuminated equally by all the parts of that spectrum, it shall

appear white; whereas if it be held nearer to the red end of the image,

than to the other, it shall turn reddish; if nearer the blue end, it

shall seem bluish[286].

18. OUR indefatigable and circumspect author farther examined his

theory by mixing the powders which painters use of several colours, in

order if possible to produce a white powder by such a composition[287].

But in this he found some difficulties for the following reasons. Each

of these coloured powders reflects but part of the light, which is

cast upon them; the red powders reflecting little green or blue, and

the blue powders reflecting very little red or yellow, nor the green

powders reflecting near so much of the red or indigo and purple, as

of the other colours: and besides, when any of these are examined in

homogeneal light, as our author calls the colours of the prism, when

well separated, though each appears more bright and luminous in its

own day-light colour, than in any other; yet white bodies, suppose

white paper for instance, in those very colours exceed these coloured

bodies themselves in brightness; so that white bodies reflect not only

more of the whole light than coloured bodies do in the day-light, but

even more of that very colour which they reflect most copiously. All

which considerations make it manifest that a mixture of these will not

reflect so great a quantity of light, as a white body of the same size;

and therefore will compose such a colour as would result from a mixture

of white and black, such as are all grey and dun colours, rather than a

strong white. Now such a colour he compounded of certain ingredients,

which he particularly sets down, in so much that when the composition

was strongly illuminated by the sun’s direct beams, it would appear

much whiter than even white paper, if considerably shaded. Nay he

found by trials how to proportion the degree of illumination of the

mixture and paper, so that to a spectator at a proper distance it

could not well be determined which was the more perfect colour; as he

experienced not only by himself, but by the concurrent opinion of a

friend, who chanced to visit him while he was trying this experiment.

I must not here omit another method of trying the whiteness of such a

mixture, proposed in one of our author’s letters on this subject[288]:

which is to enlighten the composition by a beam of the sun let into a

darkened room, and then to receive the light reflected from it upon a

piece of white paper, observing whether the paper appears white by that

reflection; for if it does, it gives proof of the composition’s being

white; because when the paper receives the reflection from any coloured

body, it looks of that colour. Agreeable to this is the trial he made

upon water impregnated with soap, and agitated into a froth[289]:

for when this froth after some short time exhibited upon the little

bubbles, which composed it, a great variety of colours, though these

colours to a spectator at a small distance discover’d themselves

distinctly; yet when the eye was so far removed, that each little

bubble could no longer be distinguished, the whole froth by the mixture

of all these colours appeared intensly white.

19. OUR author having fully satisfied himself by these and many other

experiments, what the result is of mixing together all the prismatic

colours; he proceeds in the next place to examine, whether this

appearance of whiteness be raised by the rays of these different kinds

acting so, when they meet, upon one another, as to cause each of them

to impress the sense of whiteness upon the optic nerve; or whether each

ray does not make upon the organ of sight the same impression, as when

separate and alone; so that the idea of whiteness is not excited by the

impression from any one part of the rays, but results from the mixture

of all those different sensations. And that the latter sentiment is the

true one, he evinces by undeniable experiments.

20. IN particular the foregoing experiment[290], wherein the convex

glass was used, furnishes proofs of this: in that when the paper is

brought into the situation θ γ η ϰ, beyond, beyond N the colours, that

at N disappeared, begin to emerge again; which shews that by mingling

at N they did not lose their colorific qualities, though for some

reason they lay concealed. This farther appears by that part of the

experiment, when the paper, while in the focus, was directed to be

enclined different ways; for when the paper was in such a situation,

that it must of necessity reflect the rays, which before their arrival

at the point N would have given a blue colour, those rays in this

very point itself by abounding in the reflected light tinged it with

the same colour; so when the paper reflects most copiously the rays,

which before they come to the point N exhibit redness, those same rays

tincture the light reflected by the paper from that very point with

their own proper colour.

21. THERE is a certain condition relating to sight, which affords an

opportunity of examining this still more fully: it is this, that the

impressions of light remain some short space upon the eye; as when a

burning coal is whirl’d about in a circle, if the motion be very quick,

the eye shall not be able to distinguish the coal, but shall see an

entire circle of fire. The reason of which appearance is, that the

impression made by the coal upon the eye in any one situation is not

worn out, before the coal returns again to the same place, and renews

the sensation. This gives our author the hint to try, whether these

colours might not be transmitted successively to the eye so quick,

that no one of the colours should be distinctly perceived, but the

mixture of the sensations should produce a uniform whiteness; when the

rays could not act upon each other, because they never should meet,

but come to the eye one after another. And this thought he executed

by the following expedient[291]. He made an instrument in shape like

a comb, which he applied near the convex glass, so that by moving it

up and down slowly the teeth of it might intercept sometimes one and

sometimes another colour; and accordingly the light reflected from the

paper, placed at N, should change colour continually. But now when the

comb-like instrument was moved very quick, the eye lost all preception

of the distinct colours, which came to it from time to time, a perfect

whiteness resulting from the mixture of all those distinct impressions

in the sensorium. Now in this case there can be no suspicion of the

several coloured rays acting upon one another, and making any change in

each other’s manner of affecting the eye, seeing they do not so much as

meet together there.

22. OUR author farther teaches us how to view the spectrum of colours

produced in the first experiment with another prism, so that it shall

appear to the eye under the shape of a round spot and perfectly

white[292]. And in this case if the comb be used to intercept

alternately some of the colours, which compose the spectrum, the round

spot shall change its colour according to the colours intercepted; but

if the comb be moved too swiftly for those changes to be distinctly

perceived, the spot shall seem always white, as before[293].

23. BESIDES this whiteness, which results from an universal composition

of all sorts of colours, our author particularly explains the effects

of other less compounded mixtures; some of which compound other colours

like some of the simple ones, but others produce colours different

from any of them. For instance, a mixture of red and yellow compound

a colour like in appearance to the orange, which in the spectrum lies

between them; as a composition of yellow and blue is made use of in all

dyes to make a green. But red and violet purple compounded make purples

unlike to any of the prismatic colours, and these joined with yellow

or blue make yet new colours. Besides one rule is here to be observed,

that when many different colours are mixed, the colour which arises

from the mixture grows languid and degenerates into whiteness. So when

yellow green and blue are mixed together, the compound will be green;

but if to this you add red and purple, the colour shall first grow dull

and less vivid, and at length by adding more of these colours it shall

turn to whiteness, or some other colour[294].

24. ONLY here is one thing remarkable of those compounded colours,

which are like in appearance to the simple ones; that the simple

ones when viewed through a prism shall still retain their colour,

but the compounded colours seen through such a glass shall be parted

into the simple ones of which they are the aggregate. And for this

reason any body illuminated by the simple light shall appear through

a prism distinctly, and have its minutest parts observable, as may

easily be tried with flies, or other such little bodies, which have

very small parts; but the same viewed in this manner when enlighten’d

with compounded colours shall appear confused, their smallest parts

not being distinguishable. How the prism separates these compounded

colours, as likewise how it divides the light of the sun into its

colours, has not yet been explained; but is reserved for our third

chapter.

25. IN the mean time what has been said, I hope, will suffice to

give a taste of our author’s way of arguing, and in some measure to

illustrate the proposition laid down in this chapter.

26. THERE are methods of separating the heterogeneous rays of the

sun’s light by reflection, which perfectly conspire with and confirm

this reasoning. One of which ways may be this. Let A B (in fig. 129)

represent the window shutter of a darkened room; C a hole to let in

the sun’s rays; D E F, G H I two prisms so applied together, that the

sides E F and G I be contiguous, and the sides D F, G H parallel; by

this means the light will pass through them without any separation

into colours: but if it be afterwards received by a third prism I K L,

it shall be divided so as to form upon any white body P Q the usual

colours, violet at _m_, blue at _n_, green at _o_, yellow at _r_, and

red at _s_. But because it never happens that the two adjacent surfaces

E F and G I perfectly touch, part only of the light incident upon the

surface E F shall be transmitted, and part shall be reflected. Let now

the reflected part be received by a fourth prism Δ Θ Λ, and passing

through it paint upon a white body Ζ Γ the colours of the prism, red

at _t_, yellow at _u_, green at _w_, blue at _x_, violet at _y_. If

the prisms D E F, G H I be slowly turned about while they remain

contiguous, the colours upon the body P Q shall not sensibly change

their situation, till such time as the rays become pretty oblique to

the surface E F; but then the light incident upon the surface E F shall

begin to be wholly reflected. And first of all the violet light shall

be wholly reflected, and thereupon will disappear at _m_, appearing

instead thereof at _y_, and increasing the violet light falling there,

the other colours remaining as before. If the prisms D E F, G H I be

turned a little farther about, that the incident rays become yet more

inclined to the surface E F, the blue shall be totally reflected, and

shall disappear in _n_, but appear at _x_ by making the colour there

more intense. And the same may be continued, till all the colours are

successively removed from the surface P Q to Ζ Γ. But in any case,

suppose when the violet and the blue have forsaken the surface P Q,

and appear upon the surface Ζ Γ, Ζ Γ, the green, yellow, and red only

remaining upon the surface P Q; if the light be received upon a paper

held any where in its whole passage between the light’s coming out of

the prisms D E F, G I H and its incidence upon the prism I K L, it

shall appear of the colour compounded of all the colours seen upon P

Q; and the reflected ray, received upon a piece of white paper held

any where between the prisms D E F and Δ Θ Σ shall exhibit the colour

compounded of those the surface P Q is deprived of mixed with the sun’s

light: whereas before any of the light was reflected from the surface

E F, the rays between the prisms G H I and I K L would appear white;

as will likewise the reflected ray both before and after the total

reflection, provided the difference of refraction by the surfaces D F

and D E be inconsiderable. I call here the sun’s light white, as I have

all along done; but it is more exact to ascribe to it something of a

yellowish tincture, occasioned by the brighter colours abounding in it;

which caution is necessary in examining the colours of the reflected

beam, when all the violet and blue are in it: for this yellowish turn

of the sun’s light causes the blue not to be quite so visible in it,

as it should be, were the light perfectly white; but makes the beam of

light incline rather towards a pale white.

~CHAP~. II.

Of the properties of BODIES, upon which their COLOURS depend.

AFTER having shewn in the last chapter, that the difference between

the colours of bodies viewed in open day-light is only this, that some

bodies are disposed to reflect rays of one colour in the greatest

plenty, and other bodies rays of some other colour; order now requires

us to examine more particularly into the property of bodies, which

gives them this difference. But this our author shews to be nothing

more, than the different magnitude of the particles, which compose each

body: this I question not will appear no small paradox. And indeed

this whole chapter will contain scarce any assertions, but what will

be almost incredible, though the arguments for them are so strong and

convincing, that they force our assent. In the former chapter have

been explained properties of light, not in the least thought of before

our author’s discovery of them; yet are they not difficult to admit,

as soon as experiments are known to give proof of their reality; but

some of the propositions to be stated here will, I fear, be accounted

almost past belief; notwithstanding that the arguments, by which they

are established are unanswerable. For it is proved by our author, that

bodies are rendered transparent by the minuteness of their pores, and

become opake by having them large; and more, that the most transparent

body by being reduced to a great thinness will become less pervious to

the light.

2. BUT whereas it had been the received opinion, and yet remains so

among all who have not studied this philosophy, that light is reflected

from bodies by its impinging against their solid parts, rebounding from

them, as a tennis ball or other elastic substance would do, when struck

against any hard and resisting surface; it will be proper to begin with

declaring our author’s sentiment concerning this, who shews by many

arguments that reflection cannot be caused by any such means[295]: some

few of his proofs I shall set down, referring the reader to our author

himself for the rest.

3. IT is well known, that when light falls upon any transparent body,

glass for instance, part of it is reflected and part transmitted;

for which it is ready to account, by saying that part of the light

enters the pores of the glass, and part impinges upon its solid

parts. But when the transmitted light arrives at the farther surface

of the glass, in passing out of glass into air there is as strong a

reflection caused, or rather something stronger. Now it is not to

be conceived, how the light should find as many solid parts in the

air to strike against as in the glass, or even a greater number of

them. And to augment the difficulty, if water be placed behind the

glass, the reflection becomes much weaker. Can we therefore say, that

water has fewer solid parts for the light to strike against, than the

air? And if we should, what reason can be given for the reflection’s

being stronger, when the air by the air-pump is removed from behind

the glass, than when the air receives the rays of light. Besides the

light may be so inclined to the hinder surface of the glass, that it

shall wholly be reflected, which happens when the angle which the

ray makes with the surface does not exceed about 49⅓ degrees; but if

the inclination be a very little increased, great part of the light

will be transmitted; and how the light in one case should meet with

nothing but the solid parts of the air, and by so small a change of

its inclination find pores in great plenty, is wholly inconceivable.

It cannot be said, that the light is reflected by striking against

the solid parts of the surface of the glass; because without making

any change in that surface, only by placing water contiguous to it

instead of air, great part of that light shall be transmitted, which

could find no passage through the air. Moreover in the last experiment

recited in the preceding chapter, when by turning the prisms D E F, G

H I, the blue light became wholly reflected, while the rest was mostly

transmitted, no possible reason can be assigned, why the blue-making

rays should meet with nothing but the solid parts of the air between

the prisms, and the rest of the light in the very same obliquity find

pores in abundance. Nay farther, when two glasses touch each other, no

reflection at all is made; though it does not in the least appear,

how the rays should avoid the solid parts of glass, when contiguous

to other glass, any more than when contiguous to air. But in the last

place upon this supposition it is not to be comprehended, how the most

polished substances could reflect the light in that regular manner we

find they do; for when a polished looking glass is covered over with

quicksilver, we cannot suppose the particles of light so much larger

than those of the quicksilver that they should not be scattered as

much in reflection, as a parcel of marbles thrown down upon a rugged

pavement. The only cause of so uniform and regular a reflection must be

some more secret cause, uniformly spread over the whole surface of the

glass.

4. BUT now, since the reflection of light from bodies does not depend

upon its impinging against their solid parts, some other reason must

be sought for. And first it is past doubt that the least parts of

almost all bodies are transparent, even the microscope shewing as

much[296]; besides that it may be experienced by this method. Take any

thin plate of the opakest body, and apply it to a small hole designed

for the admission of light into a darkened room; however opake that

body may seem in open day-light, it shall under these circumstances

sufficiently discover its transparency, provided only the body be very

thin. White metals indeed do not easily shew themselves transparent in

these trials, they reflecting almost all the light incident upon them

at their first superficies; the cause of which will appear in what

follows[297]. But yet these substances, when reduced into parts of

extraordinary minuteness by being dissolved in aqua fortis or the like

corroding liquors do also become transparent.

5. SINCE therefore the light finds free passage through the least

parts of bodies, let us consider the largeness of their pores, and

we shall find, that whenever a ray of light has passed through any

particle of a body, and is come to its farther surface, if it finds

there another particle contiguous, it will without interruption pass

into that particle; just as light will pass through one piece of glass

into another piece in contact with it without any impediment, or any

part being reflected: but as the light in passing out of glass, or any

other transparent body, shall part of it be reflected back, if it enter

into air or other transparent body of a different density from that

it passes out of; the same thing will happen in the light’s passage

through any particle of a body, whenever at its exit out of that

particle it meets no other particle contiguous, but must enter into a

pore, for in this case it shall not all pass through, but part of it

be reflected back. Thus will the light, every time it enters a pore,

be in part reflected; so that nothing more seems necessary to opacity,

than that the particles, which compose any body, touch but in very

few places, and that the pores of it are numerous and large, so that

the light may in part be reflected from it, and the other part, which

enters too deep to be returned out of the body, by numerous reflections

may be stifled and lost[298]; which in all probability happens, as

often as it impinges against the solid part of the body, all the light

which does so not being reflected back, but stopt, and deprived of any

farther motion[299].

6. THIS notion of opacity is greatly confirmed by the observation,

that opake bodies become transparent by filling up the pores with any

substance of near the same density with their parts. As when paper

is wet with water or oyl; when linnen cloth is either dipt in water,

oyled, or varnished; or the oculus mundi stone steeped in water[300].

All which experiments confirm both the first assertion, that light is

not reflected by striking upon the solid parts of bodies; and also

the second, that its passage is obstructed by the reflections it

undergoes in the pores; since we find it in these trials to pass in

greater abundance through bodies, when the number of their solid parts

is increased, only by taking away in great measure those reflections;

which filling the pores with a substance of near the same density

with the parts of the body will do. Besides as filling the pores of a

dark body makes it transparent; so on the other hand evacuating the

pores of a body transparent, or separating the parts of such a body,

renders it opake. As salts or wet paper by being dried, glass by being

reduced to powder or the surface made rough; and it is well known that

glass vessels discover cracks in them by their opacity. Just so water

itself becomes impervious to the light by being formed into many small

bubbles, whether in froth, or by being mixed and agitated with any

quantity of a liquor with which it will not incorporate, such as oyl

of turpentine, or oyl olive.

7. A CERTAIN electrical experiment made by Mr. HAUKSBEE may not perhaps

be useless to clear up the present speculation, by shewing that

something more is necessary besides mere porosity for transmitting

freely other fine substances. The experiment is this; that a glass cane

rubbed till it put forth its electric quality would agitate leaf brass

inclosed under a glass vessel, though not at so great a distance, as if

no body had intervened; yet the same cane would lose all its influence

on the leaf brass by the interposition of a piece of the finest muslin,

whose pores are immensely larger and more patent than those of glass.

8. THUS I have endeavoured to smooth my way, as much as I could, to

the unfolding yet greater secrets in nature; for I shall now proceed

to shew the reason why bodies appear of different colours. My reader

no doubt will be sufficiently surprized, when I inform him that the

knowledge of this is deduced from that ludicrous experiment, with which

children divert themselves in blowing bubbles of water made tenacious

by the solution of soap. And that these bubbles, as they gradually grow

thinner and thinner till they break, change successively their colours

from the same principle, as all natural bodies preserve theirs.

9. OUR author after preparing water with soap, so as to render it very

tenacious, blew it up into a bubble, and placing it under a glass,

that it might not be irregularly agitated by the air, observed as

the water by subsiding changed the thickness of the bubble, making

it gradually less and less till the bubble broke; there successively

appeared colours at the top of the bubble, which spread themselves

into rings surrounding the top and descending more and more, till they

vanished at the bottom in the same order in which they appeared[301].

The colours emerged in this order: first red, then blue; to which

succeeded red a second time, and blue immediately followed; after that

red a third time, succeeded by blue; to which followed a fourth red,

but succeeded by green; after this a more numerous order of colours,

first red, then yellow, next green, and after that blue, and at last

purple; then again red, yellow, green, blue, violet followed each other

in order; and in the last place red, yellow, white, blue; to which

succeeded a dark spot, which reflected scarce any light, though our

author found it did make some very obscure reflection, for the image of

the sun or a candle might be faintly discerned upon it; and this last

spot spread itself more and more, till the bubble at last broke. These

colours were not simple and uncompounded colours, like those which

are exhibited by the prism, when due care is taken to separate them;

but were made by a various mixture of those simple colours, as will

be shewn in the next chapter: whence these colours, to which I have

given the name of blue, green, or red, were not all alike, but differed

as follows. The blue, which appeared next the dark spot, was a pure

colour, but very faint, resembling the sky-colour; the white next to

it a very strong and intense white, brighter much than the white, which

the bubble reflected, before any of the colours appeared. The yellow

which preceded this was at first pretty good, but soon grew dilute;

and the red which went before the yellow at first gave a tincture of

scarlet inclining to violet, but soon changed into a brighter colour;

the violet of the next series was deep with little or no redness in

it; the blue a brisk colour, but came much short of the blue in the

next order; the green was but dilute and pale; the yellow and red were

very bright and full, the best of all the yellows which appeared among

any of the colours: in the preceding orders the purple was reddish,

but the blue, as was just now said, the brightest of all; the green

pretty lively better than in the order which appeared before it, though

that was a good willow green; the yellow but small in quantity, though

bright; the red of this order not very pure: those which appeared

before yet more obscure, being very dilute and dirty; as were likewise

the three first blues.

10. NOW it is evident, that these colours arose at the top of the

bubble, as it grew by degrees thinner and thinner: but what the express

thickness of the bubble was, where each of these colours appeared upon

it, could not be determined by these experiments; but was found by

another means, viz. by taking the object glass of a long telescope,

which is in a small degree convex, and placing it upon a flat glass,

so as to touch it in one point, and then water being put between them,

the same colours appeared as in the bubble, in the form of circles or

rings surrounding the point where the glasses touched, which appeared

black for want of any reflection from it, like the top of the bubble

when thinnest[302]: next to this spot lay a blue circle, and next

without that a white one; and so on in the same order as before,

reckoning from the dark spot. And henceforward I shall speak of each

colour, as being of the first, second, or any following order, as it is

the first, second, or any following one, counting from the black spot

in the center of these rings; which is contrary to the order in which

I must have mentioned them, if I should have reputed them the first,

second, or third, &c. in order, as they arise after one another upon

the top of the bubble.