But after all, even the _clearest Water_ is very far from being _pure_

and wholly _defecate_, in any part of the World that I can learn. For

ours here, I have had an Opportunity of examining it over a good part of

_England_; and cannot say I ever met with any, that, however fresh and

newly taken out of the Spring, did not exhibit, even to the naked Eye,

great numbers of exceeding small terrestrial Particles disseminated

through all parts of it. Thicker and crasser Water exhibits them in

still greater Plenty.

These are of two general kinds. The one a vegetable terrestrial Matter,

consisting of very different Corpuscles; some whereof are proper for the

formation and increment of one sort of Plant, and some of another; as

also some for the Nourishment of one part of the same Plant, and some of

another. The other kind of Particles sustain'd in Water are of a Mineral

Nature. These likewise are of different sorts. In some Springs we find

common Salt, in others _Vitriol_, in others _Alum_, _Nitre_, _Sparr_,

_Ochre_, &c. nay, frequently several of these, or other Minerals, all in

the same Spring; the Water as it drains and passes thorough the _Strata_

of Stone, Earth, and the like, taking up and bearing along such loose

Mineral Corpuscles, as it meets with in the Pores and Interstices of

those _Strata_, and bringing them on with it quite to the Spring. All

Water whatever is much charg'd with the Vegetable Matter, this being

fine, light, and easily moveable. For the Mineral, the Water of Springs

contains more of it than that of Rivers, especially when at distance

from their Sources; and that of Rivers more than the Water that falls in

Rain. This I have learn'd from several Trials, which I must not give

Account of here; my Drift in this place being only to evince the

Existence of Terrestrial Matter in Water.

Any one who desires farther Satisfaction in this, may easily obtain it,

if he only put Water into a clear Glass Viol, stopping it close, to keep

Dust and other exterior Matter out, and letting it stand, without

stirring it for some Days: He will then find a considerable Quantity of

terrestrial Matter in the Water, however pure and free it might appear

when first put into the Viol. He will in a very short time observe, as I

have frequently done, the Corpuscles that were at first, while the Water

was agitated and kept in motion, separate, and hardly visible[6], by

degrees, as the Water permits, by its becoming more still and at rest,

assembling and combining together; by that means forming somewhat larger

and more conspicuous _Moleculæ_. Afterwards he may behold these joining

and fixing each to other, by that means forming large thin Masses,

appearing like _Nubeculæ_, or Clouds in the Water; which grow more thick

and opake, by the continual appulse and accretion of fresh Matter. If

the said Matter be chiefly of the Vegetable kind, it will be sustain'd

in the Water; and discover at length a green Colour, becoming still more

and more of that Colour, I mean an higher and more saturate Green, as

the Matter thickens and encreases. That this _Matter_ inclines so much

to that _Colour_, is the less strange, since we see so large a share of

it, when constituting Vegetables wearing the same Colour in them. But if

there be any considerable quantity of meer Mineral Matter in the Water,

this, being of a greater specifick Gravity than the Vegetable, as the

Particles of it unite and combine in such Number, till they form a

_Molecula_, the Impetus of whose Gravity surpasses that of the

Resistance of the Water, subsides a great deal of it to the _bottom_.

Nor does it only fall down it self, but frequently entangling with the

_Vegetable Nubeculæ_, forces them down along with it.

The Reason why Bodies, when dissolved and reduced to extreme small

Parts, are sustain'd in Liquors that are of less specifick Gravity than

those Bodies are, hath been pointed at by a late ingenious Member of

this Society[7]. He is indeed far from having adjusted all the _Momenta_

of this Affair; however it must be admitted, that, in the _dividing_ or

_solution_ of Bodies, their Surfaces do not decrease in the same

Proportion that their Bulk does. Now the Gravity of a Body, which is the

Cause of its sinking or tendency downwards, is commensurate to its Bulk;

but the resistance that the Liquor makes, is proportion'd, not to the

Bulk, but to the Extent of the Surface of the Body immersed in it.

Whence 'tis plain, a Body may be so far divided, that its Parts may be

sustain'd in a Fluid, whose specifick Gravity is less than that of the

said Body. Nay, 'tis Matter of Fact, that they frequently are so; and we

daily see _Menstrua_ supporting the Parts of _Metals_, and other Bodies,

that are of six, ten, nay, almost twenty times the specifick Gravity of

those _Menstrua_. And as the Parts of Bodies when divided, are thus

supported in a Fluid; so when they occur and unite again, they must sink

of course, and fall to the Bottom.

Upon the whole, 'tis palpable and beyond reasonable Contest, that

_Water_ contains in it a very considerable Quantity of terrestrial

Matter. Now the Question is, to which of these, the Water, or the

Earthly Matter sustain'd in it, Vegetables owe their Growth and Augment:

For deciding of which, I conceive the following Experiments may afford

some Light; and I can safely say, they were made with due Care and

Exactness.

_Anno_ 1691.

I chose several _Glass Vials_, that were all, as near as possible, of

the same shape and bigness. After I had put what Water I thought fit

into every one of them, and taken an Account of the weight of it, I

strain'd and ty'd over the Orifice of each Vial, a Piece of Parchment,

having an hole in the middle of it, large enough to admit the Stem of

the Plant I design'd to set in the Vial, without confining or

streightning it, so as to impede its _Growth_. My Intention in this, was

to prevent the inclosed Water from evaporating, or ascending any other

way than only through the Plant to be set therein. Then I made choice of

several Sprigs of Mint, and other Plants, that were, as near as I could

possibly judge, alike fresh, sound, and lively. Having taken the weight

of each, I placed it in a Vial, order'd as above; and as the Plant

imbib'd and drew off the Water, I took care to add more of the same from

time to time, keeping an Account of the weight of all I added. Each of

the Glasses were, for better distinction, and the more easie keeping a

Register of all Circumstances, noted with a different Mark or _Letter_,

_A_, _B_, _C_, _&c._ and all set in a Row in the same Window, in such

manner that all might partake alike of _Air_, _Light_, and _Sun_. Thus

they continued from _July_ the Twentieth, to _October_ the Fifth, which

was just Seventy Seven Days. Then I took them out, weigh'd the Water in

each Vial, and the Plant likewise, adding to its weight that of all the

Leaves that had fallen off during the time it stood thus. And Lastly, I

computed how much each Plant had gain'd; and how much Water was spent

upon it. The Particulars are as follow.

(A.) _Common Spear-Mint_, set in _Spring-Water_. The Planted weighed

when put in, _July_ 20. just 27 Grains; when taken forth, _October_ 5.

42 Grains: So that in this space of 77 Days, it had gained in weight

15 Grains.

The whole Quantity of Water expended, during these 77 Days, amounted to

2558 Grains. Consequently the weight of the Water taken up, was

170-8/15 times as much as the Plant had got in weight.

(B.) _Common Spear-Mint_, _Rain-Water_. The Mint weigh'd, when put in,

Gr. 28¼; when taken out Gr. 45¾, having gain'd in 77 Days Gr.

17½.

The Dispendium of the Water Gr. 3004, which was 171-22/35 times as much

as the Plant had received in weight.

(C.) _Common Spear-Mint_, _Thames-water_. The Plant when put in, Gr.

28, when taken forth, Gr. 54. So that in 77 Days it had gained Gr. 26.

The Water expended, amounted to Gr. 2493. which was 95-23/26 times as

much as the additional weight of the Mint.

(D.) _Common Solanum_, or _Night-shade_: _Spring-water_. The Plant

weigh'd, when put in, Gr. 49; when taken out, 106; having gain'd in 77

Days 57 Gr.

The Water expended during the said time, was 3708 Gr. which was 65-3/57

times as much as the Augment of the Plant.

_This Specimen_ had several _Buds_ upon it, when first set in the

Water. _These_ in some Days became fair _Flowers_, which were at length

succeeded by _Berries_.

(E.) _Lathyris seu Cataputia Gerh._ _Spring-Water._ It weigh'd, when

put in, Gr. 98. when taken forth, Gr. 101½. The additional weight

for the whole 77 Days, being but Gr. 3½.

The Quantity of Water spent upon it during that time, Gr. 2501. which

is 714-4/7 times as much as the Plant was augmented.

_Several _other Plants_ were try'd, that did _not thrive_ in _Water_,

or succeed any better than the _Cataputia_ foregoing:_ _But 'tis

besides my purpose to give a particular _Account_ of them here._

(F, G.) _These Two Vials_ were fill'd, the former (F) with _Rain_, the

other with _Spring-water_, at the same time as those above-mention'd

were; and stood as long as they did. But they had neither of them any

Plant; my Design in these being only to inform my self, whether any

Water exhaled out of the Glasses, otherwise than _thorow_ the Bodies of

the Plants. The Orifices of these two Glasses were cover'd with

Parchment; each piece of it being perforated with an hole of the same

bigness with those of the Vials above. In this I suspended a bit of

Stick, about the thickness of the Stem of one of the aforesaid Plants,

but not reaching down to the Surface of the included Water. I put them

in thus, that the Water in these might not have more Scope to evaporate

than that in the other Vials. Thus they stood the whole 77 Days in the

same Window with the rest; when, upon Examination, I found none of the

Water in these wasted or gone off. Tho' I observed both in these, and

the rest, especially after hot Weather, small Drops of Water, not unlike

Dew, adhering to the Insides of the Glasses, that Part of them, I mean,

that was above the Surface of the enclosed Water.

The Water in these two Glasses that had no Plants in them, at the end of

the Experiment, exhibited a larger Quantity of Terrestrial Matter than

that in any of those that had the Plants in them did. The Sediment at

the bottom of the Vials was greater; and the _Nubeculæ_, diffus'd

through the Body of the Water, thicker. And of that which was in the

others, some of it proceeded from certain small Leaves that had fallen

from that part of the Stems of the Plants that was within the Water,

wherein they rotted and dissolved. The Terrestrial Matter in the

Rain-water was finer than that in the Spring-water.

_Anno 1692._

The Glasses made use of in this, were of the same sort with those in the

former Experiment; and cover'd over with Parchment in like manner. The

Plants here were all _Spear-Mint_; the most kindly, fresh, sprightly

Shoots I could chuse. The Water, and the Plants were weigh'd as above;

and the Vials set in a Line, in a South Window: where they stood from

_June_ the 2d to _July_ 28. which was just 56 Days.

(H.) _Hyde-Park Conduit Water_, alone. The _Mint_ weighed, when put in,

127 Gr. when taken out, 255 Gr. The whole Quantity of Water expended

upon this Plant, amounted to 14190 Gr.

This was all along a very kindly Plant; and had run up to above two

Foot in height. It had shot but one considerable collateral Branch; but

had sent forth many and long Roots, from which sprung very numerous,

though small and short, lesser Fibres. These lesser Roots came out of

the larger on two opposite sides, for the most part; so that each Root,

with its _Fibrillæ_, appear'd not unlike a small Feather. To these

_Fibrillæ_ adher'd pretty must Terrestrial Matter. In the Water, which

was at last thick and turbid, was a green Substance, resembling a fine

thin _Conserva_.

(I.) The _same Water_, alone. The _Mint_ weigh'd, when put in, 110 Gr.

when taken out, 249. Water expended, 13140 Gr.

This Plant was as kindly as the former, but had shot no collateral

Branches. Its Roots, the Water, and the green Substance, all much as in

the former.

(K.) _Hyde-Park Conduit-water_, in which was dissolved an Ounce and

half of _Common Garden-earth_. The _Mint_ weigh'd, when put in, 76 Gr.

when taken out, 244 Gr. Water expended, Gr. 10731.

This Plant, though it had the Misfortune to be annoy'd with many small

Insects that hapn'd to fix upon it; yet had shot very considerable

collateral Branches; and at least as many Roots as either that in H or

I; which had a much greater Quantity of Terrestrial Matter adhering to

the Extremities of them. The same green Substance here, that was in the

two preceding.

(L.) _Hyde-Park Water_, with the same Quantity of _Garden-mould_ as in

the former. The _Mint_ weigh'd, when put in, 92 Gr. when taken out, 376

Gr. The Water expended 14950 Gr.

This Plant was far more flourishing than any of the precedent; had

several very considerable collateral Branches, and very numerous Roots,

to which Terrestrial Matter adhered very copiously.

The Earth in both these Glasses was very sensibly and considerably

wasted, and less than when first put in. The same sort of green

Substance here as in those above.

(M.) _Hyde-Park Water_, distilled off with a gentle Still. The _Mint_

weigh'd, when put in, 114 Gr. when taken out 155. The Water expended,

8803 Gr.

This Plant was pretty kindly; had two small collateral Branches, and

several Roots, though not so many as that in H or I, but as much

Terrestrial Matter adhering to them as those had. The Water was pretty

thick; having very numerous small Terrestrial Particles swimming in it,

and some Sediment at the bottom of the Glass. This Glass had none of

the green Matter above mentioned, in it.

(N.) The Residue of the Water, which remain'd in the _Still_ after that

in M, was distill'd off. It was very turbid, and as high-colour'd

(reddish) as ordinary Beer. The _Mint_ weigh'd, when put in, 81 Gr.

when taken out, 175 Gr. Water expended, 4344 Gr. This Plant was very

lively; and had sent out six collateral Branches, and several Roots.

(O.) _Hyde-Park Conduit-water_, in which was dissolved a Drachm of

Nitre. The Mint set in this suddenly began to wither and decay; and died

in a few Days: As likewise did two more Sprigs, that were set in it,

successively. In another Glass I dissolv'd an Ounce of good

Garden-mould, and a Drachm of Nitre, and in a third, half an Ounce of

Wood ashes, and a Drachm of Nitre; but the Plants in these succeeded no

better than in the former. In other Glasses I dissolved several other

sorts of Earths, Clays, Marles, and variety of Manures, _&c._ I set Mint

in distill'd Mint-water; and other Experiments I made, of several kinds,

in order to get Light and Information, what hastened or retarded,

promoted or impeded Vegetation; but these do not belong to the Head I am

now upon.

(P.) _Hyde-Park Conduit-water._ In this I fix'd a Glass-Tube about ten

Inches long, the Bore about one sixth of an Inch in Diameter, fill'd

with very fine and white Sand, which I kept from falling down out of the

Tube into the Vial, by tying a thin piece of Silk over that end of the

Tube that was downwards. Upon Immersion of the lower end of it into the

Water, this by little and little ascended quite to the upper Orifice of

the Tube. And yet, in all the fifty six Days which it stood thus, a very

inconsiderable Quantity of Water had gone off, _viz._ scarce twenty

Grains; though the Sand continued moist up to the top till the very

last. The Water had imparted a green Tincture to the Sand, quite to the

very top of the Tube. And, in the Vial, it had precipitated a greenish

Sediment, mix'd with black. To the bottom and sides of the Tube, as far

as 'twas immers'd in the Water, adher'd pretty much of the green

Substance describ'd above. Other like Tubes I fill'd with Cotton, Lint,

Pith of Elder, and several other porous Vegetable Substances; setting

some of them in clear Water; others in Water tinged with Saffron,

Cochinele, _&c._ And several other Trials were made, in order to give a

mechanical Representation of the motion and distribution of the Juices

in Plants; and of some other _Phænomena_ observable in Vegetation, which

I shall not give the Particulars of here, as being not of use to my

present design.

(Q, R, S, _&c._) Several Plants set in Vials, ordered in like manner as

those above, in _October_, and the following colder Months. These throve

not near so much; nor did the Water ascend in nigh the quantity it did

in the better Seasons, in which the before recited Trials were made.

_Some Reflections upon the foregoing Experiments._

1. _In Plants of the same kind, the less they are in Bulk, the smaller

the Quantity of the fluid Mass, in which they are set, is drawn off; the

Dispendium of it, where the Mass is of equal thickness, being pretty

nearly proportion'd to the Bulk, of the Plant._ Thus that in the Glass

mark'd A, which weigh'd only 27 Grains, drew off but 2558 Grains of the

Fluid; and that in B, which weigh'd only 28¼, took up but 3004

Grains; whereas that in H, which weigh'd 127 Grains, spent 14190 Grains

of the Liquid Mass.

The Water seems to ascend up the _Vessels_ of Plants, in much the same

manner as up a Filtre; and 'tis no great wonder that a larger Filtre

should draw off more Water than a lesser; or that a Plant that has more

and larger Vessels, should take up a greater share of the Fluid in which

it is set, than one that has fewer and smaller ones can. Nor do I note

this as a thing very considerable in it self, but chiefly in regard to

what I am about to offer beneath; and that it may be seen that, in my

other Collations of Things, I made due Allowance for this Difference.

2. _The much greatest part of the fluid Mass, that is thus drawn off and

convey'd into the Plants, does not settle or abide there; but passes

through the pores of them, and exhales up into the Atmosphere._ That the

Water in these Experiments ascended only through the Vessel of the

Plants, is certain. The _Glasses_ F and G, that had no Plants in them,

though disposed of in like manner as the rest, remain'd at the End of

the Experiment, as at first; and none of the Water was gone off. And

that the greatest part of it flies off from the Plant into the

Atmosphere, is as certain. The least Proportion of the Water expended,

was to the Augment of the Plant, as 46 or 50 to 1. And in some the

weight of the Water drawn off, was 100, 200, nay, in one above 700 times

as much as the Plant had received of Addition.

This so continual an Emission and Detachment of Water, in so great

Plenty from the Parts of Plants, affords us a manifest Reason why

Countries that abound with Trees, and the larger Vegetables especially,

should be very obnoxious to Damps, great Humidity in the Air, and more

frequent Rains, than others that are more open and free. The great

Moisture in the Air, was a mighty inconvenience and annoyance to those

who first settled in _America_; which at that time was much overgrown

with Woods and Groves. But as these were burnt and destroy'd, to make

way for Habitation and Culture of the Earth, the Air mended and clear'd

up apace, changing into a Temper much more dry and serene than before.

Nor does this Humidity go off pure and alone; but usually bears forth

with it many Parts of the same Nature with those whereof the Plant,

through which it passes, consists. The _Crasser_ indeed are not so

easily born up into the Atmosphere; but are usually deposited on the

Surface of the Flowers, Leaves, and other Parts of the Plants: Hence

comes our Manna's, our Honeys, and other Gummous Exsudations of

Vegetables. But the finer and lighter Parts are with greater ease sent

up into the Atmosphere. Thence they are conveyed to our Organs of Smell,

by the Air we draw in Respiration; and are pleasant or offensive,

beneficent or injurious to us, according to the Nature of the Plants

from whence they arise. And since these owe their Rise to the Water,

that ascends out of the Earth through the Bodies of Plants, we cannot be

far to seek for the Cause why they are more numerous in the Air, and we

find a greater quantity of Odors exhaling from Vegetables, in warm,

humid Seasons, than in any other whatever.

3. _A great part of the Terrestrial Matter that is mix'd with the Water,

ascends up into the Plant as well as the Water._ There was much more

Terrestrial Matter at the end of the Experiment, in the Water of the

Glasses F and G, that had no Plants in them, than in those that had

Plants. The _Garden-mould_ dissolved in the Glasses K and L, was

considerably diminished, and carried off. Nay, the Terrestrial and

Vegetable Matter was born up in the Tubes fill'd with Sand, Cotton,

_&c._ in that Quantity, as to be evident even to Sense. And the Bodies

in the Cavities of the other Tubes, that had their lower Ends immers'd

in Water, wherein Saffron, Cochinele, _&c._ had been infused, were

tinged with Yellow, Purple, _&c._

If I may be permitted to look abroad a while, towards our Shores and

Parts within the Verge of the Sea, these will present us with a large

Scene of Plants, that, along with the Vegetable, take up into them meer

mineral Matter also in great abundance. Such are our Sea-Purslains, the

several sorts of _Alga's_, of Sampires, and other marine Plants. These

contain common Sea-salt, which is all one with the _Fossil_, in such

plenty, as not only to be plainly distinguish'd on the Palate, but may

be drawn forth of them in considerable Quantity. Nay, there want not

those who affirm, there are Plants found that will yield _Nitre_, and

other mineral Salts; of which indeed I am not so far satisfied, that I

can depend on the Thing, and therefore give this only as an hint for

Enquiry.

To go on with the Vegetable Matter, how apt and how much disposed this,

being so very fine and light, is to attend Water in all its Motions, and

follow it into each of its Recesses, is manifest, not only from the

Instances above alledg'd, but many others. Percolate it withal the Care

imaginable: Filter it with never so many Filtrations, yet some

Terrestrial Matter will remain. 'Tis true, the Fluid will be thinner

every time than other, and more disingaged of the said Matter; but never

wholly free and clear. I have filtred Water thorough several wholly free

and clear Sheets of thick Paper; and, after that, through very close

fine Cloth twelve times doubled. Nay, I have done this over and over;

and yet a considerable quantity of this Matter discover'd it self in the

Water after all. Now if it thus pass Interstices, that are so very small

and fine along with the Water, 'tis the less strange it should attend it

in its passage through the Ducts and Vessels of Plants. 'Tis true,

filtering and distilling of Water intercepts and makes it quit some of

the Earthy Matter it was before impregnated withal: But then that which

continues with the Water after this, is fine and light; and such

consequently, as is in a peculiar manner fit for the Growth and

Nourishment of Vegetables. And this is the Case of Rain-water. The

Quantity of Terrestrial Matter it bears up into the Atmosphere, is not

great. But that which it does bear up, is mainly of that light kind of

Vegetable Matter; and that too perfectly dissolved, and reduced to

single Corpuscles, all fit to enter the Tubules and Vessels of Plants:

On which Account 'tis, that this Water is so very fertile and prolifick.

The Reason, why in this Proposition, I say, only a great part of the

Terrestrial Matter that is mix'd with the Water, ascends up with it into

the Plant, is, because all of it cannot. The Mineral Matter is a great

deal of it, not only gross and ponderous, but scabrous and inflexible;

and so not disposed to enter the Pores of the Roots. And a great many of

the simple Vegetable Particles by degrees unite, and form some of them

small Clods or _Moleculæ_; such as those mention'd in H, K, and L,

sticking to the Extremities of the Roots of those Plants. Others of them

intangle in a looser manner; and form the _Nubeculæ_, and green Bodies,

so commonly observ'd in stagnant Water. These, when thus conjoin'd, are

too big to enter the Pores, or ascend up the Vessels of Plants, which

singly they might have done. They who are conversant in Agriculture,

will easily subscribe to this. They are well aware that, be their Earth

never so rich, so good, and so fit for the production of Corn or other

Vegetables, little will come of it, unless the Parts of it be separated

and loose. 'Tis on this Account they bestow the Pains they do in Culture

of it, in Digging, Plowing, Harrowing, and Breaking of the Clodded Lumps

of Earth. 'Tis the same way that Sea-salt, Nitre, and other Salts,

promote Vegetation. I am sorry I cannot subscribe to the Opinion of

those Learned Gentlemen, who imagine Nitre to be essential to Plants;

and that nothing in the Vegetable Kingdom is transacted without it. By

all the Trials I have been able to make, the thing is quite otherwise;

and when contiguous to the Plant, it rather destroys than nourishes it.

But this Nitre and other Salts certainly do; they loosen the Earth, and

separate the concreted Parts of it; by that means fitting and disposing

them to be assumed by the Water, and carried up into the Seed or Plant,

for its Formation and Augment. There's no Man but must observe, how apt

all sorts of Salts are to be wrought upon by Moisture; how easily they

liquate and run with it; and when these are drawn off, and have deserted

the Lumps wherewith they were incorporated, those must moulder

immediately, and fall asunder of Course. The hardest Stone we meet with,

if it happen, as frequently it does, to have any sort of Salt intermix'd

with the Sand, of which it consists, upon being expos'd to an humid Air,

in a short time dissolves and crumbles all to pieces; and much more will

clodded Earth or Clay, which is not of near so compact and solid a

Constitution as Stone is. The same way likewise is Lime serviceable in

this Affair. The Husbandmen say of it, that it does not fatten, but only

mellows the Ground: By which they mean, that it does not contain any

thing in it self that is of the same Nature with the Vegetable Mould, or

afford any Matter fit for the Formation of Plants; but meerly softens

and relaxes the Earth; by that means rendering it more capable of

entering the Seeds and Vegetables set in it, in order to their

Nourishment, than otherwise it would have been. The Properties of Lime

are well known; and how apt 'tis to be put into Ferment and Commotion by

Water. Nor can such Commotion ever happen when Lime is mix'd with Earth,

however hard and clodded that may be, without opening and loosening of

it.

4. _The Plant is more or less nourish'd and augmented, in Proportion as

the Water, in which it stands, contains a greater or smaller Quantity of

proper terrestrial Matter in it._ The Truth of this Proportion is so

eminently discernable through the whole Process of these Trials, that I

think no doubt can be made of it. The _Mint_ in the Glass C, was of much

the same Bulk and Weight with those in A and B. But the Water, in which

that was, being River-water, which was apparently stored more copiously

with terrestrial Matter, than the Spring or Rain-water, wherein they

stood, were; it had thriven to almost double the Bulk that either of

them had, and with a less Expence of Water too. So likewise the Mint in

L, in whose Water was dissolved a small quantity of good Garden-mould,

though it had the disadvantage[8] to be less, when first set, than

either of the Mints in H or I, whose Water was the very same with this

in L, but had none of that Earth mix'd with it; yet, in a short time the

Plant not only overtook, but much out-strip'd those and at the end of

the Experiment was very considerably bigger and heavier than either of

them. In like manner the _Mint_ in N, though less at the beginning than

that in M, being set in that thick, turbid, feculent Water, that

remained behind, after that wherein M was placed, was still'd off, had

in fine more than double its original weight and bulk; and receiv'd

above twice the additional Encrease, than that in M, which stood in the

thinner distill'd Water, had done. And, which is not less considerable,

had not drawn off half the Quantity of Water that that had.

Why, in the beginning of this Article, I limit the Proportion of the

Augment of the Plant to the Quantity of proper Terrestrial Matter in the

Water, is, because all, even the Vegetable Matter, to say nothing of the

Mineral, is not proper for the Nourishment of every Plant. There may be,

and doubtless are, some Parts in different Species of Plants, that may

be much alike, and so owe their Supply to the same common Matter; but

'tis plain all cannot. And there are other Parts so differing, that 'tis

no ways credible they should be formed all out of the same sort of

Corpuscles. So far from it, that there want not good Indications, as we

shall see by and by, that every kind of Vegetable requires a peculiar

and specifick Matter for its Formation and Nourishment. Yea, each Part

of the same Vegetable does so; and there are very many and different

Ingredients go to the Composition of the same individual Plant. If

therefore the Soil, wherein any Vegetable or Seed is planted, contains

all or most of these ingredients, and those in due quantity, it will

grow and thrive there; otherwise 'twill not. If there be not as many

sorts of Corpuscles as are requisite for the Constitution of the main

and more essential Parts of the Plant, 'twill not prosper at all. If

there be these, and not in sufficient Plenty, 'twill starve, and never

arrive to its natural Stature: Or if there be any the less necessary and

essential Corpuscles wanting, there will be some failure in the Plant;

'twill be defective in Taste, in Smell, in Colour, or some other way.

But though a Tract of Land may happen not to contain Matter proper for

the Constitution of some one peculiar kind of Plant; yet it may for

several others, and those much differing among themselves. The

Vegetative Particles are commix'd and blended in the Earth, with all the

diversity and variety, as well as all the uncertainty, conceivable. I

have given some intimations of this elsewhere[9], and shall not repeat

them here, but hope in due time to put them into a much better Light

than that they there stand in.

It is not possible to imagine, how one uniform, homogeneous Matter,

having its Principles or Original Parts all of the same Substance,

Constitution, Magnitude, Figure, and Gravity, should ever constitute

Bodies so egregiously unlike, in all those respects, as Vegetables of

different kinds are; nay, even as the different Parts of the same

Vegetable. That one should carry a resinous, another a milky, a third a

yellow, a fourth a red Juice, in its Veins; one afford a fragrant,

another an offensive Smell; one be sweet to the Taste, another bitter,

acid, acerbe, austere, &c. that one should be nourishing, another

poisonous, one purging, another astringent: In brief, that there should

be that vast difference in them, in their several Constitutions, Makes,

Properties, and Effects, and yet all arise from the very same sort of

Matter, would be very strange. And, to note by the by, this Argument

makes equally strong against those, who suppose meer Water the Matter,

out of which all Bodies are form'd.

The _Cataputia_ in the Glass E, received but very little Encrease, only

three Grains and an half all the while it stood, though 2501 Grains of

Water were spent upon it. I will not say the Reason was, because that

Water did not contain in it Matter fit and proper for the Nourishment of

that peculiar and remarkable Plant. No, it may be the Water was not a

proper _Medium_ for it to grow in; and we know there are very many

Plants that will not thrive in it. Too much of that Liquor, in some

Plants, may probably hurry the Terrestrial Matter thorough their Vessels

too fast for them to arrest and lay hold of it. Be that as it will, 'tis

most certain there are peculiar Soils that suit particular Plants. In

_England_, Cherries are observ'd to succeed best in _Kent_; Apples in

_Herefordshire_; Saffron in _Cambridgeshire_; Wood in two or three of

our _Midland Counties_; and Teazles in _Somersetshire_. This is an

Observation that hath held in all Parts, and indeed in all Ages of the

World. The most ancient Writers of Husbandry[10] took notice of it; and

are not wanting in their Rules for making choice of Soils suited to the

Nature of each kind of Vegetable they thought valuable, or worth

propagating.

But, which is a further Proof of what I am here endeavouring to advance,

that Soil that is once proper and fit for the Production of some one

sort of Vegetable, does not ever continue to be so. No, in Tract of time

it loses that Property; but sooner in some Lands, and later in others:

This is what all who are conversant in these things know very well. If

Wheat, for Example, be sown upon a Tract of Land that is proper for that

Grain, the first Crop will succeed very well; and perhaps the second,

and the third, as long as the Ground is in Heart, as the Farmers speak;

but in a few Years 'twill produce no more, if sowed with that Corn: Some

other Grain indeed it may, as Barley. And after this has been sown so

often, that the Land can bring forth no more of the same, it may

afterwards yield good Oats; and, perhaps, Pease after them. At length

'twill become barren; the Vegetative Matter, that at first it abounded

withal, being educed forth of it by those successive Crops, and most of

it born off. Each sort of Grain takes forth that peculiar Matter that is

proper for its own Nourishment. First, the Wheat draws off those

Particles that suit the Body of that Plant; the rest lying all quiet and

undisturbed the while. And when the Earth has yielded up all them, those

that are proper for Barley, a different Grain, remain still behind, till

the successive Crops of that Corn fetch them forth too. And so the Oats

and Pease, in their Turn; till in fine all is carried off, and the Earth

in great measure drain'd of that sort of Matter.

After all which, that very Tract of Land may be brought to produce

another Series of the same Vegetables; but never till 'tis supplied with

a new Fund of Matter, of like sort with that it at first contain'd. This

Supply is made several ways: By the Grounds lying fallow for some time,

till the Rain has pour'd down a fresh Stock upon it: _Or_, by the

Tiller's Care in manuring of it. And for farther Evidence that this

Supply is in reality of like sort, we need only reflect a while upon

those Manures that are found by constant Experience best to promote

Vegetation, and the Fruitfulness of the Earth. These are chiefly either

parts of Vegetables, or of Animals; which indeed either derive their own

Nourishment immediately from Vegetable Bodies, or from other Animals

that do so. In particular, the Blood, Urine, and Excrements of Animals;

Shavings of Horns, and of Hoofs; Hair, Wool, Feathers; calcin'd Shells;

Lees of Wine, and of Beer; Ashes of all sorts of Vegetable Bodies;

Leaves, Straw, Roots, and Stubble, turn'd into the Earth by Plowing or

otherwise to rot and dissolve there: These, I say, are our best Manures;

and, being Vegetable Substances, when refunded back again into the

Earth, serve for the Formation of other like Bodies.

Not wholly to confine our Thoughts to the Fields, let us look a while

into our Gardens; where we shall meet with still further Confirmations

of the same thing. The Trees, Shrubs, and Herbs cultivated in these,

after they have continued in one Station, till they have derived thence

the greater part of the Matter fit for their Augment, will decay and

degenerate, unless either fresh Earth, or some fit Manure, be applied

unto them. 'Tis true, they may maintain themselves there for some time,

by sending forth Roots further and further to a great Extent all round,

to fetch in more remote Provision; but at last all will fail; and they

must either have a fresh Supply brought to them, or they themselves be

removed and transplanted to some Place better furnished with Matter for

their Subsistence. And accordingly _Gardiners_ observe, that Plants that

have stood a great while in a Place, have longer Roots than usual; part

of which they cut off, when they transplant them to a fresh Soil, as now

not of any further use to them. All these Instances, to pass over a

great many others that might be alledg'd, point forth a particular

Terrestrial Matter, and not Water, for the Subject to which Plants owe

their Increase. Were it Water only, there would be no need of Manures;

or of transplanting them from place to place. The Rain falls in all

Places alike; in this Field and in that indifferently; in one side of an

Orchard or Garden, as well as another. Nor could there be any Reason,

why a Tract of Land should yield Wheat one Year, and not the next; since

the Rain showers down alike in each. But I am sensible I have carried on

this Article to too great a length; which yet on so ample and extensive

a Subject, 'twas not easie to avoid.

5. _Vegetables are not form'd of Water; but of a certain peculiar

Terrestrial Matter._ It hath been shewn, that there is a considerable

Quantity of this Matter contain'd both in Rain, Spring, and River-water:

That the much greatest part of the fluid Mass that ascends up into

Plants, does not settle or abide there, but passes through the Pores of

them, and _exhales_ up into the Atmosphere; That a great part of the

Terrestrial Matter, mix'd with the Water, passes up into the Plant along

with it; and that the Plant is more or less augmented in proportion, as

the Water contains a greater or smaller Quantity of that Matter. From

all which we may very reasonably infer, that _Earth, and not Water, is

the Matter that constitutes Vegetables_. The Plant in E, drew up into it

2501 Grains of the fluid Mass; and yet had received but Grains 3 and a

half of Increase from all that. The Mint in L, though it had at first

the disadvantage to be much less than that in I; yet being set in Water

wherewith Earth was plentifully mix'd, and _that_ in I, _only in Water_

without any such additional Earth, it had vastly outgrown the other,

weighing at last 145 Grains more than that did, and so having gain'd

about twice as much as that had. In like manner that in K, though 'twas

a great deal less when put in than that in I, and also was impair'd and

offended by Insects; yet being planted in Water wherein Earth was

dissolved, whereas the Water in which it stood had none, it not only

over-took, but considerably surpass'd the other; weighing at last 29

Grains more than that in I, and yet had not expended so much Water as

that, by above 2400 Grains. The Plant in N, tho' at first a great deal

less than that in M; yet being set in the foul crass Water that was left

in the Still, after that, in which M was set, was drawn off, in

Conclusion had gain'd in weight above double what that in the finer and

thinner Water had. The Proportion of the Augment of that Plant that

throve most was, to the fluid Mass spent upon it, but as 1 to 46. In

others, 'twas but as 1 to 60, 100, 200; nay, in the _Cataputia_, 'twas

but as 1 to 714. The Mint in B took up 39 Grains of Water a-day, one day

with another; which was much more than the whole weight of the Plant

originally; and yet, with all this, it gain'd not one fourth of a Grain

a-day in weight. Nay, that in H took up 253 Grains a day of the Fluid:

Which was near twice as much as its original Weight, it weighing, when

first set in the Water, but 127 Grains. And, after all, the daily

Encrease of the Plant was no more than Grains 2-15/56.

6. _Spring, and Rain-water, contain pretty near an equal Charge of

Vegetable Matter_; _River-water more than either of them._ The Plants in

the Glasses A, B, and C, were at first of much the same size and weight.

At the End of the Experiment, the Mint in A had gain'd 15 Grains out of

2558 Grains of Spring-water; that in B, Grains 17 and an half, out of

3004 Grains of Rain-water; but that in C had got 26 Grains out of only

2493 Grains of River-water. I do not found this Proposition solely upon

these Trials; having made some more, which I do not relate here, that

agree well enough with these. So that the Proportions here deliver'd,

will hold for the main; but a strict and just Comparison is hardly to be

expected. So far from it, that I make no doubt, but the Water that falls

in Rain, at some times, contains a greater share of Terrestrial Matter

than that which falls at others. A more powerful and intense Heat must

needs hurry up a larger quantity of that Matter along with the humid

Vapours that form Rain, than one more feeble and remiss ever possibly

can. The Water of one Spring may flow forth with an higher Charge of

this Matter, than that of another; this depending partly upon the

quickness of the Ebullition of the Water, and partly upon the Quantity

of that Matter latent in the _Strata_, through which the Fluid passes,

and the greater or less laxity of those _Strata_. For the same Reason,

the Water of one River may abound with it more than that of another.

Nay, the same River, when much agitated, and in commotion, must bear up

more of it, than when it moves with less rapidity and violence. That

there is a great Quantity of this Matter in Rivers; and that it

contributes vastly to the ordinary Fertility of the Earth, we have an

illustrious Instance in the _Nile_, the _Ganges_, and other Rivers that

yearly overflow the neighbouring Plains. Their Banks shew the fairest

and largest Crops of any in the whole World. They are even loaded with

the multitude of their Productions; and those who have not seen them,

will hardly be induced to believe the mighty Returns those Tracts make

in comparison of others, that have not the Benefit of like Inundations.

7. _Water serves only for a Vehicle to the Terrestrial Matter, which

forms Vegetables; and does not it self make any addition unto them._

Where the proper Terrestrial Matter is wanting, the Plant is not

augmented, though never so much Water ascend into it. The _Cataputia_ in

E, took up more Water than the Mint in C, and yet had grown but very

little, having received only three Grains and an half of additional

weight; whereas the other had received no less than twenty six Grains.

The Mint in I, was planted in the same sort of Water as that in K, was;

only the latter had Earth dissolved in the Water; and yet that drew off

13140 Grains of the Water, gaining it self no more than 139 Grains in

weight; whereas the other took up but 10731 Grains of the Water, and was

augmented 168 Grains in weight. Consequently that spent 2409 Grains more

of the Water than this in K, did, and yet was not so much encreased in

weight as this by 29 Grains. The Mint in M, stood in the very same kind

of Water as that in N, did. But the Water in M, having much less

Terrestrial Matter in it than that in N had, the Plant bore up 8803

Grains of it, gaining it self only 41 Grains the while; whereas that in

N drew off no more than 4344 Grains, and yet was augmented 94 Grains. So

that it spent 4459 Grains of Water more than that did; and yet was not

it self so much increased in weight, as that was, by 53 Grains. This is

both a very fair, and a very conclusive Instance; on which Account 'tis

that I make oftner use of it. Indeed they are all so; and to add any

thing further on this Head, will not be needful.

'Tis evident therefore Water is not the Matter that composes Vegetable

Bodies. 'Tis only the Agent that conveys that Matter to them; that

introduces and distributes it to their several Parts for their

Nourishment. That Matter is sluggish and unactive, and would lie

eternally confin'd to its Beds of Earth, without ever advancing up into

Plants, did not Water, or some like Instrument, fetch it forth and carry

it unto them. That therefore there is that plentiful Provision, and vast

Abundance of it supplied to all Parts of the Earth, is a mark of a

natural Providence superintending over the Globe we inhabit; and

ordaining a due Dispensation of that Fluid, without the Ministry of

which the Noble Succession of Bodies we behold, _Animals_, _Vegetables_,

and _Minerals_, would be all at a stand[11]. But to keep to Plants, 'tis

manifest Water, as well on this, as upon the other Hypothesis, is

absolutely necessary in the Affair of Vegetation; and it will not

succeed without it: Which indeed gave occasion to the Opinion, that

Water it self nourished, and was changed into Vegetable Bodies. They

saw, though these were planted in a Soil never so rich, so happy, so

advantageous, nothing came of it unless there was Water too in a

considerable quantity. And it must be allow'd Vegetables will not come

on or prosper where that is wanting: But yet what those Gentlemen

inferr'd thence, was not, we see, well grounded.

This Fluid is capacitated for the Office here assign'd it several ways:

By the Figure of its Parts, which, as appears from many Experiments, is

exactly and mathematically Spherical; their Surfaces being perfectly

polite, and without any the least Inequalities. 'Tis evident, Corpuscles

of such a Figure are easily susceptible of Motion, yea, far above any

others whatever; and consequently the most capable of moving and

conveying other Matter, that is not so active and voluble. Then the

Intervals of Bodies of that Figure are, with respect to their Bulk, of

all others the largest; and so the most fitted to receive and entertain

foreign Matter in them. Besides, as far as the Trials hitherto made

inform us, the constituent Corpuscles of Water are, each singly

consider'd, absolutely solid; and do not yield to the greatest External

Force. This secures their Figure against any Alteration; and the

Intervals of the Corpuscles must be always alike. By the latter, 'twill

be ever disposed to receive Matter into it; and by the former, when once

received, to bear it on along with it. Water is further capacitated to

be a Vehicle to this Matter, by the tenuity and fineness of the

Corpuscles of which it consists. We hardly know any Fluid in all Nature,

except Fire, whose constituent Parts are so exceeding subtle and small

as those of Water are. They'll pass Pores and Interstices, that neither

Air nor any other Fluid will. This enables them to enter the finest

Tubes and Vessels of Plants, and to introduce the Terrestrial Matter,

conveying it to all Parts of them; whilst each, by means of Organs 'tis

endowed with for the Purpose, intercepts and assumes into it self such

Particles as are suitable to its own Nature, letting the rest pass on

through the common Ducts. Nay, we have almost every where Mechanical

Instances of much the same Tenor. 'Tis obvious to every one, how easily

and suddenly Humidity, or the Corpuscles of Water sustained in the Air,

pervade and insinuate themselves into Cords, however tightly twisted,

into Leather, Parchment, Vegetable Bodies, Wood, and the like. This it

is that fits them for _Hygrometers_; and to measure and determine the

different quantities of Moisture in the Air, in different Places and

Seasons. How freely Water passes and carries with it Terrestrial Matter,

through Filtres, Colatures, Distillations, _&c._ hath been intimated

already.

8. _Water is not capable of performing this Office to Plants, unless

assisted by a due Quantity of Heat; and this must concur, or Vegetation

will not succeed._ The Plants that were set in the Glasses Q, R, S,

_&c._ in _October_, and the following colder Months, had not near the

quantity of Water sent up into them, or so great an additional Encrease

by much, as those that were set in _June_, _July_, and the hotter. 'Tis

plain Water has no power of moving it self; or rising to the vast height

it does in the more tall and lofty Plants. So far from this, that it

does not appear from any Discovery yet made, that even its own Fluidity

consists in the intestine Motion of its Parts; whatever some, otherwise

very learned and knowing, Persons may have thought. There is no need of

any thing more, for solving all the _Phænomena_ of Fluidity, than such a

Figure and Disposition of the Parts, as Water has. Corpuscles of that

make, and that are all absolutely Spherical, must stand so very tickle

and nicely upon each other, as to be susceptible of every Impression;

and though not perpetually in Motion, yet must be ever ready and liable

to be put into it, by any the slightest Force imaginable. It is true,

the Parts of Fire or Heat are not capable of moving themselves any more

than those of Water; but they are more subtil, light, and active, than

those are, and so more easily put into Motion. In fine, 'tis evident and

matter of Fact, that Heat does operate upon, and move the Water, in

order to its carrying on the Work of Vegetation: But how 'tis agitated

it self, and where the Motion first begins, this is no fit Place to

enquire.

That the Concourse of Heat in this Work is really necessary, appears,

not only from the Experiments before us, but from all Nature; from our

Fields and Forests, our Gardens and our Orchards. We see in _Autumn_, as

the Sun's Power grows gradually less and less, so its Effects on Plants

is remitted, and their Vegetation slackens by little and little. Its

Failure is first discernible in Trees. These are raised highest above

the Earth; and require a more intense Heat to elevate the Water, charged

with their Nourishment, to the Tops and Extremities of them. So that for

want of fresh Support and Nutriment, they shed their Leaves, unless

secur'd by a very firm and hardy Constitution indeed, as our

_ever-Greens_ are. Next the Shrubs part with theirs; and then the Herbs

and lower Tribes; the Heat being at length not sufficient to supply even

these, though so near the Earth, the Fund of their Nourishment. As the

Heat returns the succeeding Spring, they all recruit again; and are

furnish'd with fresh Supplies and Verdure: But first, those which are

lowest and nearest the Earth, Herbs, and they that require a lesser

degree of Heat to raise the Water with its Earthy Charge into them: Then

the Shrubs and higher Vegetables in their Turns; and lastly, the Trees.

As the Heat increases, it grows too powerful, and hurries the Matter

with too great Rapidity thorough the finer and more tender Plants: These

therefore go off, and decay; and others that are more hardy and

vigorous, and require a greater share of Heat, succeed in their Order.

By which Mechanism, provident Nature furnishes us with a very various

and differing Entertainment; and what is best suited to each Season, all

the Year round.

As the Heat of the several Seasons affords us a different Face of

Things; so the several distant Climates shew different Scenes of Nature,

and Productions of the Earth[12]. The Hotter Countries yield ordinarily

the largest and tallest Trees; and those in too much greater variety

than the colder ever do. Even those Plants which are common to both,

attain to a much greater Bulk in the Southern than in the Northern

Climes. Nay, there are some Regions so bleak and chill, that they raise

no Vegetables at all to any considerable Size. This we learn from

_Greenland_, from _Iseland_, and other Places of like cold Site and

Condition. In these no Tree ever appears; and the very Shrubs they

afford, are few, little, and low.

Again, in the warmer Climates, and such as do furnish forth Trees and

the larger Vegetables, if there happen a remission or diminution of the

usual Heat, their Productions will be impeded and diminished in

proportion. Our late Colder Summers have given us proof enough of this.

For though the Heat we have had, was sufficient to raise the Vegetative

Matter into the lower Plants, into our Corns, our Wheat, Barley, Pease

and the like; and we have had plenty of Straw-berries, Ras-berries,

Currans, Goosberries, and the Fruits of such other Vegetables as are low

and near the Earth: Yea, and a moderate store of Cherries, Mulberries,

Plumbs, Filberts, and some others that grow somewhat at a greater

Height; yet our Apples, our Pears, Walnuts, and the Productions of the

taller[13] Trees have been fewer, and those not so kindly, so thoroughly

ripen'd, and brought to that Perfection they were in the former more

benign and their warm Seasons. Nay, even the lower Fruits and Grains

have had some share in the common Calamity; and fallen short both in

Number and Goodness of what the hotter and kinder Seasons were wont to

shew us. As to our Grapes, Abricots, Peaches, Nectarens, and Figs, being

transplanted hither out of hotter Climes, 'tis the less wonder we have

of late had so general a Failure of them.

Nor is it the Sun, or the ordinary emission of the Subterranean Heat

only, that promotes Vegetation; but any other indifferently, according

to its Power and Degree: This we are taught by our Stoves, hot Beds, and

the like. All Heat is of like kind; and where-ever is the same Cause,

there will be constantly the same Effect. There's a Procedure in every

part of Nature, that is perfectly regular and geometrical, if we can but

find it out; and the further our Searches carry us, the more shall we

have occasion to admire this, and the better 'twill compensate our

Industry.

[1] _Terra Parens._ Γῆη μὴτηρ πάντων. _Terra Matter._

[2] _Nat. History, Cent._ 5. §. 411.

[3] _Complexionum atque Mistion. Element. Figm._

[4] Mr. _Boyle_, _Scept. Chym. par. 2._

[5] _Provided the _Silver_ be _pure_ and absolutely _refin'd_: For the

least admixture of _Copper_ will produce _a blue Tincture_ in the

_Menstruum_; as _that_ of some _other Bodies_, one _different_._

[6] _To say nothing of those that were not discernible._

[7] Mr. _W. Molineux_, _Philosophical Trans. No. 181_.

[8] _Confer. Prop. 1. supra._

[9] _Nat. Hist. Earth_, p. 228. & seq.

[10] _Vid. Varronem, Columellam, & reliquos Rei Rusticæ Scriptores._

[11] _Conf. Nat. Hist. Earth_, p. 47. & seq. uti & p. 128, _&c._

[12] _Conf. Nat. Hist. Earth_, Pag. 267. & seq.

[13] _The Dwarf Apple and Pear trees have succeeded better. And indeed

in Trees of the same kind, those that keep closest to the Earth always

produce the most and best Fruit. For which Reason 'tis that the

Gardiners check and restrain the Growth of better Fruit-trees, and

prevent their running up to too great a Height._

_An Account of the Measure of the thickness of Gold upon Gilt Wire;

together with Demonstration of the exceeding Minuteness of the Atoms

or constituent Particles of Gold; as it was read before the _Royal

Society_, by _E. Halley_._

What are the constituent Parts of Matter, and how there comes to be so

great a diversity in the weight of Bodies, to all appearance equally

solid and dense, such as are Gold and Glass, (whose specifick Gravities

are nearly as 7 to 1) seems a very hard Question to those that shall

rightly consider it: For from undoubted Experiment, Gravity is in all

Bodies proportionable to the Quantity of Matter in each; and there is no

such thing as a Propension of some more, others less, towards the

Earth's Center; since the Impediment of the Air being removed, all

Bodies descend, be they never so loose or compact in Texture, with equal

Velocity. It follows therefore, That there is 7 times as much Matter in

Gold, as in a piece of Glass of the same Magnitude; and consequently,

that at least six parts of seven in the Bulk of Glass, must be Pore or

Vacuity: This some Favourers of the Atomical Philosophy have endeavoured

to solve, by supposing the primary or constituent Atoms of Gold to be

much larger than those of other Bodies, and consequently the Pores

fewer; whereas in other Bodies, the great multitude of the interspersed

Vacuities does diminish their Weights.

Being desirous to examine this Notion of the Magnitude of Atoms of Gold,

I bethought my self of the extreme Ductility of that Metal, which is

seen in the beating of it into Leaf, and above all in the drawing fine

Gilt-wire, by means whereof, I believed I might most exactly obtain the

true thickness of the Coat of Gold, that appears, even with the

Microscope, so well to represent Gold it self, that not the least point

of Silver appears through it. In order to this, I inform'd my self among

the Wire-drawers, what Gold they us'd to their Silver; and they told me,

That the very best double Gilt Wire was made out of Cylindrick Ingots, 4

Inches in Circumference, and 28 Inches long, which weigh 16 Pounds Troy;

on these they bestow 4 Ounces of Gold, that is, to every 48 Ounces of

Silver one of Gold; and that two Yards of the super-fine Wire weighs a

Grain. Hence at first sight it appear'd, that the length of 98 Yards is

in weight 49 Grains, and that a single Grain of Gold covers the said 98

Yards, and that the 10000th part of a Grain is above ⅓ of an Inch

long; which yet may be actually divided into 10, and so the 100000th

part of a Grain of Gold be visible without a Microscope. But being

desirous to compute the thickness of the Skin of Gold, by means of the

specifick Gravities of the Metals, viz. Silver 10⅓, and Gold 18⅔,

I found the Diameter of such Wire the 1/386 part of an Inch, and its

Circumference the 1/123 part; but the Gold in thickness not to exceed

the 1/134500 part of an Inch; whence it may be concluded, that the Cube

of the hundredth part of an Inch would contain above 2433000000, (or the

Cube of 1345) of such Atoms. And it may likewise be marvelled at, that

Gold being stretcht to so great a degree, as is here demonstrated,

should yet shew it self of so even and united a Texture, as not to let

the white Colour of the Silver under it appear through any the least

Pores; which argues, that even in this exceeding thinness very many of

those Atoms may still lie one over the other: Which is a Consideration

may merit the Thoughts of this Honourable Society, as tending to examine

that renowned Atomical Doctrine, which has of late much obtain'd among

the Learned.

_An Account of the several Species of _Infinite Quantity_, and of the

Proportions they bear one to the other; as it was read before the

_Royal Society_, by _E. Halley_._

That all Magnitudes infinitely great, or such as exceed any assignable

Quantity, are equal among themselves, though it be vulgarly received for

a Maxim, is not yet so common as it is erroneous; and the Reason of the

mistake seems to be, That the Mind of Man, coming to contemplate the

Extensions of what exceeds the bounds of its Capacity, and of which the

very Idea does include a Negation of Limits; it comes to pass that we

acquiesce generally, and it suffices to say such a Quantity is infinite.

But if we come more nearly to examine this Notion, we shall find, that

there are really besides infinite _Length_ and infinite _Area_, no less

than three several sorts of infinite Solidity; all of which are

_Quantitates sui generis_, having no more relation or proportion the one

to the other, than a Line to a Plane, or a Plane to a Solid, or a Finite

to an Infinite. But that among themselves, each of those Species of

Infinites are in given Proportions, is what I now intend to make plain,

if possible.

But first, infinite Length, or a Line infinitely long, is to be

considered either as beginning at a Point, and so infinitely extended

one way, or else both ways from the same Point; in which case the one,

which is a beginning infinity, is the one half of the whole, which is

the Summ of the beginning and ceasing Infinity; or, as I may say, of

Infinity, _à parte ante_, and _à parte post_: Which is analogous to

Eternity in Time or Duration, in which there is always as much to follow

as is past, from any point or moment of Time: Nor doth the Addition or

Subduction of finite Length or Space of time alter the case either in

Infinity or Eternity, since both the one or the other cannot be any part

of the whole.

As to infinite _Surface_ or _Area_, any right Line, infinitely extended

both ways on an infinite Plane, does divide that infinite Plane into

equal Parts; the one to the right, and the other to the left of the said

Line: But if from any Point in such a Plane, two right Lines be

infinitely extended, so as to make an Angle, the infinite Area,

intercepted between those infinite right Lines, is to the whole infinite

Plane, as the Arch of a Circle, on the Point of Concourse of those

Lines, as a Centre, intercepted between the said Lines, is to the

Circumference of the Circle; or as the Degrees of the Angle to the 360

Degrees of a Circle. For Example, two right Lines meeting at a right

Angle do include, on an infinite Plane, a quarter part of the whole

infinite Area of such a Plane.

But if so be, two parallel infinite Lines be supposed drawn on such an

infinite Plane, the Area intercepted between them will be likewise

infinite; but at the same time will be infinitely less, than that Space

which is intercepted between two infinite Lines that are inclined,

though with never so small an Angle; for that in the one Case, the given

finite distance of the parallel Lines diminishes the Infinity in one

Degree of Dimension; whereas in a Sector, there is Infinity in both

Dimensions; and consequently, the Quantities are the one infinitely

greater than the other, and there is no proportion between them.

From the same Consideration arise the Three several Species of infinite

Space or Solidity, as has been said; for a Parallelepipede, or a

Cylinder, infinitely long, is greater than any finite Magnitude how

great soever; and all such Solids, supposed to be formed on given Bases,

are as those Bases, in proportion to one another. But if two of these

three Dimensions are wanting, as in the Space intercepted between two

parallel Planes infinitely extended, and at a finite distance; or with

infinite Length and Breadth, with a finite Thickness; All such Solids

shall be as the given finite distances one to another: But these

Quantities, though infinitely greater than the other, are yet infinitely

less than any of those, wherein all the three Dimensions are infinite.

Such are the Spaces intercepted between two inclined Planes infinitely

extended; the Space intercepted by the Surface of a Cone, or the sides

of a Pyramid likewise infinitely continued, _&c._ of all which

notwithstanding, the Proportions one to another, and to the τὸ πᾶν, or

vast Abyss of infinite Space (wherein is the _Locus_ of all things that

are or can be; or to the Solid of infinite Length, Breadth, and

Thickness, taken all manner of ways) are easily assignable. For the

Space between two Planes, is to the whole, as the Angle of those Planes

to the 360 Degrees of the Circle. As for Cones and Pyramids, they are as

the Spherical Surface, intercepted by them, is to the Surface of the

Sphere; and therefore Cones are as the versed Sines of half their

Angles, to the Diameter of the Circle: These three sorts of infinite

Quantity are analogous to a Line, Surface and Solid, and after the same

manner cannot be compared, or have any proportion the one to the other.

Besides these, there are several other Species of infinite Quantity,

arising from the Contemplation of Curves, and their Asymptotes; which,

by reason of the difficulty of the Subject, cannot be made so plain to

most Readers: But what has been already said, may be sufficient to

evince what we undertook to explain.

_An Account of Dr. _Robert Hook_'s Invention of the Marine Barometer,

with its Description and Uses; published by order of the Royal

Society, by _E. Halley_, R. S. S._

Since it was found that the _Torricellian Tube_, commonly call'd the

_Mercurial Barometer_, by the rising and falling of the _Quick-silver_

therein, doth presage the Changes of the Air, in relation to fair and

foul Weather; upon several Years Observation of it, it has been proved

and adjusted for that purpose by Dr. _Robert Hook_; and there have been

by him many attempts to improve the Instrument, and render the Minute

Divisions on the Scale thereof more sensible. He also judging that it

might be of great use at Sea, contrived several ways to make it

serviceable on Board of Ship; one of which he explain'd to the _Royal

Society_ at their Weekly Meeting in _Gresham College_, _January 2.

1667/8_. Since which time he hath further cultivated the Invention, and

some Years ago produced before the said _Society_, the Instrument I am

now to describe, which for its subtilty and usefulness, seemeth to

surpass all other performances of the like Nature.

'Till such time as the Author's present Indisposition will give him

leave to bestow freely his Thoughts on this Subject upon the Publick, it

is the Opinion of the Society, that such an Account be given of this

Contrivance, as may render it known, and recommend it to the Mariners

use, for which it was principally intended.

The _Mercurial Barometer_ requiring a perpendicular Posture, and the

_Quick-silver_ vibrating therein with great Violence upon any Agitation,

is therefore uncapable of being used at Sea (tho' it hath lately been

contrived to be made portable), so it remain'd to find out some other

Principle, wherein the Position of the Instrument was not so

indispensably necessary: For this, all those that use the Sea are

obliged to the great facility Dr. _Hook_ has always shewn, in applying

Philosophical Experiments to their proper uses.

It is about forty Years since, that the _Thermometers_ of _Robert de

Fluctibus_, depending on the Dilatation and Contraction of included Air

by Heat and Cold, have been disused, upon discovery that the Airs

pressure is unequal; that inequality mixing it self with the Effects of

the warmth of the Air in that Instrument. And instead thereof was

substituted the seal'd _Thermometer_, including Spirit of Wine (first

brought into _England_, out of _Italy_, by Sir _Robert Southwell_) as a

proper Standard of the temper of the Air, in relation to Heat and Cold;

that Ætherial Spirit being of all the known Liquors the most susceptible

of Dilatation and Contraction, especially with a moderate degree of

either Heat or Cold. Now this being allow'd as a Standard, and the other

_Thermometer_ that includes Air, being graduated with the same

Divisions, so as at the time when the Air was included, to agree with

the Spirit-_Thermometer_ in all the degrees of Heat and Cold, noting at

the same time the precise height of the _Mercury_ in the common

Barometers: It will readily be understood, that whensoever these two

_Thermometers_ shall agree, the pressure of the Air is the same it was,

when the Air was included, and the Instrument graduated: That if in the

Air-_Thermometer_ the Liquor stand higher than the Division marked

thereon, corresponding with that on the Spirit-glass, it is an

indication that there is a greater pressure of the Air at that time,

than when the Instrument was graduated. And the contrary is to be

concluded, when the Air-glass stands lower than the Spirit, _viz._ that

then the Air is so much lighter, and the _Quick silver_, in the ordinary

Barometer lower than at the said time of Graduation.

And the Spaces answering to an Inch of _Mercury_, will be more or less,

according to the quantity of Air so included, and the smallness of the

Glass Cane, in which the Liquor rises and falls, and may be augmented

almost in any proportion, under that of the Specifick Gravity of the

Liquor of the _Thermometer_ to _Mercury_. So as to have a Foot or more

for an Inch of _Mercury_, which is another great convenience.

It has been observed by some, that in long keeping this Instrument, the

Air included either finds a means to escape, or deposites some Vapours

mixt with it, or else for some other cause becomes less Elastick,

whereby, in process of time, it gives the height of the _Mercury_

somewhat greater than it ought; but this, if it should happen in some of

them, hinders not the usefulness thereof, for that it may at any time

very easily be corrected by Experiment, and the rising and falling

thereof are the things chiefly remarkable in it, the just height being

barely a Curiosity.

In these Parts of the World, long Experience has told us, that the

rising of the _Mercury_ forebodes fair Weather after foul, and an

Easterly or Northerly Wind; and that the falling thereof, on the

contrary, signifies Southerly or Westerly Winds, with Rain, or stormy

Winds, or both; which latter it is of much more consequence to provide

against at Sea than at Land; and in a Storm, the _Mercury_ beginning to

rise is a sure sign that it begins to abate, as has been experienced in

high Latitudes, both to the Northwards and Southwards of the Æquator.

The Form of this Instrument is shown in the Cut, by Tab. 4. Fig. 1.

wherein,

AB represents the Spirit-_Thermometer_, graduated from 0, or the

freezing Point, through all the possible degrees of the Heat or Cold of

the Air, at least in these Climates.

CD, is the Air-_Thermometer_, graduated after the same manner with the

like Degrees.

EF, is a Plate applied to the side of the _Thermometer_ CD, graduated

into Spaces answering to Inches and parts of an Inch of _Mercury_, in

the common Barometers.

G, a Hand standing on the Plate at the height of the _Mercury_ thereon,

as it was when the Instrument was graduated, as suppose here at 29½

Inches.

LM, a Wire on which the Plate EF, slips up and down, parallel to the

Cane of the _Thermometer_ CD.

K, any Point at which the Spirit stands at the time of Observation;

suppose at 38 on the Spirit-_Thermometer_; Slide the Plate EF till the

Hand G stand at 38 on the Air-_Thermometer_, and if the Liquor therein

stand at 38 likewise, then is the pressure of the Air the same as at the

time of Graduation, _viz._ 29,5; but if it stand higher, as at 30, at I;

then is the pressure of the Air greater; and the division on the sliding

Plate against the Liquor, shews the present height of the _Mercury_ to

be twenty nine Inches seven Tenths. And this may suffice as to the

manner of using it.

I had one of these Barometers with me in my late Southern Voyage, and it

never failed to prognostick and give early notice of all the bad Weather

we had, so that I depended thereon, and made provision accordingly; and

from my own Experience I conclude that a more useful Contrivance hath

not for this long time been offer for the benefit of Navigation.

These Instruments are made according to the Direction of Dr. _Hook_, by

Mr. _Henry Hunt_, Operator to the Royal Society, who will furnish any

Gentlemen with them, and give them Directions how to use them.

_A Discourse concerning the Proportional Heat of the Sun in all

Latitudes, with the Method of collecting the same; as it was read

before the Royal Society, in one of their late Meetings. By _E.

Halley_._

There having lately arisen some Discourse about that part of the Heat of

Weather, simply produced by the Action of the Sun; and I having

affirmed, that if that were considered, as the only Cause of the Heat of

the Weather, I saw no Reason, but that under the Pole the solstitical

Day ought to be as hot as it is under the Æquinoctial, when the Sun

comes vertical, or over the Zenith: For this Reason, that for all the 24

Hours of that Day under the Pole, the Sun's Beams are inclined to the

Horizon, with an Angle of 23½ Degrees; and under the Æquinoctial,

though he come vertical, yet he shines no more than 12 Hours, and is

again 12 Hours absent; and that for 3 Hours 8 Minutes of that 12 Hours,

he is not so much elevated as under the Pole; so that he is not 9 of the

whole 24, higher than 'tis there, and is 15 Hours lower. Now the simple

Action of the Sun is, as all other Impulses or Stroaks, more or less

forceable, according to the _Sinus_ of the Angle of Incidence, or to the

Perpendicular let fall on the Plain, whence the vertical Ray (being that

of the greatest Heat,) being put _Radius_, the force of the Sun on the

Horizontal Surface of the Earth will be to that, as the _Sinus_ of the

Sun's Altitude at any other time. This being allow'd for true, it will

then follow, that the time of the continuance of the Sun's shining being

taken for a _Basis_, and the _Sines_ of the Sun's Altitudes erected

thereon as Perpendiculars, and a Curve drawn through the Extremities of

those Perpendiculars, the _Area_ comprehended shall be proportionate to

the Collection of the Heat of all the Beams of the Sun in that space of

time. Hence it will follow, that under the Pole the Collection of all

the Heat of a tropical Day, is proportionate to a Rectangle of the

_Sine_ of 23½ _gr._ into 24 Hours, or the Circumference of a Circle;

that is, the _Sine_ of 23½ _gr._ being nearly 4 Tenths of _Radius_;

as 3/10 into 12 Hours. Or the Polar Heat is equal to that of the Sun

containing 12 Hours above the Horizon, at 53 _gr._ height, than which

the Sun is not 5 Hours more elevated under the Æquinoctial.

But that this Matter may the better be understood, I have exemplified it

by a Scheme, (_Tab. 4. Fig. 2_) wherein the _Area ZGHH_, is equal to the

_Area_ of all the _Sines_ of the Sun's Altitude under the Æquinoctial,

erected on the respective Hours from Sun-rise to the Zenith; and

the _Area ♋HH♋_ is in the same proportion to the Heat of the

same 6 Hours under the Pole on the Topical Day; and _⨀HHQ_, is

proportional to the collected Heat of 12 Hours, or half a Day under the

Pole, which space _⨀HHQ_, is visibly greater than the other _Area

HZGH_, by as much as the _Area HGQ_ is greater than the _Area ZG⨀_;

which, that it is so, is visible to sight, by a great excess; and so

much in proportion does the Heat of the 24 Hours Sun-shine under the

Pole, exceed that of the 12 Hours under the Æquinoctial: Whence,

_Cæteris paribus_, it is reasonable to conclude, that were the Sun

perpetually under the Tropick, the Pole would be at least as warm, as it

is now under the Line it self.

But whereas the Nature of Heat is to remain in the Subject, after the

Cause that heated is removed, and particularly in the Air; under the

Æquinoctial, the 12 Hours absence of the Sun does very little still the

Motion impressed by the part Action of his Rays, wherein Heat consists,

before he arise again: But under the Pole the long absence of the Sun

for 6 Months, wherein the extremity of Cold does obtain, has so chill'd

the Air, that it is as it were frozen, and cannot, before the Sun has

got far towards it, be any way sensible of his presence, his Beams being

obstructed by thick Clouds, and perpetual Fogs and Mists, and by that

Atmosphere of Cold, as the late Honourable Mr. _Boyle_ was pleased to

term it, proceeding from the everlasting Ice, which in immense

Quantities does chill the Neighbouring Air, and which the too soon

retreat of the Sun leaves unthawed, to encrease again, during the long

Winter that follows this short interval of Summer. But the differing

Degrees of Heat and Cold, in differing Places, depend in great measure

upon the Accidents of the Neighbourhood of high Mountains, whose height

exceedingly chills the Air brought by the Winds over them; and of the

Nature of the Soil, which variously retains the Heat, particularly the

Sandy, which in _Africa_, _Arabia_, and generally where such Sandy

Desarts are found, do make the Heat of the Summer incredible to those

that have not felt it.

In the prosecution of this first Thought, I have solved the Problem

generally, _viz._ to give the proportional Degree of Heat, or the Sum of

all the _Sines_ of the Sun's Altitude, while he is above the Horizon in

any oblique Sphere, by reducing it to the finding of the Curve Surface

of a Cylindrick Hoof, or of a given part thereof.

Now this Problem is not of that difficulty as appears at first sight,

for in _Tab. 4. Fig. 3._ let the Cylinder ABCD be cut obliquely with the

Ellipse BKDI, and by the Center thereof H, describe the Circle IKLM; I

say, the Curve Surface IKLB is equal to the Rectangle of IK and BL, or

of HK and 2 BL or BC: And if there be supposed another Circle, as NQPO,

cutting the said Ellipse in the Points P, Q; draw PS, QR, parallel to

the Cylinders Axe, till they meet with the aforesaid Circle IKLM in the

Points R, S, and draw the Lines RTS, QVP bisected in T and V. I say

again, that the Curve Surface RMSQDP is equal to the Rectangle of BL or

MD and RS, or of 2 BL or AD and ST or VP; and the Curve Surface QNPD is

equal to RS × MD----the Arch RMS × SP, or the Arch MS × 2 SP: Or it is

equal to the Surface RMSQDP, substracting the Surface RMSQNP. So

likewise the Curve Surface QBPO is equal to the Sum of the Surface

RMSQDP, or RS × MD, and of the Surface RLSQOP, or the Arch LS × 2 SP.

This is the most easily demonstrated from the Consideration, That the

Cylindrick Surface IKLB is to the inscrib'd Spherical Surface IKLE,

either in the whole, or in its Analogous Parts, as the tangent BL is to

the Arch EL, and from the Demonstrations of _Archimedes de Sphæra &

Cylindro, Lib. I. Prop._ XXX, and XXXVII, XXXIIX. which I shall not

repeat here, but leave the Reader the pleasure of examining it himself;

nor will it be amiss to consult Dr. _Barrow_'s Learned Lectures on that

Book, Publish'd at _London_, _Anno 1684_, _viz._ _Probl._ IX. and the

Corollaries thereof.

Now to reduce our Case of the Sum of all the _Sines_ of the Sun's

Altitude in a given Declination and Latitude to the aforesaid Problem,

let us consider (_Tab. 4. Fig. 4._) which is the _Analemma_ projected on

the Plain of the _Meridian_, Z the Zenith, P the Pole, HH the Horizon,

ææ the Æquinoctial, ♋♋, ♑♑ the two Tropicks, ♋1 the _Sine_ of the

Meridian Altitude in ♋; and equal thereto, but perpendicular to the

Tropick, erect ♋I, and draw the Line TI intersecting the Horizon in T,

and the Hour Circle of 6, in the Point 4, and 64 shall be equal to 6R,

or to the Sine of the Altitude at 6: And the like for any other Point in

the Tropick, erecting a Perpendicular thereat, terminated by the Line T

I: Through the Point 4 draw the Line 4, 5, 7 parallel to the Tropick,

and representing a Circle equal thereto; then shall the Tropick ♋♋ in

_Fig. 4._ answer to the Circle NOPQ, in _Fig. 3._ the Circle 457 shall

answer the Circle IKLM, T4I shall answer to the Elliptick Segment QIBKP,

6R or 64 shall answer to SP, and 5I to BL, and the Arch ♋T, to the Arch

LS, being the semidiurnal Arch in that Latitude and Declination; the

_Sine_ whereof, tho' not expressible in _Fig. 4._ must be conceived as

Analogous to the Line TS or UP in _Fig. 3._

The Relation between these two Figures being well understood, it will

follow from what precedes, That, _the sum of the _Sines_ of the Meridian

Altitudes of the Sun in the two Tropicks, (and the like for any two

opposite Parallels) being multiplied by the _Sine_ of the semidiurnal

Arch, will give an _Area_ Analogous to the Curve Surface RIMSQDP; and

thereto adding in Summer, or substracting in Winter, the Product of the

length of the semidiurnal Arch, (taken according to _Van Ceulen_'s

Numbers) into the difference of the above-said _Sines_ of the Meridian

Altitude: The sum in one case, and difference in another, shall be as

the Aggregate of all the _Sines_ of the Sun's Altitude, during his

appearance above the Horizon; and consequently of all his Heat and

Action on the Plain of the Horizon in the proposed Day_. And this may

also be extended to the parts of the same Day; for if the aforesaid Sum

of the _Sines_ of the Meridian Altitudes, be multiplied by half the Sum

of the _Sines_ of the Sun's Horary distance from Noon, when the Times

are before and after Noon; or by half their difference, when both are on

the same side of the Meridian; and thereto in Summer, or therefrom in

Winter, be added or substracted the Product of half the Arch answerable

to the proposed interval of Time, into the difference of the _Sines_ of

Meridian Altitudes, the Sum in one case and Difference in the other,

shall be proportional to all the Action of the Sun during that space of

time.

I fore-see it will be Objected, that I take the _Radius_ of my Circle on

which I erect my Perpendiculars always the same, whereas the Parallels

of Declination are unequal; but to this I answer, That our said Circular

Bases ought not to be Analogous to the Parallels, but to the Times of

Revolution, which are equal in all of them.

It may perhaps be useful to give an Example of the Computation of this

Rule, which may seem difficult to some. Let the Solstitical Heat in

♋ and ♑ be required at _London_, _Lat._ 51° 32'.

380-2'8 _Co-Lat._

23 -30 _Decl. ⨀_

------

61 -58 _Sinus_ = ,882674

14 -58 _Sinus_ = ,258257

------

_Summa_ 1,140931

_Diff._ ,624417

_Diff. Ascen._ 3300-1'1.

_Arch. Semid. æstiv._ 123-11.

_Ar. Sem. hyb. 56-49. S._ ,638923

_Arch. æstiv. mensura_ 2,149955

_Arc. hyb. mensura_ ,991683

Then 1,140931 in ,836923, + 624417 in 2,149955 = 2,29734.

And 1,140931 in 836929 - ,624417 in ,991638 = 33895.

So that 2,29734 will be as the Tropical Summers Day Heat, and 0,33895 as

the Action of the Sun in the Day of the Winter Solstice.

After this manner I computed the following Table for every tenth Degree

of Latitude, to the Æquinoctial and Tropical Sun, by which an Estimate

may be made of the intermediate Degrees.

+------+--------------+--------------+--------------+

| | Sun in | Sun in | Sun in |

| Lat. | ♈ ♎ | ♋ | ♑ |

+------+--------------+--------------+--------------+

| 0 | 20000 | 18341 | 18341 |

| 10 | 19696 | 20290 | 15834 |

| 20 | 18794 | 21737 | 13166 |

| 30 | 17321 | 22651 | 10124 |

| 40 | 15321 | 23048 | 6944 |

+------+--------------+--------------+--------------+

| 50 | 12855 | 22991 | 3798 |

| 60 | 10000 | 22773 | 1075 |

| 70 | 6840 | 23543 | 000 |

| 80 | 3473 | 24673 | 000 |

| 90 | 0000 | 25055 | 000 |

+------+--------------+--------------+--------------+

Those that desire more of the Nature of this Problem, as to the Geometry

thereof, would do well to compare the XIII. _Prop. Cap. V._ of the

Learned Treatise, _De Calculo Centri Gravitatis_, by the Reverend Dr.

_Wallis_, Published _Anno 1670_.

From this Rule there follow several Corollaries worth Note: As I. That

the Æquinoctial Heat, when the Sun comes Vertical, is as twice the

Square of _Radius_, which may be proposed as a Standard to compare with,

in all other Cases. II. That under the Æquinoctial, the Heat is as the

_Sine_ of the Sun's Declination. III. That in the Frigid Zones when the

Sun sets not, the Heat is as the Circumference of a Circle into the

_Sine_ of the Altitude at 6. And consequently, that in the same Latitude

these Aggregates of Warmth, are as the _Sines_ of the Sun's

Declinations; and in the same Declination of _Sol_, they are as the

_Sines_ of the Latitude, and generally they are as the _Sines_ of the

Latitude into the _Sines_ of Declination. IV. That the Æquinoctial Days

Heat is every where as the Co-sine of the Latitude. V. In all places

where the Sun sets, the difference between the Summer and Winter Heats,

when the Declinations are contrary, is equal to a Circle into the _Sine_

of the Altitude at six in the Summer Parallel, and consequently those

differences are as the _Sines_ of Latitude into, or multiplied by the

_Sines_ of Declination. VI. From the Table I have added, it appears,

that the Tropical Sun under the Æquinoctial, has, of all others, the

least Force. Under the Pole it is greater than any other Days Heat

whatsoever, being to that of the Æquinoctial as 5 to 4.

From the Table and these Corollaries may a general _Idea_ be conceived

of the Sum of all the Actions of the Sun in the whole Year, and that

part of the Heat that arises simply from the Presence of the Sun be

brought to a Geometrical Certainty: And if the like could be performed

for Cold; which is something else than the bare Absence of the Sun, as

appears by many Instances, we might hope to bring what relates to this

part of _Meteorology_ to a perfect Theory.

_Concerning the Distance of the Fix'd Stars. By the Honourable _Francis

Roberts_, Esq; S. R. S._

The Ancient Astronomers, who had no other way of computing the Distances

of the Heavenly Bodies, but by their Parallax to the Semi-diameter of

the Earth; and being never able to discover any in the fix'd Stars, did

from thence rightly enough infer, that their Distance was very great,

and much exceeding that of the Planets, but could go no farther

otherwise than by uncertain guess.

Since the _Pythagorean_ System of the World has been reviv'd by

_Copernicus_, (and now by all Mathematicians accepted for the true one)

there seem'd Ground to imagine that the Diameter of the Earth's Annual

Course (which, according to our best Astronomers, is at least 40000

times bigger than the Semi-diameter of the Earth) might give a sensible

Parallax to the fix'd Stars, though the other could not, and thereby

determine their Distance more precisely.

But though we have a Foundation to build on so vastly exceeding that of

the Ancients, there are some Considerations may make us suspect that

even this is not large enough for our purpose.

Monsieur _Hugens_ (who is very exact in his Astronomical Observations)

tells us, he could never discover any visible Magnitude in the fix'd

Stars, though he used Glasses which magnified the apparent Diameter

above 100 times.

Now, since in all likelyhood the fix'd Stars are Suns, (perhaps of a

different Magnitude) we may as a reasonable _Medium_ presume they are

generally about the bigness of the Sun.

Let us then (for Example) suppose the Dog-Star to be so. The Distance

from us to the Sun being about 100 times the Sun's Diameter (as is

demonstrable from the Sun's Diameter being 32 Minutes) it is evident,

that the Angle under which the Dog-Star is seen in Mr. _Hugens_'s

Telescope, must be near the same with the Angle of its Parallax to the

Sun's Distance, or Semi-diameter of the Earth's Annual Course; so that

the Parallax to the whole Diameter, can be but double such a quantity,

as even to Mr. _Hugens_'s nice Observation is altogether insensible.

The Distance therefore of the fix'd Stars seems hardly within the reach

of any of our Methods to determine; but from what has been laid down, we

may draw some Conclusions that will much illustrate the prodigious

vastness of it.

1. That the Diameter of the Earth's Annual Orb (which contains at least

160 Millions of Miles) is but as a Point in comparison of it; at least

it must be above 6000 times the Distance of the Sun. For if a Star

should appear thro' the aforesaid Telescope half a Minute broad (which

is a pretty sensible Magnitude) the true apparent Diameter would not

exceed 18 3d Minutes, which is less than the 6000th part of the apparent

Diameter of the Sun, and consequently the Sun's Distance not the 6000th

part of the Distance of the Star.

2. That could we advance towards the Stars 99 Parts of the whole

Distance, and have only 1/100 Part remaining, the Stars would appear

little bigger to us than they do here; for they would shew no otherwise

than they do through a Telescope, which magnifies an Hundred-fold.

3. That at least Nine Parts in Ten of the Space between us and the fix'd

Stars, can receive no greater Light from the Sun, or any of the Stars,

than what we have from the Stars in a clear Night.

4. That Light takes up more time in travelling from the Stars to us,

than we in making a _West-India_ Voyage (which is ordinarily perform'd

in six Weeks.) That a Sound would not arrive to us from thence in 50000

Years, nor a Cannon-bullet in a much longer time. This is easily

computed, by allowing (according to Mr. _Newton_) Ten Minutes for the

Journey of Light from the Sun hither, and that a Sound moves about 1300

Foot in a Second.

_The Famous Mr. _Isaac Newton_'s Theory of the _Moon_._

This _Theory_ which hath been long expected by all the true Lovers of

_Astronomy_, was communicated from Mr. _Newton_ to Dr. _Gregory_,

_Astronomy_ Professor at _Oxford_, and by him published in his _Astron.

Elem. Philos._ and _Geomet._ p. 336. From whence, as it was lately

translated into _English_, I thought fit to insert it here.

By this Theory, what by all Astronomers was thought most difficult and

almost impossible to be done, the Excellent Mr. _Newton_ hath now

effected; _viz._ to determine the Moon's Place even in her Quadratures,

and all other Parts of her Orbit, besides the Syzygys, so accurately by

Calculation, that the Difference between that and her true Place in the

Heavens, shall scarce be above two minutes in her Syzygys, or above

three in her Quadratures, and is usually so small, that it may well

enough be reckon'd only as a Defect in the Observation. And this Mr.

_Newton_ experienced, by comparing it with very many Places of the Moon,

observ'd by Mr. _Flamsteed_, and communicated to him.

The Royal Observatory at _Greenwich_, is to the West of the Meridian of

_Paris_, 2 degrees, 19 minutes. Of _Uraniburgh_, 12 degrees, 51 minutes,

30 seconds. And of _Gedanum_, 18 degrees, 48 minutes.

The mean Motions of the Sun and Moon, accounted from the Vernal Æquinox

at the Meridian of _Greenwich_, I make to be as followeth.

The last Day of _December 1680_, at Noon (_Old Stile_) the mean Motion

of the Sun was 9 Signs, 20 degrees, 34 minutes, 46 seconds. Of the Sun's

Apogæum, was 3 S. 7 deg. 23 min. 30 seconds.

That the mean Motion of the Moon at that time, was 6 S. 1 degree, 45

minutes, 45 seconds. And of her Apogee, 8 S. 4 degrees, 28 minutes, 5

seconds. Of the ascending Node of the Moon's Orbit, 5 S. 24 deg. 14 min.

35 seconds, _&c._

And on the last Day of _December, 1700_, at Noon, the mean Motion of the

Sun was 9 S. 20 degrees, 43 minutes, 50 seconds. Of the Sun's Apogee,

3 S. 7 degrees, 44 minutes, 30 seconds. The mean Motion of the Moon was

10 S. 15 degrees, 19 minutes, 50 seconds. Of the Moon's Apogee, 11 S. 8

degrees, 18 minutes, 20 seconds. And of her ascending Node, 4 S. 27

degrees, 24 minutes, 20 seconds. For in 20 _Julian_ Years, or 7305 Days,

the Sun's Motion is 20 Revol. 0 S. 0 degrees, 9 minutes, 4 seconds. And

the Motion of the Sun's Apogee, 21 minutes, 0 seconds.

The Motion of the Moon in the same time, is 267 Revol. 4 S. 13 degrees,

34 minutes, 5 seconds. And the Motion of the Lunar Apogee, is 2 Revol.

3 S. 3 degrees, 50 minutes, 15 seconds. And the Motion of her Node, 1

Revol. 0 S, 26 degrees, 50 minutes, 15 seconds.

All which Motions are accounted from the Vernal Æquinox: Wherefore if

from them there be subtracted the Recession or Motion of the Æquinoctial

Point, in _Antecedentia_, during that space, which is 16 minutes, 40

seconds, there will remain the Motions in reference to the fix'd Stars

in 20 _Julian_ Years; _viz._ the Sun's 19 Revol. 11 S. 29 degrees, 52

minutes, 24 seconds. Of his Apogee, 4 minutes, 20 seconds. And the

Moon's 267 Revol. 4 S. 13 degrees, 17 minutes, 25 seconds. Of her

Apogee, 2 Revol. 3 S. 3 degrees, 33 minutes, 35 seconds. And of the Node

of the Moon, 1 Revol. 0 S. 27 degrees, 6 minutes, 55 seconds.

According to this Computation, the _Tropical Year_ is 365 Days, 5 Hours,

48 Minutes, 57 Seconds. And the _Sydereal Year_ is 365 Days, 6 Hours, 9

Minutes, 14 Seconds.

These mean Motions of the Luminaries are affected with various

Inequalities: Of which,

1. There are the Annual Equations of the aforesaid mean Motions of the

Sun and Moon, and of the Apogee and Node of the Moon.

The Annual Equation of the mean Motion of the Sun, depends on the

Eccentricity of the Earth's Orbit round the Sun, which is 16-11/12 of

such Parts, as that the Earth's mean Distance from the Sun shall be

1000: Whence 'tis call'd the _Equation of the Centre_; and is, when

greatest, 1 degree, 56 minutes, 20 seconds.

The greatest Annual Equation of the Moon's mean Motion, is 11 degrees,

49 seconds; of her Apogee, 20 minutes, and of her Node, 9 minutes, 30

seconds.

And these four Annual Equations are always mutually proportional one to

another: Wherefore when any of them is at the greatest, the other three

will also be greatest; and when any one lessens, the other three will

also be diminished in the same Ratio.

The Annual Equation of the Sun's Centre being given, the three other

corresponding Annual Equations will be also given; and therefore a Table

of that will serve for all. For if the Annual Equation of the Sun's

Centre be taken from thence, for any Time, and be call'd P, and let

1/10P = Q, Q + 1/60Q = R, 1/6P = D, D + 1/30D = E, and D - 1/50D = 2F;

then shall the Annual Equation of the Moon's mean Motion for that time

be R, that of the Apogee of the Moon will be E, and that of the Node F.

Only observe here, That if the Equation of the Sun's Centre be required

to be added; then the Equation of the Moon's mean Motion must be

subtracted, that of her Apogee must be added, and that of the Node

subducted, And on the contrary, if the Equation of the Sun's Centre were

to be subducted, the Moon's Equation must be added, the Equation of her

Apogee subducted, and that of her Node added.

There is also an _Equation of the Moon's mean Motion_, depending on the

situation of her Apogee, in respect of the Sun; which is greatest when

the Moon's Apogee is in an Octant with the Sun, and is nothing at all

when it is in the Quadratures or Syzygys. This Equation, when greatest,

and the Sun in _Perigæo_, is 3 Minutes, 56 Seconds. But if the Sun be in

_Apogæo_, it will never be above 3 Minutes, 34 Seconds. At other

Distances of the Sun from the Earth, this Equation, when greatest, is

reciprocally as the Cube of such Distance. But when the Moon's Apogee is

any where but in the _Octants_, this Equation grows less, and is mostly

at the same distance between the Earth and Sun, as the Sine of the

double Distance of the Moon's Apogee, from the next Quadrature or

Syzygy, to the Radius.

This is to be added to the Moon's Motion, while her Apogee passes from a

Quadrature with the Sun to a Syzygy; but this is to be subtracted from

it, while the Apogee moves from the Syzygy to the Quadrature.

There is moreover another _Equation of the Moon's Motion_, which depends

on the Aspect of the Nodes of the Moon's Orbit with the Sun: And this is

greatest, when her Nodes are in _Octants_ to the Sun, and vanishes

quite, when they come to their Quadratures or Syzygys. This Equation is

proportional to the Sine of the double Distance of the Node from the

next Syzygy, or Quadrature; and at greatest, is but 47 seconds. This

must be added to the Moon's mean Motion, while the Nodes are passing

from their Syzygys with the Sun, to their Quadratures with him; but

subtracted while they pass from the Quadratures to the Syzygys.

From the Sun's true Place, take the equated mean Motion of the Lunar

Apogee, as was above shew'd, the Remainder will be the Annual Argument

of the said Apogee. From whence the _Eccentricity of the Moon_, and the

_second Equation_ of her Apogee may be computed after the manner of the

following (_which takes place also in the Computation of any other

intermediate Equations_).

Tab. 3. Fig. 6. Let T represent the Earth, TS, a Right Line joining the

Earth and Sun, TACB, a Right Line drawn from the Earth to the middle or

mean Place of the Moon's Apogee, equated, as above: Let the Angle STA be

the Annual Argument of the aforesaid Apogee, TA the least Eccentricity

of the Moon's Orbit, TB the greatest. Bissect AB in G; and on the Centre

C, with the Distance AC describe a Circle AFB, and make the Angle BCF =

to the double of the Annual Argument. Draw the Right Line TF, that shall

be the Eccentricity of the Moon's Orbit; and the Angle BTF, is the

second Equation of the Moon's Apogee required.