_An Estimate of the Quantity of the Vapours raised out of the Sea
derived from Experiment: Together with an Account of the Circulation
of the watry Vapours of the Sea, and of the Cause of Springs,
presented to the Royal Society. By Mr. _E. Halley, F. R. S.__
That the Quantity of Aqueous Vapours contain'd in the Medium of the Air,
is very considerable, seems most evident from the great Rains and Snows
which are sometimes observ'd to fall, to that degree, that the Water
thus discharg'd out of the Interstices of the Particles of Air, is in
weight a very sensible part of the incumbent Atmosphere: But in what
proportion these Vapours rise, which are the Sources not only of Rains,
but also of Springs or Fountains (as I design to prove) has not, that I
know of, been any where well examin'd, tho' it seem to be one of the
most necessary Ingredients of a Real and Philosophical Meteorology, and,
as such; to deserve the Consideration of this Honourable Society. I
thought it might not be unacceptable to attempt by Experiment to
determine the Quantity of the Evaporations of Water, as far as they
arise from Heat, which upon Trial succeeded as follows.
We took a Pan of Water, about 4 inches deep, and 7 Inches 9/10 Diameter,
in which we placed a Thermometer, and by means of a Pan of Coals, we
brought the Water to the same degree of Heat, which is observed to be
that of the Air in our hottest Summer; the Thermometer nicely shewing
it: This done, we affixed the Pan of Water, with the Thermometer in it,
to one end of the Beam of a Pair of Scales, and exactly counterpois'd it
with weights in the other Scale; and by the application or removal of
the Pan of Coals, we found it very easie to maintain the Water in the
same degree of Heat precisely. Doing thus we found the weight of the
Water sensibly to decrease; and at the end of two hours we observed that
there wanted half an Ounce _Troy_, all but 7 grains, or 233 grains of
Water, which in that time had gone off in Vapour; tho' one could hardly
perceive it smoke, and the Water were not sensibly warm. This Quantity
in so short a time seem'd very considerable, being little less than 6
ounces in 24 hours, from so small a Surface as a Circle of 8 inches
Diameter. To reduce this Experiment to an exact Calculus, and determine
the thickness of the Skin of Water that had so evaporated, I assume the
Experiment alledg'd by Dr. _Edward Bernard_ to have been made in the
_Oxford_ Society, _viz._ That the Cube-foot _English_ of Water weighs
exactly 76 Pounds _Troy_; this divided by 1728, the number of Inches in
a Foot, will give 253⅓ grains, or ½ ounce 13⅓ grains for the
weight of a Cube-inch of Water; wherefore the weight of 233 grains is
233/253 or 35 Parts of 38 of a Cube-inch of Water. Now the Area of the
Circle whose Diameter is 7-9/10 Inches, is 49 square Inches: by which
dividing the Quantity of Water evaporated, _viz._ 35/38 of an Inch, the
Quote 35/1862 or 1/53 shews that the thickness of the Water evaporated
was the 53d part of an Inch; but we will suppose it only the 60th part,
for the Facility of Calculation. If therefore Water as warm as the Air
in Summer, exhales the thickness of a 60th part of an Inch in two hours
from its whole Surface, in 12 hours it will exhale the ⅒ of an Inch;
which Quantity will be found abundantly sufficient to serve for all the
Rains, Springs, and Dews; and account for the _Caspian_ Sea, being
always at a stand, neither wasting nor overflowing; as likewise for the
Current said to set always in at the Streights of _Gibralter_, tho'
those Mediterranean Seas receive so many and so considerable Rivers.
To estimate the Quantity of Water arising in Vapours out of the Sea, I
think I ought to consider it only for the time the Sun is up, for that
the Dews return in the Night, as much if not more Vapours than are then
emitted; and in Summer the Days being no longer than 12 hours, this
Excess is ballanc'd by the weaker Action of the Sun, especially when
rising before the Water be warmed: So that if I allow ⅒ of an Inch of
the Surface of the Sea, to be raised _per diem_ in Vapours, it may not
be an improbable Conjecture.
Upon this Supposition, every 10 square Inches of the Surface of the
Water, yields in Vapour _per diem_ a Cube-inch of Water; and each square
Foot half a Wine-pint; every Space of 4 Foot square, a Gallon; a Mile
square, 6914 Tons; a square Degree suppose of 69 _English_ Miles, will
evaporate 33 Millions of Tons: And if the Mediterranean be estimated at
forty degrees long and four broad, allowances being made for the Places
where it is broader, by those where it is narrower (and I am sure I
guess at the least) there will be 160 Square degrees of Sea; and
consequently, the whole Mediterranean must lose in Vapour, in a Summer's
day, at least 5280 Millions of Tons. And this Quantity of Vapour, tho'
very great, is as little as can be concluded from the Experiment
produced: And yet there remains another Cause, which cannot be reduced
to Rule, I mean the Winds, whereby the Surface of the Water is licked up
some times faster than it exhales by the heat of the Sun; as is well
known to those that have consider'd those drying Winds which blow
sometimes.
To estimate the Quantity of Water, the Mediterranean Sea receives from
the Rivers that fall into it, is a very hard Task, unless one had the
Opportunity to measure their Chanels and Velocity; and therefore we can
only do it by allowing more than enough; that is, by assuming these
Rivers greater than in all probability they be, and then comparing the
Quantity of Water voided by the _Thames_, with that of those Rivers,
whose Waters we desire to compute.
The Mediterranean receives these considerable Rivers; the _Iberus_, the
_Rhone_, the _Tiber_, the _Po_, the _Danube_, the _Neister_, the
_Borystenes_, the _Tanais_, and the _Nile_; all the rest being of no
great Note, and their Quantity of Water inconsiderable: These nine
Rivers, we will suppose each of them to bring down ten times as much
Water as the River _Thames_; not that any of them is great in reality,
but to comprehend with them all the small Rivulets that fall into the
Sea, which otherwise I know not how to allow for.
To calculate the Water of the _Thames_, I assume that at _Kingston_
Bridge where the Flood never reaches, and the Water always runs down,
the breadth of the Chanel is 100 Yards, and its Depth 3, it being
reduced to an Equality (in both which Suppositions I am sure I take with
the most) hence the Profil of the Water in this Place is 300 square
Yards: This multiplied by 48 Miles (which I allow the Water to run in 24
hours, at 2 Miles an hour) or 84480 Yards, gives 25344000 Cubick-yards
of Water to be evacuated every Day; that is, 20300000 Tons _per diem_;
and I doubt not, but in the excess of my Measures of the Chanel of the
River, I have made more than sufficient allowance for the Waters of the
_Brent_, the _Wandel_, the _Lea_, and _Darwent_, which are all worth
notice, that fall into the _Thames_ below _Kingston_.
Now if each of the aforesaid 9 Rivers yield 10 times as much Water as
the _Thames_ doth, 'twill follow that each of them yields but 203
Millions of Ton _per diem_, and the whole 9, but 1827 Millions of Tons
in a day; which is but little more than ⅓ of what is proved to be
raised in vapour out of the Mediterranean in 12 hours time. Now what
becomes of this Vapour when rais'd, and how it comes to pass that the
Current always sets in at the Mouth, of the Streights of _Gibralter_,
shall immediately be shew'd: But first it is necessary to advertise the
Reader, that in making the Experiment herein mention'd, the Water used
had been salted to the same degree as is the common Sea-water, by the
Solution of about a 40th part of Salt.
Having thus shew'd by Experiment the Quantity of Water raised in Vapour
from the Surface of the Sea in a Days time, which was so far approv'd of
by some Honourable Members of this Society, that I receiv'd their
Commands to prosecute these Enquiries; and particularly, in relation to
the Method used by Nature, to return the said Vapours again into the
Sea; which is so justly perform'd, that in many hundred of Years we are
sufficiently assured that the Sea has not sensibly decreased by the loss
in Vapour; nor yet abounded by the immense Quantity of fresh it receives
continually from the Rivers. To demonstrate this Equilibre of Receipt
and Expence in the whole Sea, is a Task too hard for me to undertake,
yet in obedience to those whom I have the Honour to serve, I shall here
offer, what to me has hitherto seem'd the most satisfactory Account of
this grand _Phænomenon_: I have in another place attempted to explain
the manner of the rising of Vapour by Warmth, by shewing, that if an
Atom of Water were expanded into a Shell or Bubble, so as to be ten
times as big in Diameter as when it was Water; such an Atom would become
specifically lighter than Air, and rise so long as that _Flatus_ or warm
Spirit that first separated it from the Mass of Water, shall continue to
distend it to the same Degree; and that Warmth declining, and the Air
growing cooler and also specifically lighter, the Vapours consequently
shall stop at a certain Region of the Air, or else descend, which may
happen upon several accounts, as I shall by and by endeavour to make
out; yet I undertake not that this is the only principal of the rise of
Vapours, and that there may not be a certain sort of Matter, whose
_Conatus_ may be contrary to that of Gravity; as is evident in
Vegetation, where in the Tendency of the Sprouts is directly upwards, or
against the Perpendicular. But what ever is the true Cause, it is in
Fact certain, that warmth does separate the Particles of Water, and emit
them with a greater and greater Velocity, as the heat is more and more
intense; as is evident in the Steam of a boiling Cauldron, wherein
likewise the Velocity of the ascent of the Vapours does visibly decrease
till they disappear, being dispersed into and assimulated with the
Ambient Air. Vapours being thus raised by warmth, let us for a first
Supposition put, that the whole Surface of the Globe were all Water very
deep, or rather that the whole Body of the Earth were Water, and that
the Sun had its diurnal course about it: I take it, that it would
follow, that the Air of it self would imbibe a certain Quantity of
aqueous Vapours, and retain them like Salts dissolved in Water; that the
Sun warming the Air, and raising a more plentiful Vapour from the Water
in the day-time, the Air would sustain a greater proportion of Vapour,
as warm Water will hold more dissolved Salts, which upon the absence of
the Sun in the Nights would be all again discharged in Dews, analogous
to the Precipitation of Salts on the cooling of the Liquors; nor is it
to be believed that in such Case there would be any diversity of
Weather, other than periodically, every Year alike; the mixture of all
terrestrious, saline, heterogenious Vapours being taken away, which as
they are variously compounded and brought by the Winds, seem to be the
Causes of those various Seasons which we now find. In this case the
Aiery Regions every where, at the same height, would be equally
replenished with the Proportion of Water it could contain, regard being
only to be had to the different degree of warmth, from the nearness or
distance of the Sun; and an eternal East-wind would blow all round the
Globe, inclining only to the same side of the _East_, as the Latitude
doth from the Equator; as is observed in the Ocean between the Tropicks.
Next let us suppose this Ocean interspersed with wide and spacious
Tracts of Land, with high Ridges of Mountains, such as the _Pyrenean_,
the _Alps_, the _Apennine_, the _Carpathian_ in _Europe_, _Taurus_,
_Caucasus_, _Imaus_, and several others in _Asia_; _Atlas_ and the
_Montes Lunæ_, with other unknown Ridges in _Africa_, whence came the
_Nile_, the _Nigre_, and the _Zaire_: And in _America_, the _Andes_ and
the _Apalatean_ Mountains; each of which far surpass the usual height to
which the Aqueous Vapours of themselves ascend, and on the tops of which
the Air is so cold and rarified, as to retain but a small part of those
Vapours, that shall be brought thither by Winds. Those Vapours therefore
that are raised copiously in the Sea, and by the Wind, are carried over
the low Land to those Ridges of Mountains, are there compelled by the
Stream of the Air to mount up with it to the tops of the Mountains,
where the Water presently precipitates, gleeting down by the Crannies of
the Stone; and part of the Vapour entering into the Caverns of the
Hills, the Water thereof gathers as in an Alembick into the Basons of
Stone it finds; which being once fill'd, all the overplus of Water that
comes thither runs over by the lowest place, and breaking out by the
sides of the Hills, forms single _Springs_. Many of these running down
by the Valleys or Guts between the Ridges of the Hills, and coming to
unite, form little Rivulets, or Brooks: Many of these again, meeting in
one common Valley and gaining the plain Ground, being grown less rapid,
become a River; and many of these being united in one common Channel,
make such Streams as the _Rhine_, the _Rhone_, the _Danube_; which
latter, one would hardly think the Collection of Water condensed out of
Vapour, unless we consider how vast a Tract of Ground that River drains,
and that it is the Sum of all those Springs which break out on the South
side of the _Carpathian_ Mountains, and on the North side of the immense
Ridge of the _Alps_, which is one continued Chain of Mountains from
_Switzerland_, to the _Black-Sea_. And it may almost pass for a Rule,
that the magnitude of a River, or the quantity of Water it evacuates, is
proportionable to the length and height of the Ridges from whence its
Fountains arise. Now this Theory of _Springs_ is not a bare
_Hypothesis_, but founded on Experience, which it was my luck to gain in
my abode at St. _Helena_, where in the Night-time, on the tops of the
Hills, about 800 Yards above the Sea, there was so strange a
condensation, or rather precipitation of the Vapours, that it was a
great Impediment to my Cœlestial Observations; for in the clear Sky,
the Dew would fall so fast, as to cover, each half quarter of an Hour,
my Glasses with little drops; so that I was necessitated to wipe them so
often, and my Paper on which I wrote my Observations would immediately
be so wet with Dew, that it would not bear Ink: By which it may be
suppos'd how fast the Water gathers in those mighty high Ridges I but
now nam'd.
Thus is one part of the Vapours blown upon the Land return'd by the
Rivers into the Sea, from whence they came; another part by the cool of
the Night falls in Dews, or else in Rains, again into the Sea before it
reaches the Land, which is by much the greatest part of the whole
Vapours, because of the great extent of the Ocean, which the motion of
the Wind does not traverse in a very long space of Time; and this is the
Reason why the Rivers do not return so much into the _Mediterranean_, as
is extracted into Vapour. A third part falls on the Low-Lands, and is
the _Pabulum_ of Plants, where yet it does not rest, but is again
exhaled in Vapour by the action of the Sun, and is either carried by the
Winds to the Sea to fall in Rain or Dew there, or else to the Mountains
to be there turn'd into Springs; and tho' this does not immediately come
to pass, yet after several Vicissitudes of rising in Vapour, and falling
in Rain or Dews, each Particle of the Water is at length return'd to the
Sea from whence it came. Add to this, that the Rain-waters after the
Earth is fully sated with moisture, does, by the Vallies or lower parts
of the Earth, find its way into the Rivers, and so is compendiously sent
back to the Sea. After this manner is the Circulation perform'd, and I
doubt not but this Hypothesis is more reasonable than that of those who
derive all Springs from the Rain-waters, which yet are perpetual and
without diminution, even when no Rain falls for a long space of time; or
that derive them from a Filtration or Percolation of the Sea-waters,
thro' certain imaginary Tubes or Passages within the Earth wherein they
lose their Saltness. This, besides many others, labouring under this
principal Absurdity, that the greatest Rivers have their most copious
Fountains farthest from the Sea, and whether so great quantities of
fresh Water cannot reasonably be deriv'd any other way than in Vapour.
This, if we may allow final Causes, seems to be the design of the Hills,
that their Ridges being plac'd thro' the midst of the Continents, might
serve, as it were, for Alembicks to distil fresh Water for the use of
Man and Beast, and their heights to give a descent to those Streams to
run gently, like so many Veins, of the _Macrocosm_ to be the more
beneficial to the Creation. If the difference between Rain and Dew, and
the cause why sometimes 'tis Cloudy, at other times Serene, be inquir'd,
I can offer nothing like a proper Solution thereof, only with submission
to propose Conjectures, which are the best I can find, _viz._ That the
Air being heaped up by the meeting of two contrary Winds, when the
_Mercury_ is high, the Vapours are the better sustain'd and kept from
Co-agulating or Condensing into Drops, whereby Clouds are not so easily
generated, and the Night the Vapours fall down single, as they rose in
imperceptible Atoms of Water: Whereas, when the _Mercury_ is low, And
the Air rarified by the Exhaustion thereof, by two contrary Winds
blowing from the place; the Atoms of Air keep the Vapours not so well
separated, and they coalesce into visible Drops in the Clouds, and from
thence are easily drawn into greater Drops of Rain; to which 'tis
possible and not improbable, that some sort of Saline or Angular
Particles of Terrestrial Vapour being immix'd with the Aqueous, which I
take to be Bubbles, may cut or break their Skins or Coats, and so
contribute to their more speedy Condensation into Rain.
_The True Theory of the Tides, extracted from that admired Treatise of
Mr. _Isaac Newton_, Intitled, _Philosophiæ Naturalis Principia
Mathematica_; Being a Discourse presented with that Book to the late
King _James_, by Mr. _Edmund Halley_._
_It may, perhaps, seem strange, that this Paper, being no other than a
particular Account of a Book long since published, should now appear
here; but the Desires of several honourable Persons, which could not be
withstood, have obliged us to insert it here, for the sake of such, who
being less knowing in Mathematical Matters, and therefore not daring to
adventure on the Author himself, are notwithstanding, very curious to be
inform'd of the Causes of Things; particularly of so general and
extraordinary _Phænomena_, as are those of the Tides. Now this Paper
having been drawn up for the late King _James_'s Use, (in whose Reign
the Book was publish'd) and having given good Satisfaction to those that
got Copies of it; it is hoped the Savans of the higher Form will indulge
us this Liberty we take to gratifie their Inferiours in point of
Science; and not be offended, that we here insist more largely upon Mr.
_Newton_'s _Theory of the Tides_, which, how plain and easie soever we
find, is very little understood by the common Reader._
The sole Principle upon which this Author proceeds to explain most of
the great and surprizing Appearances of Nature, is no other than that of
_Gravity_, whereby in the Earth all Bodies have a tendency towards its
Centre; as is most evident: And from undoubted Arguments it's proved,
that there is such a Gravitation towards the Centre of the Sun, Moon,
and all the Planets.
From this Principle, as a necessary Consequence, follows the Sphærical
Figure of the Earth and Sea, and of all the other Cœlestial Bodies:
And tho' the tenacity and firmness of the Solid Parts, support the
Inequalities of the Land above the Level; yet the Fluids, pressing
equally and easily yielding to each other, soon restore the
_Æquilibrium_, if disturbed, and maintain the exact Figure of the Globe.
Now this force of Descent of Bodies towards the Centre, is not in all
places alike, but is still less and less, as the distance from the
Center encreases: And in this Book it is demonstrated, that this Force
decreases as the Square of the distance increases; that is, the weight
of Bodies, and the Force of their Fall is less, in parts more removed
from the Center, in the proportion of the Squares of the Distance. So as
for Example, a Ton weight on the Surface of the Earth, if it were raised
to the height of 4000 Miles, which I suppose the Semidiameter of the
Earth, would weigh but ¼ of a Ton, or 5 Hundred weight: If to 12000
Miles, or 3 Semidiameters from the Surface, that is 4 from the Center,
it would weigh but 1/16 part of the Weight on the Surface, or a Hundred
and Quarter: So that it would be as easie for the Strength of a Man at
that height to carry a Ton weight, as here on the Surface a 100¼. And
in the same Proportion does the Velocities of the fall of Bodies
decrease: For whereas on the Surface of the Earth all things fall 16
Foot in a second; at one Semidiameter above, this fall is but four Foot;
and at three Semidiameters, or four from the Centre, it is but 1/16 of
the Fall at the Surface, or but one Foot in a second: And at greater
Distances both Weight and Fall become very small, but yet at all given
Distances is still some thing, tho' the Effect become insensible. At the
distance of the Moon (which I will suppose 60 Semidiameters of the
Earth) 3600 Pounds weigh but one Pound, and the fall of Bodies is but of
1/3600 a Foot in a second, or 16 Foot in a Minute; that is, a Body so
far off descends in a Minute no more than the same at the Surface of the
Earth would do in a Second of Time.
As was said before, the same force decreasing after the same manner is
evidently found in the Sun, Moon, and all the Planets; but more
especially in the Sun, whose Force is prodigious; becoming sensible even
in the immense distance of _Saturn_: This gives room to suspect, that
the force of Gravity is in the Cœlestial Globes proportional to the
quantity of Matter in each of them: And the Sun being at least ten
Thousand times as big as the Earth, its Gravitation or attracting Force,
is found to be at least ten Thousand times as much as that of the Earth,
acting on Bodies at the same distance.
This Law of the decrease of Gravity being demonstratively proved, and
put past contradiction; the Author with great Sagacity, inquires into
the necessary Consequences of this Supposition; whereby he finds the
genuine Cause of the several Appearances in the Theory of the Moon and
Planets, and discovers the hitherto unknown Laws of the Motion of
Comets, and of the Ebbing and flowing of the Sea. Each of which are
Subjects that have hitherto taken up much larger Volumes; but Truth
being uniform, and always the same, it is admirable to observe how
easily we are enabled to make out very abstruse _and difficult Matters_,
when once true and genuine Principles are obtain'd: And on the other
hand it may be wondred; that, notwithstanding the great facility of
truth, and the perplexity and nonconsequences that always attend
erroneous Suppositions, these great Discoveries should have escaped the
acute Disquisitions of the best Philosophical Heads of all past Ages,
and be reserv'd to these our Times. But that wonder will soon cease, if
it be consider'd how great improvements Geometry has receiv'd in our
Memory, and particularly from the profound Discoveries of our
incomparable Author.
The Theory of the Motion of the primary _Planets_ is here shewn to be
nothing else, but the contemplation of the Curve Lines which Bodies cast
with a given Velocity, in a given Direction, and at the same time drawn
towards the Sun by its gravitating Power, would describe. Or, which is
all one, that the Orbs of the Planets are such Curve Lines as a Shot
from a Gun describes in the Air, being cast according to the direction
of the Piece, but bent in a crooked Line by the supervening Tendency
towards the Earths Centre: And the Planets being supposed to be
projected with a given Force, and attracted towards the Sun, after the
aforesaid manner, are here proved to describe such Figures, as answer
punctually to all that the Industry of this and the last Age has
observed in the Planetary Motions. So that it appears, that there is no
need of solid Orbs and Intelligences, as the Antients imagin'd, nor yet
of _Vortices_ or Whirlpools of the Cœlestial Matter, as _Des Cartes_
supposes; but the whole Affair is simply and mechanically performed,
upon the sole Supposition of a Gravitation towards the Sun; which cannot
be denied.
The Motion of _Comets_ is here shewn to be compounded of the same
Elements, and not to differ from Planets, but in their greater
swiftness, whereby overpowering the Gravity that should hold them to the
Sun, as it doth the Planets, they flie off again, and distance
themselves from the Sun and Earth, so that they soon are out of our
sight. And the imperfect Accounts and Observations Antiquity has left
us, are not sufficient to determine whether the same Comet ever return
again. But this Author has shewn how Geometrically to determine the Orb
of a Comet from Observations, and to find his Distance from the Earth
and Sun, which was never before done.
The third thing here done is the Theory of the Moon, all the
Inequalities of whose Motion are proved to arise from the same
Principles, only here the effect of two Centers operating on, or
attracting a projected Body, comes to be considered; for the Moon,
though principally attracted by the Earth, and moving round it, does
together with the Earth, move round the Sun once a Year, and is,
according as she is nearer or farther from the Sun, drawn by him more or
less than the Center of the Earth, about which she moves; whence arise
several Irregularities in her Motion, of all which, the Author in this
Book, with no less Subtility than Industry, has given a full account.
And though by reason of the great Complication of the Problem, he has
not yet been able to make it purely Geometrical, 'tis to be hoped, that
in some farther Essay he may surmount the difficulty: And having
perfected the Theory of the Moon, the long desir'd Discovery of the
Longitude (which at Sea is only practicable this way) may at length be
brought to light, to the great Honour of your Majesty, and Advantage of
your Subjects.
All the surprising Phænomena of the Flux and Reflux of the Sea, are in
like manner shewn to proceed from the same Principle; which I design
more largely to insist on, since the Matter of Fact is in this Case much
better known to your Majesty than in the foregoing.
If the Earth were alone, that is to say, not affected by the Actions of
the Sun and Moon, it is not to be doubted, but the Ocean, being equally
press'd by the force of Gravity towards the Center, would continue in a
perfect Stagnation, always at the same height, without either Ebbing or
Flowing; but it being here demonstrated, that the Sun and Moon have a
like Principle of Gravitation towards their Centers, and that the Earth
is within the Activity of their Attractions, it will plainly follow,
that the Equality of the pressure of Gravity towards the Center will
thereby be disturb'd; and though the smallness of these Forces, in
respect of the Gravitation towards the Earth's Center, renders them
altogether imperceptible by any Experiments we can devise, yet the Ocean
being fluid and yielding to the least force, by its rising shews where
it is less press'd, and where it is more press'd by its sinking.
Now if we suppose the force of the Moon's Attaction to decrease as the
Square of the Distance from its Center increases (as in the Earth and
other Cœlestial Bodies) we shall find, that where the Moon is
perpendicularly either above or below the Horizon, either in Zenith or
Nadir, there the force of Gravity is most of all diminished, and
consequently that there the Ocean must necessarily swell by the coming
in of the Water from those parts where the Pressure is greatest, _viz._
in those places where the Moon is near the Horizon: But that this may be
the better understood, I thought it needful to add the following Figure,
(_Vide Fig. 1. Plate 1._) where _M_ is the Moon, _E_ the Earth, _C_ its
Center, and _Z_ the place where the Moon is in the Zenith, _N_ where in
the Nadir.
Now by the Hypothesis it is evident, that the Water in _Z_, being
nearer, is more drawn by the Moon, than the Center of the Earth _C_, and
that again more than the Water in _N_; wherefore the Water in _Z_ hath a
tendency towards the Moon, contrary to that of Gravity, being equal to
the excess of the Gravitation in _Z_, above that in _C_: And in the
other case, the Water in _N_, tending less towards the Moon than the
Center _C_, will be less pressed, by as much as is the difference of the
Gravitation towards the Moon in _C_ and _N_. This rightly understood, it
follows plainly, that the Sea, which otherwise would be Spherical, upon
the Pressure of the Moon, must form it self into a Spheroidal or Oval
Figure, whose longest Diameter is where the Moon is vertical, and
shortest where she is in the Horizon; and that the Moon shifting her
Position as she turns round the Earth once a Day, this Oval of Water
shifts with her, occasioning thereby the two Floods and Ebbs observable
in each 25 Hours.
And this may suffice, as to the general Cause of the Tides; it remains
now to shew how naturally this Motion accounts for all the Particulars
that have been observ'd about them; so that there can be no room left to
doubt, but that this is the true cause thereof.
The Spring Tides upon the New and Full Moons, and Neap Tides on the
Quarters, are occasion'd by the attractive Force of the Sun in the New
and Full, conspiring with the Attraction of the Moon, and producing a
Tide by their united Forces: Whereas in the Quarters, the Sun raises the
Water where the Moon depresses it, and the contrary; so as the Tides are
made only by the difference of their Attractions. That the force of the
Sun is no greater in this Case, proceeds from the very small Proportion
the Semi-diameter of the Earth bears to the vast distance of the Sun.
It is also observ'd, that _cæteris paribus_, the Æquinoctial Spring
Tides in _March_ and _September_, or near them, are the Highest, and the
Neap Tides the lowest; which proceeds from the greater Agitations of the
Waters, when the fluid _Spheroid_ revolves about a great Circle of the
Earth, than when it turns about in a lesser Circle; it being plain that
if the Moon were constituted in the Pole, and there stood, that the
_Spheroid_ would have a fix'd Position, and that it would be always high
Water under the Poles, and low Water every where under the Æquinoctial:
And therefore the nearer the Moon approaches the Poles, the less is the
agitation of the Ocean, which is of all the greatest, when the Moon is
in the Æquinoctial, or farthest distant from the Poles. Whence the Sun
and Moon, being either conjoined or opposite in the Æquinoctial, produce
the greatest Spring Tides; and the subsequent Neap Tides, being produc'd
by the Tropical Moon in the Quarters, are always the least Tides;
whereas in _June_ and _December_, the Spring Tides are made by the
Tropical Sun and Moon, and therefore less vigorous; and the Neap Tides
by the Æquinoctial Moon, which therefore are the stronger: Hence it
happens, that the difference between the Spring and Neap Tides in these
Months, is much less considerable than in _March_ and _September_. And
the reason why the very highest Spring Tides are found to be rather
before the Vernal and after the Autumnal Equinox, _viz._ in _February_
and _October_, than precisely upon them, is, because the Sun is nearer
the Earth in the Winter Months, and so comes to have a greater effect in
producing the Tides.
Hitherto we have consider'd such Affections of the Tides as are
Universal, without relation to particular Cases; what follows from the
differing Latitudes of places, will be easily understood by the
following Fig. (_Vide Fig. 2. Plate 1._)
Let _ApEP_ be the Earth cover'd over with very deep Waters, _C_ its
Center, _P_, _p_, its Poles, _AE_ the Æquinoctial, _F_, _f_, the
parallel of Latitude of a Place, _D_, _d_, another Parallel at equal
distance on the other side of the Æquinoctial, _H_, _h_, the two Points
where the Moon is vertical, and let _K_, _k_, be the great Circle,
wherein the Moon appears Horizontal. It is evident, that a Spheroid
describ'd upon _Hh_, and _Kk_, shall nearly represent the Figure of the
Sea, and _Cf_, _CD_, _CF_, _Cd_, shall be the heighths of the Sea in the
places _f_, _D_, _F_, _d_, in all which it is High-water: And seeing
that in twelve Hours time, by the diurnal Rotation of the Earth, the
Point _F_ is transferr'd to _f_, and _d_ to _D_: The height of the Sea
_CF_ will be that of the High-water when the Moon is present, and _Cf_
that of the other High-water, when the Moon is under the Earth: Which in
the case of this Figure is less than the former _CF_. And in the
opposite Parallel _Dd_, the contrary happens. The Rising of the Water
being always alternately greater and less in each place, when it is
produc'd by the Moon declining sensibly from the Æquinoctial; that being
the greatest of the two High-waters in each diurnal Revolution of the
Moon, wherein she approaches nearest either to the Zenith or Nadir of
the place: Whence it is, that the Moon in the Northern Signs, in this
part of the World, makes the greatest Tides when above the Earth, and in
Southern Signs, when under the Earth; the Effect being always the
greatest where the Moon is farthest from the Horizon, either above or
below it. And this alternate Increase and Decrease of the Tides has been
observ'd to hold true on the Coast of _England_, at _Bristol_ by Captain
_Sturmy_, and at _Plymouth_ by Mr. _Colepresse_.
But the Motions hitherto mentioned are somewhat alter'd by the Libration
of the Water, whereby, though the Action of the _Luminaries_ should
cease, the Flux and Reflux of the Sea would for some time continue: This
Conservation of the impress'd Motion diminishes the differences that
otherwise would be between two consequent Tides, and is the reason why
the highest Spring-Tides are not precisely on the New and Full Moons,
nor the Neaps on the Quarters; but generally they are the third Tides
after them, and sometimes later.
All these things would regularly come to pass, if the whole Earth were
cover'd with Sea very deep; but by reason of the shoalness of some
places, and the narrowness of the Streights, by which the Tides are in
many cases propagated, there arises a great diversity in the Effect, and
not to be accounted for, without an exact Knowledge of all the
Circumstances of the Places, as of the Position of the Land, and the
Breadth and Depth of the Channels by which the Tide flows; for a very
slow and imperceptible Motion of the whole Body of the Water, where it
is (for Example) 2 Miles deep, will suffice to raise its Surface 10 or
12 Feet in a Tides time; whereas, if the same quantity of Water were to
be convey'd up a Channel of 40 Fathoms deep, it would require a very
great Stream to effect it, in so large Inlets as are the Channel of
_England_, and the _German_ Ocean; whence the Tide is found to set
strongest in those places where the Sea grows narrowest; the same
quantity of Water being to pass through a smaller Passage: This is most
evident in the _Streights_, between _Portland_ and _Cape de Hague_ in
_Normandy_, where the Tide runs like a Sluce; and would be yet more
between _Dover_ and _Calais_, if the Tide coming about the Island from
the North did not check it. And this force being once impress'd upon the
Water, continues to carry it above the level of the ordinary height in
the Ocean, particularly where the Water meets a direct Obstacle, as it
is at St. _Malo's_; and where it enters into a long Channel, which
running far into the Land, grows very streight at its Extremity; as it
is in the _Severn-Sea_ at _Chepstow_ and _Bristol_.
This shoalness of the Sea, and the intercurrent Continents are the
reason, that in the open Ocean the time of High water is not at the
Moons appulse to the Meridian, but always some Hours after it; as it is
observ'd upon all the West Coast of _Europe_ and _Africa_, from
_Ireland_ to the _Cape of Good Hope_: In all which a S. W. Moon makes
High-water, and the same is reported to be on the West side of
_America_. But it would be endless to account all the particular
Solutions, which are easie Corollaries of this _Hypothesis_; as why the
_Lakes_, such as the _Caspian Sea_, and _Mediterranean Seas_, such as
the _Black Sea_, the _Streights_ and _Baltick_, have no sensible Tides:
For _Lakes_ having no Communication with the Ocean, can neither increase
nor diminish their Water, whereby to rise and fall; and Seas that
communicate by such narrow Inlets, and are of so immense an Extent,
cannot in a few Hours time receive or empty Water enough to raise or
sink their Surface any thing sensibly.
Lastly, to demonstrate the Excellency of this Doctrine, the Example of
the Tides in the Port of _Tunking_ in _China_, which are so
extraordinary, and differing from all others we have yet heard of, may
suffice. In this Port there is but one Flood and Ebb in 24 Hours; and
twice in each Month, _viz._ when the Moon is near the Æquinoctial there
is no Tide at all, but the Water is stagnant; but with the Moons
Declination there begins a Tide, which is greatest when she is in the
Tropical Signs: Only with this difference, that when the Moon is to the
Northward of the Æquinoctial, it Flows when she is above the Earth, and
Ebbs when she is under, so as to make High-water at Moons-setting, and
Low-water at Moons-rising: But on the contrary, the Moon being to the
Southward, makes High-water at rising, and Low-water at setting; it
Ebbing all the time she is above the Horizon. As may be seen more at
large in the _Philosophical Transactions_, Numb. 162.
The Cause of this odd Appearance is propos'd by Mr. _Newton_, to be from
the concurrence of two Tides; the one propagated in six Hours out of the
great _South-Sea_ along the Coast of _China_; the other out of the
_Indian-Sea_, from between the Islands in twelve Hours, along the Coast
of _Malacca_ and _Cambodia_. The one of these Tides, being produc'd in
North Latitude, is, as has been said, greater, when the Moon being to
the North of the Equator is above the Earth, and less when she is under
the Earth. The other of them, which is propagated from the _Indian Sea_,
being raised in South-Latitude, is greater when the Moon declining to
the South, is above the Earth, and less when she is under the Earth: So
that of these Tides alternately greater and lesser, there comes always
successively two of the greater and two of the lesser together every
Day; and the High-water falls always between the times of the arrival of
the two greater Floods; and the Low-water between the arrival of the two
lesser Floods. And the Moon coming to the Æquinoctial, and the alternate
Floods becoming equal, the Tide ceases, and the Water stagnates: But
when she has pass'd to the other side of the Equator, those Floods which
in the former Order were the least, now becoming the greatest, that That
before was the time of High-water, now becomes the Low-water, and the
Converse. So that the whole appearance of these strange Tides, is
without any forcing naturally deduc'd from these Principles, and is a
great Argument of the Certainty of the whole _Theory_.
_A Theory of the _Variation_ of the _Magnetical Compass_. By Mr. _Ed.
Halley_, Fellow of the Royal Society._
The Variation of the Compass (by which I mean the Deflection of the
Magnetical Needle from the true Meridian) is of that great Concernment
in the Art of Navigation, that the neglect thereof, does little less
than render useless one of the noblest Inventions Mankind ever yet
attained to. And for this cause all Ships of Consequence (especially
those bound beyond the Equator) carry with them Instruments on purpose
to observe this Variation: That so the Course steer'd by the Compass,
may be reduc'd to the true Course in respect of the Meridian.
Now although the great utility that a perfect Knowledge of the Theory of
the Magnetical Direction would afford to Mankind in general, and
especially to those concern'd in Sea Affairs, seems as sufficient
incitement to all Philosophical and Mathematical Heads, to take under
serious Consideration the several _Phænomena_, and to endeavour to
reconcile them by some general Rule: Yet so it is; that almost all the
Authors, from whom a Discourse of this kind ought to have been expected,
pass by in silence the Difficulties they here Encounter. And those that
mention this Variation: By affirming it to proceed from Causes
altogether uncertain (as are the casual lying of Iron Mines and
Loadstones in the Earth) put a stop to all further Contemplation; and
give discouragement to those that would otherwise undertake this
Enquiry. 'Tis true, that not long since one Mr. _Bond_, an old Teacher
of Navigation, put forth a small Treatise, wherein he pretends to
calculate the Variation: But he limits his Hypothesis to the City of
_London_, affirming himself (as he had a great deal of reason) that the
same _Calculus_ is not sufficient for other Places; whereby it appears
that this Rule is far short of the so much desir'd general one.
Now although (through want of sufficient Observations, and some other
Difficulties, which I shall anon shew) I cannot pretend perfectly to
establish the Numbers and Rules of a _Calculus_, which shall precisely
answer to the Variations of all parts of the World: Yet I suppose it
will not be unacceptable to the Curious to propose something of a Light
into this abstruse Mystery; which, if no other, may have this good
Effect, to stir up the Philosophical _Genii_ of the Age to apply
themselves more attentively to this useful Speculation. But before I
proceed, 'twill be necessary to lay down the Grounds upon which I raise
my Conclusions; and at once to give a Synopsis of those Variations,
which I have reason to look upon as sure, being mostly the Observations
of Persons of good Skill and Integrity.