Miscellanea Curiosa.
Reading edition
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 79⁄10 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.
A TABLE OF VARIATIONS.
Names of Places. Longitude from Lon. Latitude Anno Dom. Variation Observ'd.
d m d m d m
London 0 0 51 32 N 1580 11 15 E
1622 6 0 E
1634 4 5 E
1672 2 30 W
Paris 2 25 E 48 51 N 1683 4 30 W
1640 3 00 E
1666 0 0
1681 2 30 W
Uraniburg 13 0 E 55 54 N 1672 2 35 W
Copenhagen 12 53 E 55 41 N 1649 1 30 E
1672 3 35 W
Dantzick 19 0 E 54 23 N 1679 7 00 W
Mompelier 4 0 E 43 37 N 1674 1 10 W
Brest 4 25 W 48 23 N 1680 1 45 W
Rome 13 0 E 41 50 N 1681 5 0 W
Bayonne 1 20 W 43 30 N 1680 1 20 W
Hudson's Bay 79 40 W 51 00 N 1668 19 15 W
In Hud. Straights 57 00 W 61 00 N 1668 29 30 W
In Baffin's Bay at Sir Thomas Smith's Sound 80 00 W 78 00 N 1616 57 00 W
At Sea 50 00 W 38 40 N 1682 7 30 W
At Sea 31 30 W 43 50 N 1682 5 30 W
At Sea 42 0 W 21 0 N 1678 0 40 E
Cape St. Aug. of Brazile 35 30 W 8 0 S 1670 5 30 E
Cape Frio 41 10 W 22 40 S 1670 12 10 E
At Sea off of the Mou. of the River Plate 53 00 W 39 30 S 1670 20 33 E
At the East Entrance of Magellan Straits 68 00 W 52 30 S 1670 17 00 E
At the W. Entrance of the Magellan Straits 75 00 W 53 00 S 1670 14 10 E
Baldivia 73 00 W 40 00 S 1670 8 10 E
At Cape d'Agulbas 16 30 E 34 50 S 1622 2 99 W
1675 8 00 W
At Sea 1 0 E 34 30 S 1675 0 00
At Sea 20 0 W 34 0 S 1675 10 30 E
At Sea 32 0 W 24 0 S 1675 10 30 E
At St. Helena 6 30 W 16 00 S 1677 0 40 E
At Ascension 14 30 W 7 50 S 1678 1 00 E
At Johanna 44 00 E 12 15 S 1675 19 30 W
At Monbasa 40 00 E 4 00 S 1675 16 00 W
At Zocatra 56 00 E 12 30 N 1674 17 00 W
At Aden, at the Mo. of the Red Sea 47 30 E 13 00 N 1674 15 00 W
At Diego Roiz 61 0 E 20 0 S 1676 20 30 W
At Sea 64 30 E 0 0 1676 15 30 W
At Sea 55 0 E 27 0 S 1676 24 00 W
At Bombay 72 30 E 19 0 N 1676 12 00 W
At Cape Comorin 76 00 E 8 15 N 1680 8 48 W
At Ballafore 87 00 E 21 30 N 1680 8 20 W
At Fort St. George 80 00 E 13 15 N 1680 8 10 W
At the W. Point of Java 104 00 E 6 40 S 1676 3 10 W
At Sea 58 00 39 0 S 1677 27 30 W
At the Isle of St. Paul 72 0 E 38 0 S 1677 23 30 W
At Van Dimen's Land 142 0 E 42 25 S 1642 0 0
At New Zealand 170 0 E 40 50 S 1642 9 0 E
At Three Kings Isle in New Zealand. 169 30 E 34 35 S 1642 8 40 E
At the Isle Rotterdam in the South Sea 184 00 E 20 15 S 1642 6 20 E
On the Coast of N. Guin. 149 00 E 4 30 S 1643 8 45 E
At the W. P. of N. Guin. 126 00 E 0 26 S 1643 5 30 E
Tho' I could wish we could obtain from the Spaniards what Variations they find in their Voyages from the Manilhas towards Acapulco, through the North part of the South Sea; as likewise what it is at Japan from the Dutch: Yet (considering the number of these Observations I have collected, and that they are made in parts of the World so remote from Europe, and from one another) I suppose that the Theory that answers these will scarce fail in those Regions from whence we have as yet no account. But first we must make some Remarks upon the foregoing Table: And, First,
That in all Europe the Variation at this time is West, and more in the Eastern Parts thereof than the Western: As likewise, that it seems throughout to be upon the increase that way.
Secondly, That on the Coast of America, about Virginia, New-England and New-Foundland, the Variation is likewise Westerly; and that it increases all the way as you go Northerly along the Coast, so as to be above 20 Degrees at New-Found-Land, nearly 30 gr. in Hudson's Straights, and not less than 57 Degrees in Baffin's Bay; also, that as you Sail Eastward from this Coast, the Variation diminishes. From these two it is a Legitimate Corollary: That Somewhere between Europe, and the North part of America, there ought to be an Easterly Variation, or at least no Westerly. And so I conjecture it is about the Eastermost of the Tercera Islands.
Thirdly, That on the Coast of Brasile there is East Variation, which increases very notably as you go to the Southward, so as to be 12 Degrees at Cape Frio, and over against the River of Plate 20½ Degrees: And from thence Sailing South-Westerly to the Straits of Magellan it decreases 17 Degrees, and at the West Entrance but 14 Degrees.
Fourthly, That at the Eastward of Brasile, properly so call'd, this Easterly Variation decreases, so as to be very little at St. Helena and Ascension, and to be quite gone, and the Compass Point true about 18 Degrees of Longitude West from the Cape of Good-hope.
Fifthly, That to the Eastward of the aforesaid Places a Westward Variation begins, which Reigns in the whole Indian Sea, and arises to no less than Eighteen Degrees under the Equator it self, about the Meridian of the Northern part of Madagascar; and near the same Meridian, but in 39 Degrees South Latitude it is found full 27½ Degrees: From thence Easterly the West Variation decreases, so as to be little more than eight Degrees at Cape Comorin, and than three Degrees upon the Coast of Java; and to be quite extinct about the Molucca Islands, as also a little to the Westwards of Van Diemens Land found out by the Dutch in 1642.
Sixthly, That to the Eastward of the Molucca's and Van Diemens Land in South Latitude there arises another Easterly Variation, which seems not so great as the former, nor of so large Extent; for that at the Island Rotterdam it is sensibly less than upon the East Coast of New Guinea; and, at the rate it decreases, it may well be suppos'd, that about 20 Degrees farther East, or 225 Degrees East Longitude from London, in the Latitude of 20 Degrees South, a Westerly Variation begins.
Seventhly, That the Variations observ'd by the Honourable Sir John Norborough at Baldivia, and at the West Entrance of the Straights of Magellan do plainly shew, that That East Variation, noted in our third Remark, is decreasing apace; and that it cannot reasonably extend many Degrees into the South Sea from the Coast of Peru and Chili, leaving room for a small Westerly Variation, in that Tract of the unknown World that lies in the mid-way between Chili and New-Zealand, and between Hounds-Island and Peru.
Eighthly, That in Sailing North-West from St. Helena by Ascension, as far as the Equator, the Variation continues very small East, and as it were constantly the same: So that in this part of the World the Course, wherein there is no Variation, is evidently no Meridian, but rather North-West.
Ninthly, That the Entrance of Hudson's Straights, and the Mouth of the River of Plate, being nearly under the same Meridian, at the one place the Needle varies 29½ Degrees to the West; at the other 20½ Degrees to the East. This plainly demonstrates the impossibility of reconciling these Variations by the Theory of Bond; which is by two Magnetical Poles and an Axis, inclin'd to the Axis of the Earth; from whence it would follow, That under the same Meridian the Variation should be in all places the same way.
These things being premised may serve as a sure Foundation to raise the Superstructure of a Theory upon. But first it would not be amiss to shew hereby the mistake of Gilbert and Des Cartes: The first whereof supposes, that the Earth it self being in all its parts Magnetical, and the Water not; wheresoever the Land is, thither also should the Needle turn, as to the greater quantity of Magnetical Matter. But this in many Instances is not true; but most remarkably upon the Coast of Brazile, where the Needle is so far from being attracted by the Land, that it turns the quite contrary way, leaving the Meridian to lye N b E, which is just along the Coast. As to the Position of Des Cartes, that the Iron and Loadstones hid in the Bowels of the Earth and the Bottom of the Sea, may be the Causes that the Needle varies; if we consider for how great a part of the Earths Surface, ex. gr. in the whole Indian Sea, the Needle declines the same way, and that regularly, 'twill follow that the attracting Substance that occasions it, must be very far distant. Now by Experience we find the little force that Iron Guns have upon the Compass in Ships (their Vertue, though they be Demiculverin, or greater Cannon, being not perceptible at four or five Yards distance) and the Experiments now before the Royal Society do plainly shew, how little a Magnetism there is in most crude Iron Oars: What quantity thereof must be then suppos'd to make so powerful a Diversion at two or three Thousand Miles distance? Yet I cannot deny that in some places near the Shoar, or in Shoal-Water, the Needle may be irregularly directed from the aforesaid Causes, and that not a little, as Gassendus gives a notable instance of the Island Elba in the Mediterranean Sea: But these differences from the general Direction are always signs of the nearness of those Magnetical Substances, for the Production whereof that Island Elba has been famous from all Antiquity. Besides, against both Des Cartes and Gilbert, the change of the Variation, which has been within these Hundred Years last past more than 15 gr. at London, is an entire Demonstration; tho' Des Cartes does not stick to say, that the transportation of Iron from place to place, and the growth of new Iron within the Earth, where there was none before, may be the cause thereof. The same holds likewise against the Hypothesis of Magnetical Fibres, which Kircher maintains.
Now to propose something that may answer the several appearances, and introduce nothing strange in Philosophy, after a great many close Thoughts, I can come to no other Conclusion than that, The whole Globe of the Earth is one great Magnet, having four Magnetical Poles, or Points of Attraction, near each Pole of the Equator. Two; and that, in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is govern'd thereby, the nearest Pole being always predominant over the more remote. The parts of the Earth wherein these Magnetical Poles lie, cannot as yet be exactly determin'd for want of sufficient Data to proceed Geometrically; but, as near as Conjecture can reach, I reckon that the Pole, which is at present nearest to us, lies in or near the Meridian of the Lands-end of England, and not above seven Degrees from the Pole Arctick; by this Pole the Variations in all Europe and Tartary, and the North Sea are principally govern'd, though with regard to the other Northern Pole, whose situation is in a Meridian passing about the middle of California, and about 15 gr. from the North Pole of the World; to this the Needle has chiefly respect in all the North America, and in the two Oceans on either side thereof, from the Azores Westward to Japan, and farther. The two Southern Poles are rather farther distant from the South Pole of the World: The one about sixteen Degrees therefrom, is in a Meridian, some twenty Degrees to the Westward of Magellan Straights, or ninety five Degrees West from London: This commands the Needle in all the South-America, in the Pacifick Sea, and the greatest part of the Ethiopick Ocean. The Fourth and last Pole seems to have the greatest Power, and largest Dominions of all, as it is the most remote from the Pole of the World, being little less than 20 Degrees distant therefrom in the Meridian, which passes through Hollandia Nova, and the Island Celebes about one hundred and twenty Degrees East from London; this Pole is predominant in the South part of Africa, in Arabia and the Red Sea, in Persia, India, and its Islands, and all over the Indian Sea, from the Cape of Good-Hope Eastwards to the middle of the great South Sea, that divides Asia from America. This seems to be the present Disposition of the Magnetical Vertue throughout the whole Globe of the Earth; it remains to shew how this Hypothesis makes out all the Variations that have been observ'd of late; and how it answers to our several Remarks drawn from the Table. And first it is plain, that (our European North Pole being in the Meridian of the Lands-end of England) all places more Easterly than that will have it on the West side of their Meridian, and consequently the Needle, respecting it with its Northern Point, will have a Westerly Variation, which will still be greater as you go to the Eastwards, till you come to some Meridian of Russia, where 'twill be greatest, and from thence decrease again. Thus at Brest the Variation is but 1¾ Degrees, at London 4½ Degrees; but at Dantzick seven Degrees West. To the Westward of the Meridian of the Lands-end, the Needle ought to have an Easterly Variation; were it not that (by approaching the American Northern Pole, which lies on the West side of the Meridian, and seems to be of greater force than this other) the Needle is drawn thereby Westwards, so as to counterballance the Direction given by the European Pole, and to make a small West Variation in the Meridian of the Lands-end it self. Yet I suppose that about the Meridian of the Isle Tercera, our nearest Pole may so far prevail as to give the Needle a little turn to the East, though but for a very small space: The Counterballance of those two Poles permitting no considerable Variation in all the Eastern Parts of the Atlantick Ocean; nor upon the West Coasts of England and Ireland, France, Spain and Barbary. But to the Westwards of the Azores the Power of the American Pole overcoming that of the European, the Needle has chiefly respect thereto, and turns still more and more towards it as you approach it. Whence it comes to pass, that on the Coast of Virginia, New-England, New-found-Land, and in Hudson's-Straights the Variation is Westward; that it decreases as you go from thence towards Europe, and that it is less in Virginia and New-England, than in New-found-Land, and Hudson's-Straights. This Westerly Variation again decreases, as you pass over the North America; and about the Meridian of the middle of California the Needle again points due North; and from thence Westward to Yedzo and Japan, I make no doubt but the Variation is Easterly, and half the Sea over no less than fifteen Degrees, if there be any truth in this Hypothesis of mine. Therefore I propose this as a Trial, that the whole may be scann'd thereby; and I conceive it will not be hard to know of the Spaniards how it is, who so frequently sail through that Ocean, in their return from the Manilha Isles. This East Variation extends over Japan, Yedzo, East-Tartary, and part of China, till it meet with the Westerly, which is govern'd by the European North Pole, and which I said was greatest some where in Russia.
Towards the Southern Pole the effect is much the same, only that here the South Point of the Needle is attracted. Hence it will follow, that the Variation on the Coast of Brazile, at the River of Plate, and so on to the Straights of Magellan, should be Easterly (as in our third Remark); if we suppose a Magnetical Pole situate about twenty Degrees more Westerly than the Straights of Magellan. And this Easterly Variation doth extend Eastward over the greatest part of the Ethiopick Sea, till it be counterpoised by the Vertue of the other Southern Pole; as it is about mid-way between the Cape of Good-Hope, and the Isles of Tristan d' Acuntia. From thence Eastwards, the Asian South Pole (as I must take the liberty to call it) becoming prevalent, and the South point of the Needle being attracted thereby, there arises a West Variation, very great in quantity and extent, because of the great distance of this Magnetical Pole of the World. Hence it is, that in all the Indian Sea as far as Hollandia Nova, and farther, there is constantly West Variation; at that under the Equator it self it arises to no less than eighteen Degrees, where 'tis most. About the Meridian of the Island Celebes, being likewise that of this Pole, this Westerly Variation ceases, and an Easterly begins; which reaches, according to my Hypothesis, to the middle of the South-Sea, between Zelandia Nova, and Chili, leaving room for a small West Variation govern'd by the American South Pole, which I shew'd to be in the Pacifick Sea, in the sixth and seventh Remark.
What I have now said, does plainly shew the sufficiency of this Hypothesis for solving the Variations that are at this time observ'd in the temperate and frigid Zones, where the Direction of the Needle chiefly depends upon the Counterpoise of the forces of two Magnetical Poles of the same Nature; and I suppose I have shewn how it comes to pass, that under the same Meridian the Variation should be in one place 29½ West, and another 20½ East; as I have noted in my ninth Remark.
In the Torrid Zone, and particularly under the Equinoctial, respect must be had to all four Poles, and their Positions well consider'd, otherwise it will not be easie to determine what the Variations shall be; the nearest Pole being always the strongest; yet not so, as not to be counterballanc'd sometimes by the united forces of two more remote; a notable Instance whereof is in our eighth Remark, where I took notice, that in sailing from St. Helena by the Isle of Ascension, to the Equator, on a N. W. Course, the Variation is very little Easterly, and in that whole Tract unalterable; for which I give this Reason, That the South American Pole (which is considerably the nearest in the aforesaid Places) requiring a great Easterly Variation, is counterpoised by the contrary Attraction of the North-American and the Asian-South-Pole; each whereof singly are in these Parts, weaker than the American-South-Pole; and upon the North West Course, the Distance from this latter is very little varied; and as you recede from the Asian-South-Pole, the Ballance is still preserv'd by the access towards the North-American-Pole. I mention not in this Case the European-North-Pole, its Meridian being little remov'd from those of these places; and of it self requiring the same Variations we here find. After the same manner we might proceed to conclude the Variations in other places under and near the Equator; but I purposely leave it for an Exercise to the Thoughts of the serious Reader, who is desir'd to help his Imagination, by having before him a Map or Globe of the Earth: And to mark thereon the Magnetical Poles in the Longitudes and Latitudes I assign them. (Vide Plate 2.)
Thus, I hope, I have not lost my Pains and Study in this difficult Subject; believing that I have put it past doubt, That there are in the Earth four such Magnetical Points or Poles, which occasion the great variety and seeming irregularity which is observed in the Variations of the Compass. But to calculate exactly what it is, in any place assign'd, is what I dare not yet pretend to, though I could wish it were my happiness to be able to oblige the World with so useful a piece of Knowledge; there are Difficulties that occur, that render the thing as yet not feasible; for first there are a great many Observations requisite, which ought to be made at the same time; not at Sea, but ashore, with greater Care and Attention than the generality of Sailors apply. And besides, it remains undetermin'd in what proportion the attractive Power decreases, as you remove from the Pole of a Magnet, without which it were a vain attempt to go about to calculate. There is yet a further Difficulty, which is the Change of the Variation, one of the Discoveries of this last Century; which shews, that it will require some hundreds of Years to establish a compleat Doctrine of the Magnetical System. From the foregoing Table it should seem, that all the Magnetical Poles had a motion Westward: But if it be so, 'tis evident, that it is not a Rotation about the Axis of the Earth; for then the Variations would continue the same, in the same parallel of Latitude (the Longitude only chang'd) as much as is the motion of the Magnetical Poles, but the contrary is found by Experience; for there is no where in the Latitude of 15½ North between England and America, a Variation of eleven Degrees East at this time; as it was once here at London; it seems therefore, that our European Pole is grown nearer the Pole Arctick than it was heretofore, or else that it has lost part of its Vertue. But whether these Magnetical Poles move altogether with one motion, or with several; whether equally or unequally; whether Circular or Libratory: If Circular, about what Center; if Libratory, after what manner; are Secrets as yet utterly unknown to Mankind, and are reserv'd for the Industry of future Ages.
An Account of the Cause of the Change of the Variation of the Magnetical Needle, with an Hypothesis of the Structure of the Internal Parts of the Earth; as it was proposed to the Royal Society in one of their late Meetings. By Mr. Edmund Halley.
HAving in the precedent Discourse delivered a Theory of the Variation of the Magnetical Compass, wherein I did collect as many Observations as at that time I could procure, and having carefully compar'd them together, I came at length to this general conclusion, That the Globe of the Earth might be supposed to be one great Magnet, having four Magnetical Poles or Points of Attraction, near each Pole of the Equator two; and that in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is chiefly govern'd thereby; the nearest Pole being always predominant ever the more remote. And I there have endeavour'd to state and limit the present Position of those Poles in the Surface of our Globe, which the Reader pleasing to consult, will save us the pains of repeating. But after all, tho' that Discourse was favourably receiv'd both at home and abroad, as seeming to render a tolerable account of the observ'd Variations, yet I found two Difficulties not easie to surmount; the one was, that no Magnet I had ever seen or heard of, had more than two opposite Poles, whereas the Earth had visibly four, and perhaps more. And secondly, it was plain that these Poles were not, at least all of them, fixt in the Earth, but shifted from place to place, as appear'd by the great Changes in the Needles Direction within this last Century of Years, not only at London, (where this great Discovery was first made) but almost all over the Globe of Earth; whereas it is not known or observ'd that the Poles of a Load-stone ever shifted their place in the Stone, nor (considering the compact hardness of that Substance) can it easily be suppos'd; though the Matter of Fact be too notorious and universal, not to be accounted for.
These Difficulties had wholly made me despond, and I had long since given over an Inquiry I had so little hopes of, when in accidental Discourse, and least expecting it, I stumbl'd on the following Hypothesis; in delivering whereof, if I shall seem to advance any thing that looks like Extravagant or Romantick, the Reader is desir'd to suspend his Censure, till he have consider'd the force and number of the many Arguments which concur to make good so new and so bold a Supposition.
Though it be sufficiently known and allow'd, that the Needles Variation changes, it will be necessary however to give a few Instances, whereby it may appear that this Change is gradual and universal, and the effect of a great and permanent motion: For which take the following Examples.
At London, in the Year 1580, the Variation was observ'd by Mr. Burrows to be 11° 15' East. In Anno 1622, the same was found by Mr. Gunter to be but 6° 0' East. In the Year 1634, Mr. Gellibrand found it 4° 5' East. In 1657, Mr. Bond observ'd that there was no Variation at London. Anno 1672, my self observ'd it 2° 30' to the West; and in the Year 1692, I again found it 6° 00' West. So that in 112 Years the Direction of the Needle has chang'd no less than seventeen Degrees.
At Paris, Orontius Finæus about the Year 1550, did account it about eight or nine Degrees East Variation. Anno 1640, it was found three Degrees East. Anno 1660, there was no Variation there, and Anno 1681, I found it to be 2° 30' to the West.
At Cape d' Agulhas, the most Southerly Promontary of Africa, about the Year 1600, the Needle pointed due North and South without Variation, whence the Portugueze gave its name. Anno 1622, there was two Degrees West Variation. Anno 1675, it was 8° 50' West; and in the Year 1691, it was curiously observ'd not less than eleven Degrees West.
At St. Helena, about the Year 1600, the Needle declin'd eight Degrees to the East. Anno 1623, it was but 6° 0' East. Anno 1677, when I was there, I observ'd it accurately on Shoar to be 0° 40' East; and in 1692 it was found about 1° to the Westward of the North.
At Cape Comorine in India, in the Year 1620, there was 14° 20' West Variation. In the Year 1680, there was 8° 48', but now lately in the Year 1688, it was no more than 7° 30', so that here the Needle has return'd to the East about seven Degrees in seventy Years.
In all the other Examples the Needle has gradually mov'd towards the West, and the places are too far asunder to be influenc'd by the removal of any Magnetical Matter, which may by accident be transplac'd within the Bowels, or on the Surface of the Earth. If more Examples are desir'd, the Reader may be furnished with them in the Portugueze Routier of Aleixo de Motta (written about the Year 1600) and in the Voyage of Beaulieu, both publish'd in Mr. Thevenot's first Collection of curious Voyages, Printed at Paris, Anno 1663; which he is to compare with the Journals of our late East India Voyagers, and I am assur'd, that it will be thereby evident, that the Direction of the Needle is in no place fix'd and constant, tho' in some it change faster than in others: And where for a long time it has continu'd as it were unalter'd, it is there to be understood, that the Needle has its greatest Deflection, and is become Stationary in order to return, like the Sun, in the Tropick. This, at present, is in the Indian Sea, about the Island Mauritius, where is the highest West Variation, and in a Tract tending from thence into the N. N. W. towards the Red-Sea and Egypt. And in all Places to the Westward of this Tract, all over Africa and the Seas adjoining, the West Variation will be found to have encreas'd; and to the Eastwards thereof as in the Example of Cape Comorine, to have decreased, viz. all over the East-Indies, and the Islands near it.
After the like manner in that Space of East Variation, which, beginning near St. Helena, is found all over the South America, and which at present is highest about the Mouth of Rio de la Plata, it has been observ'd, that in the Eastern Parts thereof, the Variation of the Needle gradually decreases; but whether on the contrary it increases in those places which lie more Westerly than that Tract wherein the highest East Variation is found; or how it may be in the vast Pacifick Sea, we have not Experience enough to ascertain, only we may by Analogy infer, that both the East and West Variations therein do gradually increase and decrease after the same Rule.
These Phænomena being well understood and duly consider'd, do sufficiently evince, That the whole Magnetical System is by one, or perhaps more motions translated, whether Eastwards or Westwards, I shall anon discuss; that this moving thing is very great, as extending its effects from Pole to Pole, and that the motion thereof is not per saltum, but a gradual and regular motion.
Now considering the Structure of our Terraqueous Globe, it cannot be well suppos'd that a very great part thereof can move within it, without notably changing its Center of Gravity and the Equilibre of its Parts, which would produce very wonderful Effects in changing the Axis of diurnal Rotation, and occasion strange alteration in the Seas Surface, by Inundations and Recesses thereof, such as History never yet mention'd. Besides, the solid parts of the Earth are not to be granted permeably by any other than fluid Substances, of which we know none that are any ways Magnetical. So that the only way to render this motion intelligible and possible, is to suppose it to turn about the Center of the Globe, having its Center of Gravity fix'd and immoveable in the same common Center of the Earth: And there is yet requir'd, that this moving internal Substance be loose and detached from the external Parts of the Earth whereon we live; for otherwise, were it affix'd thereto, the whole must necessarily move together.
So then the External Parts of the Globe may well be reckon'd as the Shell, and the Internal as a Nucleus or inner Globe, included within ours, with a fluid Medium between, which having the same Common Center and Axis of diurnal Rotation, may turn about with our Earth each twenty four Hours; only this outer Sphere having its turbinating motion some small matter either swifter or slower than the internal Ball: And a very minute Difference in length of time, by many Repetitions becoming sensible, the Internal Parts will by degrees recede from the External, and not keeping pace with one another, will appear gradually to move either Eastwards or Westwards by the difference of their motions.
Now supposing such an Internal Sphere having such a motion, we shall solve the two great Difficulties we encounter'd in my former Hypothesis: For if this exteriour Shell of Earth be a Magnet, having its Poles at a distance from the Poles of diurnal Rotation; and if the Internal Nucleus be likewise a Magnet, having its Poles in two other places, distant also from the Axis; and these latter by a gradual and slow motion change their place in respect of the External; we may then give a reasonable account of the four Magnetical Poles I presume to have demonstrated before; as likewise of the Changes of the Needles Variations, which till now hath been unattempted.
The Period of this Motion being wonderful great, and there being hardly an hundred Years since these Variations have been duly observ'd, it will be very hard to bring this Hypothesis to a Calculus, especially since, though the Variations do increase and decrease regularly in the same place, yet in differing places, at no great distance, there are found such casual Changes thereof as can no ways be accounted for by a regular Hypothesis; as depending upon the unequal and irregular distribution of the Magnetical Matter within the Substance of the External Shell or Coat of the Earth, which deflect the Needle from the Position it would acquire from the effect of the general Magnetism of the whole. Of this the Variations at London and Paris give a notable Instance, for the Needle has been constantly about 1°½ more Easterly at Paris than at London; though it be certain that according to the general effect, the Difference ought to be the contrary way: Notwithstanding which, the Variations in both places do change alike.
Hence, and from some other of like Nature, I conclude, That the two Poles of the External Globe are fixt in the Earth, and that if the Needle were wholly govern'd by them, the Variations thereof would be always the same, with some little Irregularities upon the account I but just now mention'd: But the Internal Sphere having such a gradual translation of its Poles, does influence the Needle, and direct it variously, according to the result of the attractive or directive Power of each Pole; and consequently there must be a Period of the Revolution of this Internal Ball, after which the Variations will return again as before. But if it shall in future Ages be observ'd otherwise, we must then conclude that there are more of these Internal Spheres, and more Magnetical Poles than Four, which at present we have not a sufficient number of Observations to determine, and particularly in that vast Mar del Zur, which occupies so great a part of the whole Surface of the Earth.
If then two of the Poles be fixt and two moveable, it remains to ascertain which they are that keep their place; and though I could wish we had the Experience of another Century of Years to found our Conclusions upon, yet I think we may safely determine, That our European North Pole (which in the precedent Discourse I suppos'd near the Meridian of the Lands-end of England, and about seven Degrees therefrom) is that That is moveable of the two Northern Poles, and that That has chiefly influenc'd the Variations in these parts of the World: For in Hudson's Bay, which is under the Direction of the American Pole, the Change is not observ'd to be near so fast as in these parts of Europe, though that Pole be much farther remov'd from the Axis.
As to the South Poles, I take the Asian Pole, which I place about the Meridian of the Island Celebes to be the fixt, and consequently the American Pole to move; from the like Observation of the slow Decrease of the Variation on the Coast of Java, and near the Meridian of the Asian Pole; though I must confess to have no account of the effects of the other beyond Magellan's Streights.
If this be allow'd me, 'tis plain that the fixt Poles are the Poles of this External Shell or Cortex of the Earth, and the other two the Poles of a Magnetical Nucleus included and moveable within the other. It likewise follows, that this Motion is Westwards, and by consequence that the aforesaid Nucleus has not precisely attained the same degree of Velocity with the exteriour Parts in their diurnal Revolution; but so very nearly equals it, that in 365 Revolves the difference is scarce sensible. This I conceive to arise from the Impulse whereby this diurnal Motion was imprest on the Earth, being given to the External Parts, and from thence in time communicated to the Internal; but not so as perfectly to equal the Velocity of the first Motion impress'd on, and still conserv'd by the superficial Parts of the Globe.
As to the quantity of this Motion it is almost impossible to define it, both from the Nature of this kind of Observation, which cannot be very accurately perform'd, as also from the small time these Variations have been observ'd, and their Change discover'd. It appears by all Circumstances, that its Period is of many Centuries of Years, and as far as may be collected from the Change of the Place, where there was no Variation, by reason of the Equilibre of the two Southern Magnetical Poles, viz. from Cape d' Agulhas to the Meridian of St. Helena (which is about 23 degr. in about ninety Years) and of the place where the Westerly Variation is in its ἀκμὴ or greatest Deflection, being about half so much, viz. from the Isle of Diego Roiz to the South West Parts of Madagascar. We may with some Reason conjecture, that the American Pole has mov'd Westwards forty six Degrees in that time, and that the whole Period thereof is perform'd in seven hundred Years, or thereabouts; so that the nice Determination of this, and of several other Particulars in the Magnetick System is reserv'd for remote Posterity; all that we can hope to do, is to leave behind us Observations that may be confided in, and to propose an Hypothesis which after Ages may examine, amend or refute. Only here I must take leave to recommend to all Masters of Ships, and all others, Lovers of Natural Truths, that they use their utmost Diligence to make, or procure to be made, Observations of these Variations in all parts of the World, as well in the North as South Latitude (after the laudable Custom of our East India Commanders) and that they please to communicate them to the Royal Society, in order to leave as compleat a History as may be to those that are hereafter to compare all together, and to compleat and perfect this abstruse Theory.
And by the way it will not be amiss to amend a receiv'd Error in the Practice of observing the Variation, which is, to take it by the Amplitude of the Rising and Setting Sun, when his Center appears in the visible Horizon; whereas he ought to be observ'd when his under Limb is still above the Horizon about ⅔ of his Diameter, or twenty Minutes, upon the score of the Refraction, and the height of the Eye of the Observer above the Surface of the Sea: Or else they are to work the Amplitudes as they do the Azimuth, reckoning the Suns Distance from the Zenith 90° 36': This, though it be of little consequence near the Æquinoctial, will make a great Error in high Latitudes, where the Sun rises and sets obliquely.
But to return to our Hypothesis, In order to explain the Change of the Variations, we have adventur'd to make the Earth hollow, and to place another Globe within it; and I doubt not but this will find Opposers enough. I know 'twill be Objected, That there is no Instance in Nature of the like thing; that if there was such a middle Globe it would not keep its place in the Center, but be apt to deviate therefrom, and might possibly chock against the Concave Shell, to the ruin, or at least endammaging thereof; That the Water of the Sea would perpetually leak through, unless we suppose the Cavity full of Water; That were it possible, yet it does not appear of what use such an inward Sphere can be of, being shut up in Eternal Darkness, and therefore unfit for the Production of Animals or Plants; with many more Objections, according to the Fate of all such new Propositions.
To these, and all other that I can foresee, I briefly Answer, That the Ring environing the Globe of Saturn is a notable Instance of this kind, as having the same common Center, and moving along with the Planet, without sensibly approaching him on one side more than the other. And if this Ring were turn'd on one of its Diameters, it would then describe such a Concave Sphere as I suppose our External one to be. And since the Ring, in any Position given, would, in the same manner, keep the Centre of Saturn in its own, it follows, that such a Concave Sphere may move with another included in it, having the same common Centre. Nor can it well be suppos'd otherwise, considering the Nature of Gravity; for should these Globes be adjusted once to the same common Centre, the Gravity of the parts of the Concave would press equally towards the Centre of the inner Ball, which equality must necessarily continue till some External Force disturb it, which is not easie to imagine in our Case. This perhaps I might more intelligibly express, by saying that the inner Globe being posited in the Centre of the Exteriour, must necessarily ascend which way soever it move; that is, it must overcome the force of Gravity pressing towards the common Centre, by an impulse it must receive from some outward Agent; but all outward Efforts being sufficiently fenc'd against by the Shell that surrounds it, it follows, that this Nucleus being once fixt in the common Centre, must always there remain.
As to the leaking of the Water through this Shell, when once a passage shall be found for it to run through, I must confess it is an Objection seemingly of weight; but when we consider how tightly great Beds of Chalk or Clay, and much more Stone do hold Water, and even Caves arch'd with Sand; no Man can doubt but the Wisdom of the Creator has provided for the Macrocosm by many more ways than I can either imagine or express, especially since we see the admirable and innumerable Contrivances wherewith each worthless Individual is furnish'd both to defend it self, and propagate its Species. What Curiosity in the Structure, what Accuracy in the Mixture and Composition of the parts, ought not we to expect in the Fabrick of this Globe, made to be the lasting Habitation of so many various Species of Animals, in each of which there want not many Instances that manifest the boundless Power and Goodness of their Divine Author; and can we then think it a hard Supposition, that the Internal Parts of this Bubble of Earth should be replete with such Saline and Vitriolick Particles as may contribute to Petrefaction, and dispose the transuding Water to shoot and coagulate into Stone, so as continually to fortifie, and, if need were, to consolidate any breach or flaw in the Concave Surface of the Shell.
And this perhaps may not without Reason be suppos'd to be the final Cause of the admixture of the Magnetical Matter in the Mass of the Terrestrial parts of our Globe, viz. To make good and maintain the Concave Arch of this Shell: For by what the Excellent Mr. Newton has shewn in his Principia Philosophiæ, it will follow, that according to the general Principle of Gravity, visible throughout the whole Universe, all those Particles that by length of time, or otherwise, shall moulder away, or become loose on the Concave Surface of the External Sphere, would fall in, and with great force descend on the Internal, unless those Particles were of another sort of Matter capable by their stronger tendency to each other, to suspend the force of Gravity; but we know no other Substances capable of supporting each other by their mutual Attraction but the Magnetical, and these we see miraculously to perform that Office, even where the Power of Gravity has its full effect, much more within the Globe where it is weaker. Why then may we not suppose these said Arches to be lin'd throughout with a Magnetical Matter, or rather to be one great Concave Magnet, whose two Poles are the Poles we have before observ'd to be fixt in the Surface of our Globe.
Another Argument, favouring this Hypothesis, is drawn from a Proposition of the same Mr. Newton, where he determines the force wherewith the Moon moves the Sea in producing the Tides: His Words are, Densitas Lunæ est ad densitatem Terra ut 680 ad 387 seu 9 ad 5 quamproximé. Est igitur corpus Lunæ densius ac magis terrestre quam Terra nostra, p. 466. Now if the Moon be more solid than the Earth, as 9 to 5, why may we not reasonably suppose the Moon, being a small Body, and a secondary Planet, to be solid Earth, Water, Stone, and this Globe to consist of the same Materials, only four Ninths thereof to be Cavity, within and between the Internal Spheres; which I would render not improbable.
To those that shall enquire of what use these included Globes can be, it must be allow'd, that they can be of very little service to the Inhabitants of this outward World, nor can the Sun be serviceable to them, either with his Light or Heat. But since it is now taken for granted, that the Earth is one of the Planets, and they all are with Reason suppos'd Habitable, though we are not able to define by what sort of Animals; and since we see all the parts of the Creation abound with Animate Beings, as the Air with Birds and Flies, the Water with the numerous varieties of Fish, and the very Earth with Reptiles of so many sorts; all whose ways of Living would be to us incredible did not daily Experience teach us. Why then should we think it strange that the prodigious Mass of Matter, whereof this Globe does consist, should be capable of some other improvement than barely to serve to support its Surface? Why may not we rather suppose that the exceeding small quantity of solid Matter, in respect of the fluid Æther, is so dispos'd by the Almighty Wisdom, as to yield as great a Surface for the use of living Creatures, as can consist with the conveniency and security of the whole? We our selves, in Cities where we are pressed for Room, commonly build many Stories one over the other, and thereby accommodate a much greater multitude of Inhabitants.
But still it will be said, That without Light there can be no living, and therefore all this apparatus of our inward Globes must be useless: To this I Answer, That there are many ways of producing Light which we are wholly ignorant of; the Medium it self may be always luminous after the manner of our Ignes fatui. The Concave Arches may in several places shine with such a Substance as invests the Surface of the Sun; nor can we, without a boldness unbecoming a Philosopher, adventure to assert the impossibility of peculiar Luminaries below, of which we have no sort of Idea. I am sure the Poets Virgil and Claudian have gone before me in this Thought, inlightning their Elysian Fields with Sun and Stars proper to those infernal, or rather internal Regions. Virg. Æneid. 6.
Largior hic compos Æther & lumine vestit Purpureo; Solemque suum sua Sidera norunt.
And Claudian lib 2. De Raptu Proserpinæ.
Amissum ne crede diem, sunt altera nobis Sidera, sunt orbes alii, luménque videbis Purius, Elysiumque magis mirabere Solem.
And though this be not to be esteem'd as an Argument, yet I may take the liberty I see others do, to quote the Poets when it makes for my purpose.
Lastly, To explain yet farther what I mean, I have adventur'd to adjoin the following Scheme, (Tab. 1. Fig. 3) wherein the Earth is represented by the outward Circle, and the three inward Circles are made nearly proportionable to the Magnitudes of the Planets Venus, Mars and Mercury, all which may be included within the Globe of Earth, and all the Arches more than sufficiently strong to bear their weight. The Concave of each Arch, which is shaded differently from the rest, I suppose to be made up of Magnetical Matter; and the whole to turn about the same common Axis pp, only with this difference, that the Outer Sphere still moves somewhat faster than the Inner. Thus the Diameter of the Earth being about eight thousand English Miles, I allow five hundred Miles for the thickness of its Shell, and another space of five hundred Miles for a Medium between, capable of an immense Atmosphere for the use of the Globe of Venus: Venus again I give a Shell of the same thickness, and leave as great a space between her Concave and Mars; so likewise from Mars to Mercury, which latter Ball we will suppose solid, and about two thousand Miles Diameter. Thus I have shew'd a possibility of a much more ample Creation, than has hitherto been imagin'd; and if this seem strange to those that are unacquainted with the Magnetical System, it is hop'd that all such will endeavour, first, to inform themselves of the Matter of Fact, and then try if they can find out a more simple Hypothesis, at least a less absurd, even in their own Opinions. And whereas I have adventur'd to make these Subterraneous Orbs capable of being Inhabited, 'twas done designedly for the sake of those who will be apt to ask cui bono, and with whom Arguments drawn from Final Causes prevail much. If this short Essay shall find a kind Acceptance, I shall be encourag'd to enquire farther, and to Polish this rough Draft of a Notion till hitherto not so much as started in the World, and of which we could have no Intimation from any other of the Phænomena of Nature.