Chapter IV: Letter THE SECOND (1)

_Concerning the Nature of Mathematical Certainty, and the various Degrees of Moral Probability proper for Conjecture._

_SIR_,

You know how much I am an Enemy to the taking of any thing for granted, merely because a Person of reputed Judgment, has been heard to say, _it absolutely is so_; an _Ipse dixit_, and implicit Faith in some Cases, may be both necessary and useful; but here, in Astronomy, I mean, every Man's Reason, by the Help of a very little Mathematicks, is able to bring wonderful Truths to Light without them; and Truths not only of the highest Importance to every Individual, but of a great and common Consequence to all Mankind: And as such, in all Ages of the World, have been judged worthy to be enquired into, by the best and wisest of Philosophers.

You are likewise very sensible how far the human Understanding is even at the best, from being infallible, and don't want to be told, how difficult it is in a Subject of this Nature to arrive at any tolerable Degree of Certainty, which before the Days of the sagacious _Euclid_, and the penetrating _Archimedes_, was a Thing not to be expected. And many things which were then but barely Objects of Conjecture and Probability, have since been demonstrated to be infallibly true. Time and Observation will undoubtedly, at last, discover every thing to us necessary to our Natures, and proper for us to know. As a Proof of which, we see human Wisdom daily increases; and while a Capacity continues to make ourselves still more acquainted with the manifest Wisdom and Power of God in the Works of his Creation, who is to tell us where to stop our Enquiries? Or who is so impious to set Bounds to a Science, which so evidently spreads through all Infinity, the Attributes of God, and an eternal Basis for future Hope?

This Branch, or rather Body of Astronomy, I believe you will find to be quite new; and though evident Truths, are the principal Thing to be regarded in it, yet as being in its infant State, where lineal Demonstration fails, as in some Cases it cannot be otherwise, I hope you will give me Leave to make use of a weaker Way of Reasoning, to convince you of the Point in Dispute, I mean of that by the Analogy of known and natural Things.

I shall be extremely unwilling to affirm any thing for a _Fact_, or Truth, without hearing, if not the real Evidence, at least a plausible Reason, next to a Conviction, or moral Certainty, along with it; and therefore I will here endeavour to explain to you what I mean by moral Certainty and also by mathematical Proof.

Mathematical Proof, or Certainty, proper for Conjectures, may, to almost every Capacity, be illustrated as follows:

Suppose you had accidentally found a very small Part of a visibly broken Medallion, with nothing more express upon it, than what is represented at _Fig._ 1. _Plate_ I. a Person totally unacquainted with the mathematical Sciences, we may naturally conclude, would not be able to make any thing of it, or in the least comprehend what it originally was, or meant; but if an Astronomer should chance to see it, who of course we are to suppose knew the Order and Proportion of the planetary Orbits, he would immediately conclude, and with great Probability, on the Side of his Conjectures, that it might be Part of a Medal representing the Solar System. In such a Case may we not very naturally suppose he would reason thus?

The Arches A and B seem to be Portions of the respective Orbits of _Saturn_ and _Jupiter_, and what may lead us to believe, that they are really so, and Part of the Solar System, is the oblique Curve C, which looks not unlike the Trajectory of a Comet.

This surely would be far from an irrational Conjecture, and consequently in some Degree probable: But this is not sufficient you'll say; To prove it we must have farther recourse to the Mathematicks, and a Mathematician would immediately thus demonstrate it to be true.

First, by compleating the Circles geometrically from the fourth Book of _Euclid_, by the Assistance of any three Points E. F. G. the original Figure will be restored, as at _Fig. 2._ And secondly, by assuming any two Points, as F, E in the Curve C, if admitted a Parabola, by a well-known Problem in Conic Sections the Heliocentric Portion X. Y. Z. will easily be projected and shewn, as in _Fig. 3._ Lastly, join this in Position to the former, and it will justly supply the Orbit, or Path of some one of the Comets; and if required, even what Comet may be discovered by comparing the Perihelion Distance Y. S. with their general Elements or Theories, in Dr. Hally's _Synopsis_ of the Motion of these Bodies. And if a farther Confirmation of the Truth of these Conjectures were wanting, the small concentric Circles at D would now be allowed beyond a Contradiction, to represent the secondary Orbits of _Saturn_; and thus the first Presumption being carried thro' several corroborating Degrees of Probability, almost past a Dispute, would become a mathematical Certainty; and the above imperfect Piece of Medallion, would evidently appear beyond a Contradiction to be Part of a Representation of the said solar System, and such as is shewn in _Plate_ II. Q. E. D. Thus in many Cases, it often happens, that from a very small Part of _orbicular Things_, we are able to determine the Form and Direction of the Whole: And hence you may conceive it no very difficult Task to a Mathematician, to describe the Orbits of all the Planets in the solar System, though he had never observed them but in one and the same Sign of the _Zodiack_; thus far I have thought it would not be amiss to explain to you the Nature of those Steps, by which we arrive at moral Certainty, and where the Subject will admit of it, Mathematical Conviction, which will not a little contribute to strengthen many of the Arguments hereafter made use of, and in some Degree serve to supply the Place of Proof, where infallible Demonstration cannot from the Nature of the Thing be discovered.

But besides the indisputable Principles of Geometry, the universal Law of Analogy and Similitude of things, have a Privilege to assist us, in Conjectures relating to the heavenly Bodies, and though not of equal Force with the former, is often as conclusive as the Subject requires. This sort of probable Evidence (as Dr. _Butler_ observes,) is essentially distinguished from "Demonstrative by this, that it admits of Degrees; and of all Variety of them, from the highest moral Certainty to the very lowest Presumption; and that which chiefly constitutes Probability, is expressed in the Word _Likely_, or Natural Likeness, as to State or Being." This general Way of arguing, I think, is allowed to be evidently natural, just and conclusive, and unquestionably to have its Weight in various Degrees, towards determining our Judgment: For Instance, should any ignorant Person, endowed with rational Principles, cut open a _Pomegranate_ of the natural Growth of _England_, and finding it full of small Globules, or Kernels, upon being presented with an every way similar Fruit, said to be the Produce of _Italy_, doubt of its being of the same Nature, and composed of like globular Seeds within; here indeed would be no mathematical Evidence to assist the Judgment, the Object of Proof being invisible, but sure from the external Similitude, the strongest Probability of their being also internally the same. Again,

Is it natural to suppose, that the first Person who found a _Lark's_ Nest, and in it several of the Female's Eggs, should have any Apprehensions of finding none in the _Nightingale's_, only because he had never seen one before, I believe the most illiterate Person of the earliest Ages, who had Curiosity enough for such a Search, would be greatly disappointed in such a Case, and far from concluding that the _Nightingale_ had none. Farther, should any one who had seen several Sorts of Fish taken out of the River _Thames_, or out of the _Nyle_, have any sort of Suspicion that he should find no such Creatures in the _Seine_ or the _Ganges_, though it should be allowed that he had never seen any such Creatures that were known to come from thence. Ocular Demonstration, in such a Case, would sure be unnecessary, and an Evidence of the first, I believe would be abundantly sufficient to convince us of what we ought to look for at least in the last: But then the Fishes of different Seas, and of Rivers are not of the same Species you'll say; but as it were infinitely diversified through all the aqueous World, this is, and must be granted, and alike Variety of _Species_ must also be granted, in the former Case of the Birds: But no Objection can possibly arise from any such Diversity, since we don't pretend to say, nor is it at all necessary, that the Beings in the sidereal Planets should be every where the same with these of our solar System, a Variety must every where be admitted, and will always be admired, where the Work is Nature's, and the Design God's.

All then that I here pretend to argue for, is a Universality of rational Creatures to people Infinity, or rather such Parts of the Creation, as from the Analogy and Nature of Things, we judge to be habitable Seats for Beings, not unlike the mortal human.

Every Animal, and every Vegetable, that, as it were, naturally exists by the Virtues, Properties, or Laws of the mineral Kingdom, has something of a secondary Nature, depending upon it as a Principle; and to say that the Stars, which are a certain visible sort of Cotemporaries in Space with the Sun, have no like planetary Bodies with ours moving round them, because we cannot possibly see them, is no less absurd and ridiculous, than to argue, that we can have no Reason to expect to find, in the proper Season, Grapes upon every Vine--Figs upon every Tree--Roses upon every Bush--only because some of them are at such a Distance, that neither Rose, Fig or Grape, can be discovered by the Eye.

This sort of Reasoning, though some perhaps may neglect it, I am perswaded you will look upon as abundantly sufficient for Things out of the Reach of Science to determine; and that the collective Body of Stars have not been discovered, to be together a proper Subject for such Conjectures before, can surely only proceed from the Want of Time, necessary to compleat the Observations proper for a Foundation to build such an Hypothesis, or Theory upon. This is the great Article in which the Moderns have so much, and ever will have, an Advantage over the Antients. And hence it will appear, That

The Improvements and Discoveries of latter Ages are not at all owing to the greater Capacity of the Moderns, but from the Advantages received, or arising from the Inventions and Progress made by the Ancients. We at first in a manner walked by their Leading-strings, and though many of them now are broke, or useless, none can deny, but that formerly they were of great Advantage in promoting and directing philosophical Enquiries.

In an Assembly of the most eminent Men of all Ages, if we may suppose such a Conference amongst the illustrious Dead, on Purpose to deliver their several Sentiments familiarly together, on the most interesting Subjects of natural Knowledge, who would not lament the Disadvantages, poor old _Thales_, an _Hipparchus_, or a _Ptolomy_, would lie under, who had nothing but the Eye of Reason to direct them, in Opposition to the Judgment of a _Brahe_, or a _æ_, who reaped so much Benefit from their compound Opticks? But on the other hand, perhaps if the solar System, was the Topic of Discourse, a [H]_Pythagorean_ might very pertinently say to a _Newtonian_, "You have not gone much farther in the Light with our Direction, than we did in the Dark alone; for you are still roving round the same Circles." Much might be said upon this Head; but I believe it would be a difficult Matter to do Justice to all Parties: So here I intend to leave them, only must observe, that Posterity will always have the Advantage over their Predecessors; and that After-ages, in all Probability, will reap so great a Benefit from the Invention and Improvement of Fluxions, that scarce any thing, which is the immediate Object of such Enquiry, will long lie concealed from a true mathematical Genius.

[Footnote H: The true System of the Planets have been discovered above two thousand Years.]

For this, in which he has surpassed all the Antients, and greatly advanced the philosophical Sciences, the World is indebted to Sir _Isaac Newton_.

But as many of his Discoveries, such as relate particularly to the Laws of the planetary System, are but as so many Confirmations of the Conjectures and Imaginations of Astronomers and Philosophers before him, it perhaps will not be amiss to acquaint you a little with the Astronomy of the Antients concerning the Universe. And before I proceed to those of my own, shew you in the first Place how far their Speculations in the visible Creation have been carried; and with these I shall conclude this preparatory Epistle.

The Universe, or mundane Space, by which the Antients comprehend all Creation, has, from time to time, according to the Progress of Science, come under a sort of Necessity of being variously modell'd agreeable to the Opinion of the several Authors, who have judged themselves wise enough to write upon it with a mathematical Foundation: And the cosmical System, by which is meant the Co-ordination of its constituent Parts has undergone almost as many Changes as its Elements are even capable of; every Age of the World, as Knowledge has increased, either from improved Imagination, or repeated Observations, producing something new concerning it.

Milton, no doubt, had all this Diversity of Opinions in View, as appears from his supposed Pre-knowledge of _Raphael_, in the following Passage, _Book._ VIII.

Hereafter, when they come to model Heaven,
And calculate the Stars, how they will weild
The mighty Frame! how build, unbuild, contrive
To save Appearances, how gird the Sphere
With centric and eccentric scribbl'd o'er;
Cycle, and Epicycle, Orb in Orb.

But the following Synopsis, I believe, will abundantly convince you that from certain Observations only, we ought to form all our Notions of it, if we either hope to arrive at Truth, or expect our Ideas should be supported by Reason.

Aristotle was of Opinion, that the Universe, or Heaven, was all one World, and St. Chrysostom, Tertullian, St. Bonaventure, Tycho Brahe, Longomontanus, Kepler, Bulialdus and Tellez, were of an united Opinion, that this one Heaven, or Universe, was all sidereal and fluid. But Aegidius, Hurtadus, Cisalpinus, and Aversa, believing the same Heaven with them to be all one World, and that sidereal, yet on the contrary held it to be solid.

Clemens, Acacius, Theodoret, Anastasius, Synaita, Procopius, Suidus, S. Bruno, and Claudianus Mamertus, supposed the universal mundane Space as divided into two Heavens, namely,

The Empyræum created the first Day,
And the Firmament created the second Day.

Two Heavens were also held by Justin Martyr, the one sidereal, and the other aerial. The first supposed by St. Gregory Nyssene, to be that of the fixed Stars, and the last, that of the Planets. But _Mastrius_ and _Bellutus_, though agreeing in the Number of Heavens, calls one the _*Primum Mobile_, and the other, the Starry Heaven.

Farther, St. Basil, St. Ambrose, Damascene, Cassiodorus, Genebrardus, Suarez, Tannerus, Hurtadus, Oviedus, Tellez, and Borrus, distinguished the Universe as divided into three Portions, or Heavens.

Or, as _Cajetan_. _Tho. Aquinas._

The first called the Empyræum, Watery,
The second supposed Sidereal, Sidereal, Watery,
And the last of all, Aerial. Aerial, Sidereal.

Again, St. _Athanasius_ adds to those of the fix'd Stars, the Planets, and the Air, that of the _Empyræum_, and makes in all four Heavens.

But as the Number of the Heavens thus increases, and will become subdivided in the subsequent Account of them, to give you a better Idea of the Order of these celestial Portions of the mundane Space, it will not be amiss to form what remains of them into regular Sections of their proper Spheres and Systems.

See _Plate_ III. in which Figure, the first represents a Section of the cosmical Theory of _Oviedus_ and _Ricciolus_: Both consisting of five Heavens, _viz._

By _Oviedus_, By _Ricciolus_,
sidereal and solid. sidereal and fluid.

The fixed Stars, A _Empyræum_, G
_Saturn_, B The Water, F
_Jupiter_, C The fixed Stars, A
_Sol_, with ♂ ☿ and ♀ included, D The Planets, H
The Moon. E The Air. I

_Fig._ II. represents that of venerable _Bede_ and _Rabanus_, _viz._ of Seven Heavens.

And according to _Bede_ But by _Rabanus_,
composed of
The Air, P The Atmosphere,
The Æther, O The upper Air,
_Olympus_, N The inferior Fire,
The Element of Fire, M The superior Fire,
The Firmament, A Sphere of the fixed Stars,
The Angelical Region, L The Crystalline Heaven,
Realm of the Trinity. K The _Empyræum_.

Fig. III. Represents the Hypotheses of _Eudoxus_, _Plato_, _Calippus_, _Cicero_, _Riccius_, _Philo_, _Remigius_, _Aben-Ezra_, _Carthusianus_, _Lyranus_, _Tostatus_, _Brugensis_, _Orontius_, _Cremoninus_, _Philalethæus_, _Amicus_, and _Ruvius_; also the _Babylonians_ and _Egyptians_.

Consisting of Eight Heavens,

All Sidereal, _viz._ The Sphere of the fix'd Stars, and those of the Seven Planets.

Fig. IV. is that of _Macrobius_, _Haly Alpetragius_, _Rabbi-Josue_, _Rabbi Moyses_, _Scotus_, _Abraham Zagutus_, _Sacroboscus_, _Claromontius_, _Avigra_, and _Arraiga_.

All of Nine Heavens,

Comprehend a _Primum Mobile_ Q, or, according to _Arriaga_, a solid _Empyræum_. The Sphere, of fixed Stars A, and the seven Regions of the solar Planets.

Fig. V. is that of the great _Alphonsus_, _Fernelius_, _Regiomontanus_, _Amicus_, _Maurolycus_ and _Langius_; also of _Azabel_, _Thebit_, and _Isaac Israelita_; and likewise of _Gulielmus Parisiensis_, and _Johannes Antonius Delphinus_.

Consisting of Ten Heavens, made up of

A _Primum Mobile_ S _Empyræum_.
A Sphere of _Tripidation_ in Longitude R _Primum Mobile_.
The Sphere of the fixed Stars A
And those of the seven solar Planets within.

_Note_, Some Authors place the Sphere of _Tripidation_ in Longitude below that of the _Aplain_, or Eighth Sphere.

Lastly, Fig. VI. is the Heaven of _Petrus Alliacensis_, the College of _Conimbra_, _Martinensis_, (and sometime) of _Clavius_; and also _Johannes Warnerus_, _Leopoldus de Austriâ_, _Johannes Antonius Maginus_; and lastly, of _Clavius_.

In all Eleven Heavens containing,

T A _Primum Mobile_, or, as others say, an _Empyræum_.
V A Sphere of Libration in Latitude.
W A Sphere of Libration in Longitude.
A The Sphere of the fixed Stars, and those of the Planets.

The Seven Planetary orbits.
]

Thus you see how many various Opinions have from time to time been embraced concerning the Fabric and Formation of the visible Universe; all of which are now and have long been exploded; and although at first advanced by Men of the greatest Learning, and of the deepest Penetration in natural Knowledge, it does not appear from any one of their Opinions, that they had any the least Notion of infinite Space, but as it were confined the Divine Being to their limited Notions, as one may say in an Egg-shell. If therefore what I shall hereafter advance, extend so far without the known Creation, that you can possibly conceive no Bounds to the Works of infinite Wisdom and Power, I hope you will be in no Danger of looking upon it as more ridiculous, or absurd, than what so many of the wisest Men of every Age have thought proper to attempt, and have judged worthy of their Attention so long before me. If any thing less so, I shall think myself happy enough in having broke, or rather passed the narrow Limits to which the Creation has for so many Years been confined, in hopes of tempting Men of greater Talents to look up wards, and pursue so noble a Subject as far as the human Understanding is capable of comprehending it.

To the Opinions above might be added many more, particularly that of _Johannes Baptista Turrianus_, and _Fracastorius_, who increased the Number of Heavens to fourteen, _viz._ seven on each Side the _Aplané_.

But of this I have said enough; in my next I shall proceed to Matter better grounded,

_And am_, &c.

LETTER the THIRD.

_Concerning the Nature, Magnitude, and Motion of the Planetary Bodies round the Sun_, &c.

_SIR_,

The younger _Pliny_, if I remember right, somewhere says, that there is, or ought to be, a wide Difference betwixt writing to a Friend, and writing to the Publick: I have indeed pleased myself with the one, but am far from thinking myself qualified for the other; I must therefore rather intreat you, though perhaps you cannot possibly overlook all my Faults as an Author, to excuse them at least in the Friend, and by such kind of unlimited Indulgence, you will give me a much greater Chance to do the Subject some Justice, though I own I despair in this first Attempt, to reconcile every thing I advance to your more cool and impartial Reasoning. But to the Business:

As I have no Ambition to have the Substance of my Theory more admired by you than understood, which is too often the Case in Works of this Nature, I must beg leave to repeat to you Part of a former Discourse, which will refresh in your Ideas the principal Laws of the System of our Sun, and make you properly acquainted with such Things as are necessary to be known in the now-established Astronomy of [I]_Copernicus_, &c. before I proceed to any new Matter.

[Footnote I: Nicolaus Copernicus, stiled by _Bulialdus_, _Vir absolutæ subtilitatis_, was a Native of _Thorn_ in _Polish Prussia_, and Canon of the Church of _Frawenburgh_; he was Scholar to _Dominicus Maria_ of _Ferrara_, to whom he was Assistant in his astronomical Observations at _Bologne_, and Professor of the Mathematicks at _Rome_, in his noble Work, _De Revolutionibus Orbium Cælestium_; he fortunately revived, happily united, and formed into an Hypothesis of his own, the several Opinions of _Philolaus_, _Heraclides Ponticus_, and _Ecphantus Pythagoreus_, _viz._ after the Opinion of _Philolaus_ he made the Earth to move about the Sun, as the Center of its annual Motion; and according to _Heraclides_ and _Ecphantus_, he likewise gave it a diurnal Rotation round its own Axis: Which System has withstood all Opposition; and as _Ricciolus_, (though a Dissenter from it) observes, _Per damna, per cædes, ab ipso sumit opes, animumque ferro._]

The Sun, you are not to learn, is the reputed Center of our _Planetary System_, and may remember, that the Earth on which we live, and these five following _Erratic Stars_, viz. Saturn, Jupiter, Mars, Venus and Mercury, have been demonstrated to move round him in the Order and Manner following.

_Saturn_ is found to complete one Revolution round the Sun in twenty-nine Years, one hundred and seventy-four Days, six Hours, and thirty-six Minutes; at the Distance of about seven hundred and seventy-seven Millions of Miles. _Jupiter_ performs a like Revolution in about eleven Years, three hundred and seventeen Days, twelve Hours, and twenty Minutes; distant from the Sun about four hundred and twenty-four Millions of Miles. _Mars_ compleats his Circuit in one Year, three hundred and twenty-one Days, twenty-three Hours, and twenty-seven Minutes; and his mean Distance is about one hundred and twenty-three Millions of Miles.

These three are called superior Planets, as being farther from the Sun than the Earth, and circumscribing its Orbit.

The Earth circumambulates her Orbit in one solar Year, _viz._ in three hundred and sixty-five Days, five Hours, forty-eight Minutes, and fifty-seven Seconds; at the mean Distance of eighty-one Millions of Miles.

The Radius of _Venus's_ Orbit is about fifty-nine Millions of Miles; and that of _Mercury_ nearly thirty-two Millions, _ditto_.

The Heliocentric Revolution of _Venus_, is made in two hundred and twenty-four Days, sixteen Hours, forty-nine Minutes, and twenty-seven Seconds; and that of _Mercury_, in eighty-seven Days, twenty-three Hours, fifteen Minutes, and fifty-four Seconds. These two last Planets are called inferior Ones, as being circumscribed by the Earth.

The Diameter of the Sun being demonstrated to be nearly seven hundred and sixty-three thousand Miles:

The proportional Magnitudes of all the above Planets will be found nearly as follows, _viz._

The Diameter of the Globe,
Of _Mercury_ 4,240 }
_Venus_ 7,900 }
the Earth 7,970 } Miles.
_Mars_ 4,440 }
_Jupiter_ 81,000 }
and _Saturn_ 61,000 }

Thus much I have thought proper to premise, and for your immediate Inspection, have added the following Schemes, that nothing may be wanting to give a general Idea of the Order of the celestial Bodies in our own System, before I attempt to lead you through the neighbouring Regions of the Stars to the more remote Tracts of Infinity.

PLATE IV.

Is a true Delineation of the solar System, with the Trajectories of three of the principal Comets, whose Periods and Orbits have been accurately determined, and are represented in their true Proportion and Position to one another, and the Order of the Planets round the Sun, marked with their respective Characters, _viz._ ♄, for _Saturn_, ♃, _Jupiter_, ♂, _Mars_, ♁, the Earth, ♀, _Venus_, and ☿, _Mercury_. The Scale being nearly five hundred and eighteen Millions of Miles to an Inch.

PLATE V.

Is a true Projection of the System of the known Comets; in which are represented nine of the chief Trajectories, from their _Aphelii_ to their _Perihelii_, all in just Proportion and Position to the Orbits of _Saturn_ and _Jupiter_, which are also represented by the two concentric Circles, supposed to be drawn round the Sun as their Center.

The Ellipsis, or Trajectory, marked A, shews the Position and Path of the Comet which appeared in the Year 1684, whose Period is supposed to be about fifty Years, and has been observed within the Region of the Planets once.

That mark'd B, is the Way of the Comet of 1682;
The Period conjectured to be about seventy-five
Years and a half, and has been observed thrice.
C, Way of the Comet of 1337;
The Period about 100 Years, observed once.
D, That of the Comet of 1661;
The Period about 129 Years, observed twice.
E, Tract of the Comet of 1618;
The Period about 160 Years, observed once.
F, Way of the Comet of 1677;
The Period about 200 Years, observed once.
G, Way of the Comet of 1744;
The Period about 300 Years, observed once.
H, Way of the Comet of 1665;
The Period about 400 Years, observed once.
I, Way of the Comet of 1680;
The Period about 575 Years, observed thrice.

The Scale of this System is equal to one Third of the former.

Here I must observe to you, as a Thing I judge may prove of great Consequence with regard to the System of Comets, which is as yet very imperfect: That I am strongly of Opinion, that the Comets in general, through all their respective Orbits, describe one common Area, that is to say, all their Orbits with regard to the Magnitude of their proper Planes, are mathematically equal to one another; which, if it once could be proved, and confirmed by Observation, the Theories of all the Comets that have been justly observed, might easily be perfected, and their Periods at once determined, which now we can only guess at, or may wait whole Ages for more Certainty of. What leads me to believe, that this may prove to be really the Case is this.

I find by Calculation, that the Orbits of the two last Comets, whose Elements have been most corrected by Sir _Isaac Newton_ and Dr. _Hally_, are to one another, according to their Numbers, nearly as [J]13 to [K]17, notwithstanding one of them is one of the most erratick that ever came under our Observation; and the other one of the most neighbouring to the Sun.

[Footnote J: 1316539,968282 Comet of 1680.]

[Footnote K: 1708155,4644 Comet of 1682.]

But it is well known to all Mathematicians, that the first of these Comets moved in so eccentric a Trajectory, that the least Error in its almost incredible Proximity to the Sun will produce a very sensible Difference in the Area of the Orbit: And accordingly, if we moderate the Perihelion Distance of this Comet, by making it but 1000 instead of [L]612, which is but increasing it a 1/35000th Part of the great Radius of the Orbit, (which is an Error every Astronomer will readily grant is very easily made) and we shall find the Orbits of the said two Comets to be exactly equal.

[Footnote L: The Number in Dr. _Hally's_ Synopsis.]

Further, I must inform you, that the Comet of 1682, which the above is compared with, seems to have been so accurately observed, that it does not appear to have altered its Perihelion Distance half a 68th Part in one intire Revolution. Now, if we can with any Show of Reason, and a Probability on our Side, bring the Areas of these two extream Comets, as I may call them, to an _Equality_, sure we may conclude, it is a Subject highly worthy to be more considered and enquired into.

PLATE VI.

Is a true Representation of the satellite Systems, proportionable to one another, and to the Orb of the Sun's Body, that a just Idea of the Distances of those secondary Planets, may be easier had from their respective primary ones.

S represents the solar Body with its Atmosphere. _Fig._ 1. is the System of _Saturn_ from the same Scale. _Fig._ 2. that of _Jupiter_ from _ditto_. And _Fig._ 3. the Orbit of the Moon round the Earth, in the same Proportion.

But as you can have but a very imperfect Idea of the Magnitude of these last Circles, with regard to the Body of the Earth or Moon,

PLATE VII.

Is a true Projection of their real Globes, at their proper Distance from each other, with their common Center of Gravity, and the Point and Line of equal Suspension betwixt them, _viz._

A, represents the Globe of the Earth.
B, that of the Moon.
C, Point, and C D, Line of equal Suspension betwixt them.
E, Common Center of Gravity, which describes the _Orbis Magnus_.
E, F, and B, G, is the Orbit of the Moon.

Farther, that nothing may be wanting to give a true Notion of the whole together,

PLATE VIII.

Is a proportional Drawing of all the primary and secondary Planets together, distinguished by their Characters, proper to attend a Globe of twelve Inches Diameter, such a one being supposed to represent the Sun.

PLATE IX.

Is an exact Scheme of the principal known Comets, in just Proportion, to the Globe of the Earth represented at A, with the Nucleus, and Part of the Tail of the Comet of 1680, B, as it was observed in its Assent from the Sun, _viz._ _a a_ the Comet's natural Atmosphere, _z z z_, the _Denser Matter_ winding itself into the Axis of the Train _x x_, the inflam'd Atmosphere and Tail dilated near the Sun. C, represents the Ball of the Comet of 1682, D, that of 1665, E, that of 1742, and F, the Head of the Comet of 1744.

And again, that you may have some Notion of the apparent Magnitudes of all these Planets and Comets, _&c._ as they appear at the Earth,

PLATE X.

Represents the Sun and Moon in the just Proportion of their mean Diameters, with two of the Comets A and B, and the five erratick Planets, as they are observed at the Earth, in a middle State of their Distances from it.

For a more full and particular Description of all the Parts of the solar System, and of the home Elements of Astronomy in general, I refer you to my _Clavis Cœlestis_, &c. where every thing concerning the Planets, Comets, and Stars; and their real and apparent Motions, are at large represented, explained, and accounted for, for the Benefit of such as have not made the Mathematicks their regular Study.

Now, to convince you that the Planets are all in their own Nature no other than dark opaque Bodies, reflecting only the borrowed Light of the Sun, I must recommend to your Observation, this natural and simple Experiment, which almost any Opportunity of seeing the _Moon_ a little before the Full, will put into your Power to make; but best and easiest when the Sun is in any of the North Signs, _i. e._ in _Summer_.

At such a time, the Sun being near setting, the Moon will appear in the eastern Hemisphere; and if there be any bright Clouds northward, or southward near her, you will plainly perceive, that the _Light_ of the one is of the same Nature with that of the other; I mean the Light of the Moon, and that of the Cloud. To me there never appeared any Difference at all; and I am perswaded, were you to make but two or three Observations of this kind, which is from Nature itself, a sort of ocular Demonstration, you cannot fail of being convinced, that the Moon's Light, such as it is, without Heat, can possibly proceed from no other Cause than that which illumines the Cloud: For if the Clouds, whose Composition we know to be but a thin light Fluid, formed of condensed Vapours only, is capable of remitting so great a Lustre, how much more may we not allow the Moon, which, Length of Time, and many other Circumstances, have long confirmed to be a durable and solid Body.

The Increase of her Lustre, indeed, during the Absence of the Sun from us, to a less penetrating Genius than your's, may possibly afford some trifling Ground of Objection to the above Conclusions, as being drawn from the Phænomena of Day-light only; by reason in the Night, we have no Clouds in equal Circumstances to compare with her.

But this I need not tell you, is all owing to her being seen through a darker Medium, and not to any real Increase of natural Light emitted from the Sun. As a Proof of which, were it necessary, you need only, shut out the Rays of the Atmosphere, by the Help of a sufficiently long Tube; and the Moon, or any other celestial Body, will appear through it, as bright in the Day-time as in the Night.

Thus all light Bodies of inferior Lustre, whether shining by their own natural Radiences, or by a borrowed Reflection, partake of the same Advantage, when removed from the more potent Influence of a superior one; and hence it is, that the [M]_Aura Ætherea_ shines out most manifest, when the Body of the Sun himself is hid, the Stars, and the _Via Lactea_ most lively and numerous in the Absence of the Moon, and those Exhalations, or Meteors, vulgarly called Falling-stars, become only visible (like Glow-worms) in the Night.

[Footnote M: An _Helios_, or golden Light, always attending the Sun, and supposed to spread itself all round his Body in the Direction of his Equator, was very visible during the total Darkness of the Eclipse of 1715, and may be always seen about the Autumnal Equinox.]

Here it may not be improper to tell you, that the Clouds are to us in effect no other than as so many Moons, whereby we have our artificial Day prolonged to us several Hours after the Sun is set, and likewise produced as much sooner before he rises; and were they to ascend by still stronger Power of Exhalation to an Elevation, all round the Atmosphere, so as to form a Sphere equal to four Times the Globe of the Earth, there would then be no such Thing as real nocturnal Darkness to any Part of the World.

The lunar Light then we may very justly conclude, proceeds originally from the Sun: And notwithstanding many more Arguments might be drawn from the Demonstration of her Phases, Eclipses, &_c._ to prove it, yet none of them need here be added, to what has been already said, to convince you of the Truth of it. This being granted, let us now consider what Effect this, or a like Quantity of borrowed Light, would have, when removed to a much greater Distance.

I may, I think, suppose, that you know so much of Opticks as to understand, that all visible Objects apparently decrease in Magnitude, as their Distance from the Eye increases. Consequently, that, if the Moon's Orbit was placed as far again from the Earth as it really is, her Globe, or rather _Disk_, would then seem to be but half as big as to us she now appears to be, and of course still farther, were she placed at ten times the Distance she is known to revolve at, her apparent Diameter would be reduced to a tenth Part only of what it now appears to be in her present Orbit, that is, one hundred Times less in visible Magnitude than her neighbouring Disk is found to be where it now is seen. And such, but something less, the two Planets _Venus_ and _Jupiter_, which are frequently, in their Turns, our Morning and Evening Stars, appear to be through a common Telescope.

Now these two Planets, together with the other three, which we find moving in regular Orbits round the Sun, are all found subject to the same [N]Changes of _Phænomena_, in their various Aspects with the Sun; and who can doubt but that they are all of the same or like Nature? But you'll say, perhaps, how are we sure that _Venus_ and _Jupiter_ have no native Light of their own, since many of the ancient Philosophers, and in particular _Anaximander_, allowed even the Moon to have some; and besides, in Philosophy, as well as in Logick, I think you hold there is no proving a Negative, at least at such a Distance.

[Footnote N: _Venus_ and _Mercury_ in every Heliocentrick Revolution, perform all the Changes of our Moon in a like Gradation and Defection of Light, both horned and gibos'd.]

To make you conceive the Impossibility of such a Light, and next to a Demonstration, convince you of the Unnaturalness of such a Supposition, I must put you in mind, that some time ago, when I was last in the Country with you, I think it was about the latter End of Autumn, near the Winter Solstice, as we were walking one Evening, I bid you take notice of the Moon, which was then near setting, and about two Days old. You may remember, her whole Globe appeared to us very conspicuously within a manifest Circle. You immediately told me, that that kind of Phænomenon the Country People called a _Stork_, or the old Moon in the new one's Arms. This I then endeavoured to explain to you, and I think made you sensible it was intirely an Effect of the Earth's, and an Appearance always to be expected at that Time of the Year. The Earth being then in the State of a Full-Moon to that Part of the lunar Orbit, and near her Perihelion, at which time, the Earth sends back a Reflection to the [O]Moon twenty-five times more potent than that of the Moon to us.

[Footnote O: Their Diameters being nearly as 1 to 5.]

Now the Planet _Venus_, from undeniable Principles of Geometry, is allowed to be nearly such another Globe as the Earth is; and since the Earth, as I have just now related, is found to reflect much more Light to the Moon, by reason of her superior Magnitude, than the Moon can possibly reverberate to Earth again; and since also 'tis plain, the Earth has no Light of its own, why then should we imagine _Venus_ to be endowed with a Lustre, which we can prove to be no more than a similar Body, and governed by the same Laws as the Earth is?

_Anaximander's_ Mistake, in supposing the Moon in some small Degree a radiant Body of itself, lay, in not considering, that the faint Illumination here described, and visible all over her Globe, soon after almost every Conjunction with the Sun; and probably in Eclipses, also proceeded from the Earth; but the thing I think is too evident to expect any sort of Contradiction, therefore I hope you will admit it as a Truth, and consequently take it for granted, that the planetary Bodies in general, are meer terrestrial, if not terraqueous Bodies, such as this we live upon; which is the Thing I have chiefly in this Letter attempted to demonstrate, or have rather explained; and now I hope, for the future, you will receive the Idea of a Plurality of Worlds more favourably, and look upon astronomical Conjectures in a less ridiculous Light than you used to do, especially since you must allow, they give our unlimited Imaginations a like all endless Field of Contemplation, not only full of the wonderful Works of Nature, but also of a visible Providence.

I think I cannot conclude this Letter to you more properly, than with the following fine Lines of Mr. _Addison's_ from the _Spectator_, Vol. VI. No. 465, which I hope you are not so polite as to look upon as an unfashionable Quotation.

The spacious Firmament on High,
With all the blue ethereal Sky,
And spangl'd Heav'ns, a shining Frame,
Their great Original proclaim:
Th' unwearied Sun, from Day to Day,
Does his Creator's Pow'r display,
And publishes to ev'ry Land
The Work of an Almighty Hand.
Soon as the Ev'ning Shades prevail,
The Moon takes up the wond'rous Tale,
And nightly to the list'ning Earth,
Repeats the Story of her Birth:
Whilst all the Stars that round her burn,
And all the Planets in their Turn,
Confirm the Tidings as they roll,
And spread the Truth from Pole to Pole.
What though, in solemn Silence, all
Move round the Dark terrestrial Ball?
What tho' nor real Voice nor Sound
Amid their radiant Orbs be found?
In Reason's Ear, they all rejoice,
And utter forth a glorious Voice,
For ever singing, as they shine,
"_The Hand that made us is divine_."

_And am_, &c.

LETTER the FOURTH.

_Of the Nature of the heavenly Bodies continued, with the Opinions of the Antients concerning the Sun and Stars._

_SIR_,

You tell me you begin to be a tolerable good _Copernican_, and would now be glad to have my Opinion further upon the Nature of the Sun and Stars, with regard to the Suggestion of their being like Bodies of Fire. This you say will go a great Way towards confirming you in the Notion you have begun to embrace of a Plurality of Systems, and a much greater Multiplicity of Worlds than our little solar System can admit of. Besides, shewing in a very evident Light, that the Authorities cited in my first Letter are founded upon the clearest Reason.

_Anaxagoras_, you say, believed the Sun to be a Lump of red-hot Iron; _Euripides_ thought it a Clod of Gold; and others still more ridiculously have imagined it to be a dark Body, void of all Heat. That the Sun is a vast Body of blazing Matter, notwithstanding the various Opinions of those primitive Sages, will, I think, hardly admit of a Question: Since the known Warmth of his prolifick Beams, and the visible Effect of the Burning-glass, puts it quite out of the Power of our present Set of Senses, at least to argue against it; and how reasonably we may imagine the Stars to be all of the same or like Nature, will sufficiently appear from these following Considerations: First, it is well known to all Mathematicians, that any visible Object of any determined Magnitude may be reduced to the Appearance of [P]a physical Point, by removing the Eye of the Observer to a proper or proportionable Distance from it, within the finite View: And that the apparent Diameter of every luminous celestial Body, will always be diminished reciprocally, in Proportion to the Distance from the Eye, till they become altogether imperceptible.

[Footnote P: What is here meant by a physical Point, is a Point visible to the naked Eye, which human Art cannot divide; and so far it partakes of the Property of a mathematical one, which is only to be conceived, and not seen.]

Thus the Disk of the Sun, which appears to us at Earth under an Angle of about half a Degree, if seen from the Planet _Saturn_, would appear not much bigger than the Planet _Venus_ or _Jupiter_, in their most neighbouring Vicinity does to us; and consequently to an Eye placed in the Aphelion Point of the Orbit of the great _Comet_ of 1680, his apparent Diameter would be so reduced as to seem but little bigger than the largest of the Stars; and by the same Analogy, or Way of Reasoning, admitting Space and Distance infinite, which I humbly apprehend is not to be disputed, were all the Matter in the Universe united, and conglobed in one Mass, with respect to ocular Sensation, it might be diminished so near to a mathematical Punctum, as to be almost adequate to our Ideas of Nothing.

This to any tolerable Optician, must be an evident Conviction of the Truth of the modern Astronomy, which now universally allow all those radiant Bodies the Stars to be of the same Nature with the Sun; and that as certainly they are no other than vast Globes of blazing Matter, all undoubtedly shining by their own native Light.

But as you have often objected to what has been said of the Distance of the Stars in general, and may possibly from a Supposition, that they are, or may be, much nearer to us, infer, that their Light, like that of the Planets, may be also borrowed from the Sun, or from some other radiant Body, which, from the Nature of the Supposition, must of Consequence be invisible to us, I judge it will not be amiss to throw a few demonstrative Arguments in your Way, in order to lead you a little out of the Path of an early Prejudice, and draw you as it were by Degrees through the Dawn of astronomical Reasoning, out of your original Error, and rescue your Imagination from the false Notions imbibed from Phænomena only in your younger Years. This I guess cannot fail of reconciling you to this more rational Way of Thinking, and make you acquainted with Truths of much Consequence, which perhaps you have yet been an intire Stranger to. The grand _Deceptio Visus_, which I must first endeavour to remove, and which as a sort of Paradox in Nature, has, as I may say, imprisoned the Understanding of many superficial Reasoners, and in general all incurious Men, is this.

Most People are too apt to think originally, that as the Heavens appear to be a vast concave Hemisphere, that the Stars must of course, as of Consequence, be fixed there, like so many radiant Studs of Fire, of various Magnitudes; and take it for granted, chiefly designed for no other Purpose than to deck and adorn the Canopy of our Night. This was long ago the Opinion of _Thales_ the _Milesian_, and wants not the Authority of many of the Antients to back it. Others, in particular [Q]_Ptolomy_ of _Pelusium_ in _Africa_, who from his Experience in this Science, is called by some the Prince of Astronomers, believed them to be Loop-holes in the vast solid celestial Firmament, emitting the Light of the Crystalline Heaven through it to all within it. The famous _Diogenes_, Cotemporary with _Plato_, conceived them to be of the Nature of Pumice-stones, and inclined to an Opinion, that they were the _Spiracula_, or Breathing-holes of Heaven. _Anaxagoras_ thought them Stones snatched up from the Earth by the Rapidity of its Motion, and set on Fire in the upper Regions above the Moon.

[Footnote Q: _Ptolomy_ supposed two Heavens above that of the fixed Stars, which he called the eighth; _viz._ a ninth, the Crystalline, and a tenth the _Primum Mobile_. See Letter the second.

The sacred Sun, above the Waters rais'd,
Thro' Heav'ns eternal, brazen Portals blaz'd;
And wide o'er Earth diffus'd his chearing Ray,
To Gods and Men to give the golden Day.

Homer.
]

But how ridiculous and absurd all these Opinions and Conjectures really are, will easily appear, if we but once consider the Nature of an unbounded Æther, and the amazing Property of infinite Space.

This, with what has been said before, will not a little assist your Imagination towards conceiving the Reasonableness of the Notion modern Astronomers are now confirmed in, of their being absolutely so many burning Balls, and which was no doubt, many Years ago, the Opinion of _Manilius_, as is evident from these Lines in his Poem of the Sphere.

For how can we the rising Stars conceive
A casual Production; or believe
Of the chang'd Heav'ns the oft renascent State
_Sol's_[R]frequent Births, and his quotidian Fate.

Sherburne.

And again, in the same Poem:

The fiery Stars, and Æther that creates
Infinite Orbs, and others dissipates.

[Footnote R: _Xenophanes_ believed the Stars to be no other than Clouds set on Fire, quenched in the Day-time, and rekindled in the Night.]

_Zoroaster_, the first of all Philosophers we read of who studied the Stars, is reported to have believed them of a fiery Nature. _Empedocles_ judged them to be Fire æthereal, struck forth in its Secretion, and blazing in the upper Regions. _Plato_ thought them Fire, with the Mixture of other Elements as Cements. _Heraclides_ Worlds by themselves, of _Earth_, _Air_, and _Fire_; and _Aristotle_, simple Bodies of the Substance of Heaven, but more condensed.

But that I may not take up too much of your Time with Opinions that has been imbibed in the Infancy of Astronomy, and has long ago been exploded, I shall attempt but one Thing more to confirm your Sentiments in this new Doctrine.

First, that the Stars are all at a Distance, not to be determined by the utmost Perfection of human Art, is manifest from their having very little, or no sensible [S]Parallax; and consequently, that any one of them is absolutely bigger or less than another, from the simple Laws of Opticks, cannot possibly come under our Observation to be ascertained; but that they all of them may be nearly of the same Size or Solidity, is as impossible, with any Shew of Reason to deny, since it is a known Principle in Geometry, that all visible Objects naturally diminish, as has been said before, or are magnified in a certain Proportion to their Distance from the Eye; and hence we may conclude, and not without Reason in its strongest Light to support us, that the smallest Stars, to the very least Denomination, are only removed respectively more distant from the Observer's Station; and that at least this we may be certain of, that they are all together undoubtedly an Infinity of like Bodies, distributed either promiscuously, or in some regular Order throughout the mundane Space: And, as _Marino_ says,

Resplendent Sparks of the first Fire!
In which the Beauty we admire,
And Light of those eternal Rays,
The uncreated Mind displays.

[Footnote S: Mr. _Bradley_, Astronomer-Royal, has, in a great measure, proved that the Aberration of the Stars hitherto mistaken for a Parallax, may arise from, and indeed seems to be no other than the progressive Motion of Light, and Change of Place to the Eye, arising from the Earth's annual Motion and Direction.]

It remains now I think to shew, and endeavour to prove, that the Stars are not only light Bodies of the Nature of the Sun, but that they are really so many Suns, all performing like Offices of Heat and Gravity, in a regular Order, throughout the visible Creation, in opposition to an Opinion you have formerly hinted at, of their being in another Sense of a secondary Nature.

All Objects within the sensible Sphere of the Sun's Attraction, or Activity, are in some measure magnified by a good Telescope: But the Stars are all placed so far without it, that the best Glasses has no other Effect upon them than making them appear more vivid or lively, but all innate opaque Bodies, reflecting only a borrowed Light from some primary one, contrary to this Property, are all observed to lose their Light, in the same Proportion, as they are magnified, and through all Glasses become more dull than otherwise they appear to the naked Eye: And hence we may infer, without any further Evidence, that the Stars are all light Bodies endowed with native Lustre; and that Bodies, like the known Planets, from the same Reasoning, it is as clear they cannot be, because their Distance, though uncertain as to the Truth of the whole, yet such a Part of it as cannot be denied, would render them all in such a Case invisible.

A Proof of this will plainly present itself, if we consider the Course of the known Comets, who all of them, without Exception, become imperceptible, and intirely disappear; though most of them much bigger than the Earth, or any of the lesser Planets, long before they arrive at their respective Aphelions.