A REVIEW

This my conjecture in respect to the competency of the author of "New Views" to decide upon the merit

OF TWO PIECES ENTITLED “NEW VIEWS OF THE of mathematical questions, is so confirmed by every

SOLAR SYSTEM, BY A VIRGINIAN,"

And published in Vol. IV, Nos. VII and XII, of the Southern
Literary Messenger.

page of his communications, that I am willing to rest this controversy upon his ability to develope and explain any one mathematical process employed in the "Principia" or the "Mechanique Celeste." I hope my readers will not consider these remarks invidious. When one presumes to "revolutionize" the whole system of mechanical philosophy, and to put aside as useless lumber the labors of the most gifted and distinguished men the world ever produced, we have a right to inquire into the qualifications of our new guide, so far as they may be legitimately deduced from his own pro

ductions.

To entertain what sentiments we please in respect to the constitution of the physical world around us, and to express those sentiments freely yet modestly, is a right we all enjoy, and which no person desires to infringe. That an individual disbelieves the Newtonian system of the universe-that he has chosen to say so in a literary journal-and that he has undertaken to exhibit the peculiar views he entertains upon the subject, is a matter of no consequence so far as the staOur author proposes to himself to show, "that our bility of that system is concerned. And had he done physical systems of astronomy are not true, either in the this with a becoming modesty, and with the true spirit distances of the planets from the sun-their velocities of an inquirer after truth, this review would not have in their paths-the kind of orbits they describe-the been penned. But when I hear a man saying of him- forces by which they are impelled through the heaself, "I stand in relation to the Copernican system, as vens-the cause of their perturbations, and the entire Copernicus stood in relation to the system of the Egyp-insufficiency of that something called gravitation to tian astronomer,”—and of others who differ from him, produce the phenomena we observe.” "that they are destitute of common sense:" when I It is then against physical astronomy only, that our author see a man, who cannot perform accurately the division professes to wage war. Both in this extract and in a reof one decimal number by another, (unless his printer mark he makes upon page 435, we see this distinction has done him injustice,)—and who is incapable of solv-clearly made between plane and physical astronomy. ing the simplest problems of uniform motion, rising up Now plane astronomy treats of the appearances, motions, and impertinently and unlearnedly attacking the labors distances and magnitudes of the heavenly bodies, and of men, not one page of whose works is he capable of is founded entirely on observations, without having any comprehending, if it contains so much as a single mathe-regard to the causes of their motions. Physical astronomatical formula, I will not forbear to rebuke him, humiliating though the task be to notice such productions. In the sequel I shall abundantly prove what I have here asserted of our author's mathematical abilities; but as a present specimen of them let us take the following problem, viz: A travels 400 miles at the rate of 4 miles per hour, and B 300 miles at the rate of 10 miles per hour; required the comparative lengths of time they are travelling.

that is,

As B's distance: A's distance :: B's time: A's time, 309: 400 :: 1: A's time; in which B's time is regarded as unity. Then A's time=

400

=1.3333.

300

my treats of these causes, and traees these causes to their effects. Then our author is self-deceived in supposing that his attack is only against the theoretical parts of the science. Expunge every thing relating to motion, distance, magnitude, from our system of plane astronomy, and what have we left? It is then not to the theory of gravitation only, as developed in modern times, that our author objects, because the motions, distances and magnitudes of the heavenly bodies are independent of all speculation as to the nature of the force which produces these motions;-but it is to those elements of the system to which the Grecians, Arabians and Egyptians made rude approximations, according to the construction and accuracy of the instruments they employed :—which were still more nearly obtained by Brahé and Kepler-and which last of all, have been accurately determined in modern times, by the great perfection of astronomical instruments. These measurements are in no respect different in principle, from those that occur in the determination of "heights and distances" by plane trigonometry. If our author knows knows better than this: and will tell him that when any thing of mathematics, I ask him to show wherein the rates of two travellers are unequal, their times of the calculation of the distance of the Moon, or Mars, travelling will be proportional to their distances divided or Venus from the earth, is different from the calculaby their rates respectively. Thus, if B travels 300tion of our distance from a terrestial object by plane miles at the rate of 10 miles per hour, his time of travelling will be 30 hours; if A travels 400 miles at the rate of 4 miles per hour, his time will be 100 hours. Then

That is B's time of travelling is to A's as 1 to 1.3333,

Substitute in this problem, for A and B and their distances and rates, Venus and Mercury and their paths and rates; and we have the problem given by our astronomer on page 769; and such precisely is his manner of solving it. Now any tyro in arithmetic

B's time: A's time :: 30: 100 :: 1 : 3.3333.

trigonometry. I expected our author to have commenced his attack in the only way which is rational, by showing first, that our instruments employed in astronomy are constructed on principles which lead to false results-and, secondly, that the application of trigonometry to those results has been made in an illeAnd this is the mathematician who is to pass con- gitimate manner. Upon these observations, and upon demnatory sentence upon the profound and elegant re- the relation subsisting between the sides and angles of searches of Newton and Lagrange and Laplace! la triangle as taught in geometry, plane astronomy is

That is, B's time of travelling is to A's as 1 to 3.3333; and not as 1 to 1.3333, as would be given by our author.

VOL. V.-14

based. Then it behooved our author to show that in both these respects the system is false. When he does this, I, for one, will give it up as untenable; but until then, I must be permitted to smile at the conceit of overturning a system, the foundations of which are as stable as the demonstrations of Euclid. But let us examine more particularly the nature of the objections urged by our author.

10. "It will be admitted by both the philosopher and the mathematician, that if the Sun is a progressive body, then the planets cannot describe round him orbits returning into themselves, as now taught by astronomers. It will also be admitted that our systems of astronomy, as they now exist, had their foundation in the supposition that the Sun is a stationary body. It is now, I believe, generally admitted by astronomers in England, France, and Germany, that the Sun is not a stationary body. Then if we admit this fact, and the whole phenomena of the heavens tend to prove it, there is not a diagram in any of our systems of astronomy, which represents the solar system as it is. I have no hesitation in saying, that the progressive motion of the Sun proves clearly that the whole system as it now exists requires recasting." July No., page 433. (Compare pages 434, 769.)

rolls, a curve called the cycloid; the properties of which are wholly different from those of a circle': but are we to be charged with stupidity when we assert that the nail revolves in a circle about the axle? Were a progressive motion given to an orery in operation-for instance, were it placed upon the deck of a smooth sailing vessel, would this progressive motion alter in any respect the relative motions of the machine? And as the relative motions of objects upon the surface of the Earth are unaffected by the motion they all have in common with the Earth; just so the relative motions of the bodies composing the solar system, would not be affected by any common progressive motion they might have in space. And, furthermore, as we must make abstraction of the rotatory and orbitual motion of the Earth, in order to investigate and understand to any useful purpose the motions of bodies around us; so also, we must make abstraction of any supposed orbitual motion of our system, in order to understand any thing about the phenomena of the heavens. The diagrams of astronomy, therefore, were never intended to represent the absolute paths of the planets in space; but their relative paths-the only ones essential in the The great majority of the "astronomers in England, study of the system. No astronomer ever asserted that France and Germany, admit that the Sun is not a sta- the path described in space by the first of Jupiter's sationary body." But do they at the same time reject tellites is a circle, or that in any revolution it passes any principle or result of the Newtonian system? If through the same points in space, it passed through in they do not, (and their writings show this,) and if the revolution just preceding; but they all assert that their opinion be worth appealing to at all, then it evi- its path in respect to Jupiter is a circle. Recur to the dently follows, that they do not regard the progressive nail in the rim of the carriage wheel: in each revomotion of the Sun as incompatible with the system as lution of the wheel, the nail passes through very it is at present taught. If this doctrine of the orbitual different points in space from those it did in the motion of the Sun is believed by modern astronomers, revolution just preceding, yet in respect to the axle, as he says it is, if it forms a part of the modern sys-the nail is revolving in a circle. And just as we tem, why war against it as such, and yet receive it call the circle, the path of the nail about the axle, so do we into his own system and hold it up as its contra-distin-call the circle the path or orbit of the first satellite about guishing feature? If it be false in the one, it cannot Jupiter. Once more: suppose a material circular ring be true in the other. to be attached to Jupiter as a centre, of a radius equal That our system has a motion of translation, I hold to the distance of the first satellite; and the satellite to to be highly probable. This opinion was maintained slide around and around the ring, as the ring is carried with ability by Mayer in 1760-by Lalande in 1776-along by the planet in its revolution about the Sun. and by Herschell in 1783. The arguments of the two first were wholly of an analogical character; the last named astronomer supposed that he had discovered a proof of translation in the widening of the stars about the region of the constellation Hercules. But any one may convince himself that we are not in a condition to decide upon this question, by referring to "Biot's Astronomie," vol. 3, chap. 3. Additions; or to Delambre's Astronomie, vol. 3, chap. 32.

The satellite would always be found on some part of this ring; and in this sense we speak of an orbit returning into itself. When we say then, that the first satellite revolves in an orbit which returns into itself, we do not intend to imply, that in each revolution, the satellite traverses the same points in space, but that in respect to its primary it is always found in a curve whose property it is to return into itself; for example in a circle or an ellipse, and not in a parabola, an hyperbola, or a spiral.

But in whatever way this question shall ultimately be determined, it will require no change to be made in I have used in these illustrations, Jupiter's first satela single diagram or demonstration of modern astronomy; lite, because its path about its primary is sensibly circuas a few considerations will show. Were our author to lar, and therefore it was not improper to speak of its take a pair of dividers, and placing one of its legs upon orbit as a true circle. They are, however, equally a point, were he to sweep the other leg around, would he applicable to those orbits which are elliptic. For, supdeny that he describes a circle about that point? And pose Jupiter to be in the focus of a material elliptic ring, yet to be consistent he must do so; for the leg as it the dimensions and position of which suited the orbit moves around the point is carried rapidly on by the ro-assigned to the fourth satellite, and to accompany Jupitation of the Earth on its axis, as well as by the motion ter in its revolution about the Sun: the fourth satellite, of the Earth about the Sun; and does in fact describe in space a curve of a very complex character, and wholly different from a circle. A nail, in the rim of a carriage wheel rolling over a level surface, describes, in a plane vertical to the one on which the wheel

if supposed to slide along this ring, would have the same motions with those now observed; and who in this case would deny that its orbit about Jupiter was elliptic and returned within itself. To use mathematical language, which is after all, the plainest and most

diameter at his nearest approach to the Earth; we have the system, if it exists, can in no manner affect the reI have shown in (1o,) that the progressive motion of

lative motions of the bodies which compose it. Different velocities have been assigned to the planets, therefore, for reasons quite different from those stated in the above extract. Velocity, from its nature, must be meawhich is within 0.04 of a second of the result of observa-sured by the space passed over in a portion of time tion. And were we to test in a similar manner the magnitudes and distances assigned to the other heavenly bodies, they would all be found to be perfectly consistent

latter be correct, the former cannot be wrong. Now [tory result, that which the system requires as a consein respect to the distance of a planet, our instru-quence of its own principles. Thus, if the Moon were ments give us the angle that the Earth would subtend removed to such a distance as was necessary to make if seen from the planet. The real diameter of the its periodical time equal to that of Mercury; if there be Earth we know by actual measurement: then to find any truth in the Newtonian system, the orbit of Mercuthe distance of the planet, we have only to find the ry should be much greater than that of the Moon, behypothenuse of a plane right-angled triangle, in which cause the force exerted by the Sun is to the force exerted the radius of the Earth is one side, and the angle above by the Earth, at equal distances, as 354936 to 1. And referred to is the angle opposite to that side. Our if the path of Mercury be greater than that of the Moon, author can refer to any treatise on astronomy and see and these paths are described in the same time, it follows the details of the solution which are few and simple; of necessity that the velocity of Mercury must be and if he has any objections against the indications of greater than that of the Moon. So that this result, the instruments we employ in these measurements, or which is held up as a fact contradictory to the system, the trigonometrical results deduced from them, and will is just that which the system requires. Now, our auspecifically state them, they will be confuted. To as- thor may deny that the Sun exerts a greater force upon sert merely that these processes are wrong, will make Mercury than the Earth exerts upon the Moon. But an impression upon no one who has attended at all to this has nothing to do with the matter now in hand. this subject; and our author owes it to himself, to say We are trying the consistency of the Newtonian sysnothing of the interests of science, to show explicitly | tem with itself: we must look therefore at its results in wherein they are defective. In respect to the periodi- the light of its own principles. It is quite another thing cal time of a planet, it is only necessary to observe the to prove these principles false. In this exertion of a two periods at which the planet's latitude is zero, in greater force by the Sun, consists the error of comparing order to obtain this element. It is useless then to a body moving around the Sun, with one moving around talk about velocities, until distances and periodical times the Earth. Let our author turn to any treatise on dyare shown to be false; for, as remarked above, if these namics, and he will find that the force operating upon be correct, the velocities cannot be false. Our author, revolving bodies enters into all investigations respecttherefore, has not touched in the slightest degree, the ing velocity, periodical time and distance: and hence, grounds upon which astronomers assert the planets to to have omitted this primary consideration in the comhave the velocities usually assigned them; and for this parison he instituted, was to violate the principles not reason, I might here dismiss, as irrelevant, the foregoing only of astronomy, but also of mechanics. And if our extract: but since he says that he does not perceive the author places no reliance in the laws of mechanics, as at incorrectness of the comparison therein instituted, I will present developed and taught; then he should have add a remark or two by way of pointing it out. commenced with enlightening the public upon that subject. And the only hope of subverting the physical system of astronomy, consists in the possibility of subverting the whole science of mechanics: for its laws were merely extended by Newton, first to the Moon, then to the planets; and were found adequate not only to explain the leading phenomena, but the minutest changes observed in the system; nay farther, to serve as an instrument of research, by which perturbations and periodical and secular variations were discovered, which had not been detected by the most skilful observers, but which subsequent observation confirmed. Now, our author may call the force which causes a stone, when unsupported, to fall towards the centre of the Earth, what he pleases, and we shall not quarrel with him. But for this we do contend; that this force, be its nature what it may, when developed upon dyna[mical principles, and extended, according to the laws of the Newtonian system, to the heavenly bodies, perfectly explains every motion, every perturbation, every variation in the elements of their orbits, with the last degree of accuracy.

The reader will bear in mind, that our author is testing the consistency of the Newtonian system with itself. Now, the consistency of any theory with itself can be tested only by comparing its own principles and results among themselves. It is true that a comparison may be instituted between the principles and results of any theory and some other principles and results considered as better known and more accurately determined; and this is not only a legitimate, but a very satisfactory mode of deciding upon the truth of a theory. But then we are comparing the theory with something else besides itself: and so far as the Newtonian theory of the universe is concerned, it invites the most rigid comparison between its principles and results, and those facts and principles which are considered the best established within the compass of human knowledge. But here, however, the object of our author is, to compare the system with itself. Then by what right does he compare it with a principle, which finds no place in the system ;nay more, which is not to be found in any department of science? Whence did he derive the principle, either in respect to circular or elliptic motion, that the periodical times are as the distances? Not from dynamics; for there it is proved that the squares of the periodical times are as the cubes of the distances. Not from Newton's system, for that is based upon the dynamical law just referred to. And yet, it is upon this principle that he calculates the periodical time of the Moon, supposed to be removed to three times its present distance. Had he committed no error in this particular, it is certainly a very novel method of showing the inconsistency of the Newtonian system, by adducing as a contradic

I am the more astonished at our author's conceit of a common velocity belonging to all the planets, since on page 750 he speaks of the importance of studying the system of Jupiter and his satellites as a true type of the whole solar system. He certainly has studied that system to very little purpose. Does he there find the periodical times to be as the distances? Certainly not: and yet this must be so, in order for the satellites to have a common velocity about their primary. If the semi-diameter of Jupiter at his mean distance, be assumed equal to unity, the mean distances of the satellites from