that the merit of his work chiefly confifts in an attempt to treat the science of Algebra with the fame perfpicuity, and accuracy of reasoning, that have been thought necessary in books of Geometry. This might have been the cafe, as far as we can judge of the Author's abilities, from the rest of his work, had not his great defire of reftraining the use of the Negative Sign, mifled him from the moft fimple path, into the most abftrufe reafoning; for he treats of the Square and Cube Roots, with all the elegance and clearness that the subject will admit of: but the fcheme of rejecting Negative Roots, makes him fpin out the fubject much farther than was neceffary; efpecially the Cube Roots, which take up no less than two hundred and fifty pages. Whether any Reader will undertake to perufe this part of the work, and afterwards think his time not mif-fpent, is a query difficult to folve.

We have received the following Paper from the ingenious and induftrious Mr. Cadwalladar Golden, dated New-York, Auguft 6th, 1759; with whofe Intentions we now comply, in transmitting its contents to the view of our Readers.

TH

HE Principles of Action in Matter were published in 1751, and the Author having thoughts of publishing a new edition, in which fome mistakes in the astronomical part of the first edition are corrected, and the principles farther extended, and applied to other general parts of Natural Philofophy, he deems it previously neceffary to remove some objections, which have been made by perfons for whofe judgment he has the greatest regard.

It is, in general, thought to be contradictory to what Sir Ifaac Newton has demonftrated. This, the Author thinks, arifes from a miftake, and want of attention. Sir Ifaac demonftrates the motion of the Planets from three principles. 1. From their velocity in their orbits, every where reciprocal to the fquares of their diftances from the fun. 2. From their gravitation to the fun, every where, likewife, reciprocal to the fquares of their diftances from the fun. And 3. From that force by which a Planet would fly off in a Tangent to the Curve which it defcribes, fuppofing that the force, by which its velocity is reciprocal to the fquares of the distances, and its gravitation, ceafe to act. The motion of a Planet in

+Vid. Review, vol. VII. page 459.

1

its

its orbit is the effect of all these three principles acting at the fame time. So far the Principles of Action agree with wha Sir Ifaac has demonftrated.

Sir Ifaac does not enquire into the caufe of the Planets velocity, every where reciprocal to the fquares of the ditances from the fun; he affumes it as a fact confirmed by every obfervation. He proves, from the nature of the Curve which the Planets defcribe, that they gravitate to the fun, in a Ratio reciprocal to the fquares of their diftances from the fun, without enquiring into the cause of their gravitation. He deduces the Planets projectile force, by which they would fly off in a Tangent, fuppofing all other force to cease, from that power of Matter by which it refifts all change in its prefent ftate. Many of Sir Ifaac Newton's followers and Commentators have fallen into a miftake, that this projectile force arifes from a projectile motion communicated to the Planet at the beginning of its motion; whereas it is only, and Sir Ifaac declares it to be, a neceflary confequence, or a complicated effect of its motion in its orbit, and its vis Inertia. It is from this mistake that a prejudice arifes to the Principles of Action.

It is true, that the Author of the Principles of Action affirms, that if the motion of a Planet arifes only from a projectile motion once impreffed, and if it approach to the fun, and its motion be only accelerated by its gravitation in a direction to the fun, the Planet can never recede from the fun; but muft continually approach to it, fuppofing that the principle ccafes to act by which its velocity is every where reciprocal to the fquares of its diftance from the fun. In faying this, he in no manner contradicts what Sir Ifaac Newton has demonftrated, he only contradicts a falfe conception of some Commentators on Sir Ifaac's Philofophy.

The method which Sir Ifaac Newton has taken, in confidering the effects of the Planets vis Inertia, as a projectile motion in the tangent of the orbit, has led many into the before mentioned mistake: and thereby it has been difficult to conceive the motion of a Planet in its orbit, from the caufes affigned. The Author of the Principles of Action has confidered the effects of the Planets vis Inertia in a different light, viz. By its continuing the effects of the action of light, at one time in a motion from the fun, and the effects of the re-action of the Æther, at another time in a motion toward the fun, each alternately, and precifely in the time of one revolution in its orbit. He fhews in what manner this al

ternate motion is produced: and he thinks thereby the reafon of the Planets motion in its orbit may be more eafily conceived, than by the method which Sir Ifaac Newton has taken.

The attempt to explain the caufe of Gravitation, gave another ftrong prejudice against the Principles of Action, to those who thought that the mutual attraction of bodies is by an innate power in Matter. It is hoped that this objection is now entirely removed by Sir Ifaac Newton's letters to Dr. Bentley, which have been published fince the the Principles of Action. In one of these letters Sir Ifaac_writes as follows. "That Gravity fhould be innate, inherent, ❝ and essential to Matter, fo that one body may act on an"other at a diftance, through a Vacuum, without the me"diation of any thing elfe, by and through which their ac❝tion and force may be conveyed, is to me fo great an ab"furdity, that I believe no man, who has in philofophical "matters a competent faculty of thinking, can fall into it. "Gravity must be caufed by an agent acting conftantly, ac"cording to certain laws; but whether this agent be mate"rial or immaterial, I have left to the confideration of my "Readers." After this an attempt to fhew what this agent is, may be well excufed. The Author of the Principles of Action thinks, that it is a different being from inert Matter, and different from intelligent Beings. He has likewife attempted to difcover the laws of its action.

After an attentive reflection, it will be clearly seen, that the motion of a Planet in its orbit cannot be from a projectile motion alone, impreffed in the beginning, and Gravitation : and in time it will appear, that this fuppofition is no less abfurd, than the innate mutual attraction of Bodies. Before any Body can move by its vis Inertia in the tangent to a curve, it must first be supposed to move in that curve. There must be fome agent continually acting, to give motion to a Planet, and to continue that motion. The Author of the Principles of Action thinks that LIGHT is the moving power, which communicates motion originally to all bodies. The density of Light, and confequently its force, are at the feveral diftances from the fun reciprocal to the fquares of the distances, precifely as the velocity of the Planets is at their feveral diftances. This alone gives a ftrong prefumption, that Light is the agent which gives motion to the Planets: and when likewife numerous phænomena may be obferved, at all times, and in all places, which fhew that bodies receive motion ori

Vid. Review, vol. XIV. page 590.

ginally

ginally from Light, little doubt can remain, that Light is the moving power.

The power of Light in giving motion to the Planets is so very obvious, that it must long before now have been generally allowed, were it not for one objection, which feems to be of great force. It is this, the motion of the rays of Light is in directions from the center of the fun, and the force of gravitation is in directions to the fun's center; in fuch cafe it cannot be conceived, that by any actions in these oppofite directions, any direction of motion can be given, but to or from the fun. For example, if two balls, moving in oppofite directions, impel a third ball at reft between them, in the fame inftant, and the two balls move with equal force, the third ball receives no motion; but if the force of one of them be greater than that of the other, the third ball moves in the direction of that of greater force.

This is allowed to be true; but there is no fimilitude between the impulfe of the two balls and the actions of Light and Gravitation, and therefore no conclufion can be justly drawn from one to the other. The motion of the two balls is, by motion fomehow communicated to them, and continued by the refifting power in the bodies of the balls. This motion can be given only in one direction, and be continued in the fame direction; and the impulfe cannot be conceived without refiftance in all the three balls; but the action of the primitive powers is in all directions. Every body at reft refifts equally in all directions. Light is emitted from every point of a luminous body, and in all directions from every point, where no refifting body interpofes. When the motion of the rays is ftopped, by their incidence on fome refifting body, they are reflected from every point of the folid parts of that body, and in all directions from every point: for every part of a luminous body, and every part of an illuminated body may be seen by an eye placed in any direction from the luminous or illuminated body. The reflection of rays is not by any power or force in the refifting body: for it can only refift or ftop, it cannot give motion in any direction. The reflection of Light is therefore by the power of moving effential to it. Again, the rays from every point of luminous or illuminated bodies, interfect, and are interfected, in every part, by rays from every other point, and by rays from every other thing, which pafs in the space where they move, without any of them being ftopped, or turned from their rectilineal motion. From hence it follows, that the rays of Light are mutually penetrable, or have no refiftance. Many other phænomena

phenomena of Light confirm this. It is evident, therefore that Light does not give motion by impulfe, as one body in - motion moves another.

It is a fundamental Theorem in Sir Ifaac Newton's Theory, that if a body be impelled by two different powers, in the direction of the fides of a Parallelogram, the body will move in the Diagonal. Let us confider the reafon of this Theorem. Can it be any other than that every power or caufe will produce its effect in whatever manner or direction it can? In the case of two powers acting in the direction of the fides of a Parallelogram, they cannot both produce their effect, in any other direction than that of the Diagonal; and do it in that direction.

It is a general rule or maxim, confirmed by all obfervation, that each of the primitive powers exerts its force in all directions; and that when its action in any direction is obftructed, by the action of fome oppofite or negative power, it exerts its force in any other direction, in which no oppofition, or the leaft, is made. This may be illuftrated by numerous inftances, of which one at prefent is thought to be fufficient. The force of gunpowder feems evidently to arife by the inftantaneous emiffion of Light, from every part of the gunpowder. If it be fired in the open air, it exerts its force in all directions; but if it be confined, as in a gun barrel, it exerts its whole force in the direction of the bore of the gun, whichever way the gun be directed.

By difcovering that the velocity of the earth in its orbit. arifes from the Light of the fun, an error, which Sir Ifaac Newton has fallen into, is discovered. Who is that man who never errs? From the effects of Gravitation, Sir Ifaac concluded, that the axis of the earth must have a nutation, and that thereby the obliquity of the Ecliptic must be lefs at the winter Solstice, than at the fummer; but, by confidering the oppofite effects of the emiffion of Light from the fun, the Author of the Principles of Action affirmed, that the obliquity of the Ecliptic must be greater at the winter than at the fum mer Solstice. Since a copy for a fecond edition was fent to London, he has been informed, that this is confirmed by a Long feries of obfervations at Paris. He has likewife been bold enough to affert another fact, as a teft of the truth and of the ufe of his theory, in contradiction to the opinion hitherto of all Aftronomers; tho' he had it not in his power to confirm the fame by obfervation. Aftronomers have hitherto taken it for granted, without proof, that the earth's rotation on its axis is at all times equal; but he afferts, that it REV. Nov. 1759Ee

must