a measures fifty yards in a minute, which added make one hundred; are not the celerities, as the forces, equal? And, since force and celerity in the same quantity of matter are always in proportion to each other, why should we, when the quantity of matter is doubled, allow the force to continue unimpaired, and yet suppose one half of the celerity to be lost? * I wonder the more at our author's mistake in this point, since in the same number I find him observing; "We may easily conceive that a body, as 3a, 4a, &c., would make three or four bodies equal to once a, each of which would require once the first force to be moved with the celerity c." If then, in 3a, each a requires once the first force f, to be moved with the celerity c, would not each move with the force f, and celerity c? and consequently the whole be 3a moving with 3f and 3c? After so distinct an observation, how could he miss of the consequence, and imagine that lc and 3c were the same? Thus, as our author's abatement of celerity in

Dr. Franklin's reasoning seems only to prove, that, where bodies of different masses have equal force, they "measure equal space in equal times." For, allowing that 2a moves one hundred yards in a minute (because it moves two separate fifty yards in that time), yet surely that space is not the same with that of the one hundred yards moved by la, in the same time, thougn it may be equal to it; for the body 2a (that is, a and a), in the first case, describes a broad double space; and the body la, in the second case, describes a long and single space. There is a farther consideration which may show the difference of celerity and force. For when Dr. Franklin says, in his second paragraph, that "there is no mass of matter, how great soever, but may be moved, with any velocity, by any continued force, how small soever," I ask whether the moving body must not have its force rather in the shape of much celerity, than of much matter, for this purpose; since without much celerity it would not move fast enough to apply its force to give the required velocity; even though its quantity of matter, and consequently of force, were infinite. Equal celevity therefore in moving bodies is their measuring equal space, along a continued line, in equal time." Equal space measured along a number of smaller parallel lines, suits cases of equal motion indeed, but, according to this corrected definition, not of equal celerity. — B. V

the case of 2a moved by If is imaginary, so must be his additional resistance. And here again, I am at a loss to discover any effect of the vis inertia.

In No. 6, he tells us, "that all this is likewise certain when taken the contrary way, viz. from motion to rest; for the body a, moving with a certain velocity, as c, requires a certain degree of force or resistance to stop that motion," &c. &c.; that is, in other words, equal force is necessary to destroy force. It may be so. But how does that discover a vis inertia? Would not the effect be the same, if there were no such thing? A force If strikes a body la, and moves it with the celerity 1c, that is, with the force 1f; it requires, even according to our author, only an opposing If to stop it. But ought it not (if there were a vis inertia) to have not only the force lf, but an additional force equal to the force of vis inertiæ, that obstinate power by which a body endeavours with all its might to continue in its present state, whether of motion or rest? I say, ought there not to be an opposing force equal to the sum of these? The truth, however, is, that there is no body, how large soever, moving with any velocity, how great soever, but may be stopped by any opposing force, how small soever, continually applied. At least, all our modern philosophers agree to tell us so.

Let me turn the thing in what light I please, I cannot discover the vis inertiæ, nor any effect of it. It is allowed by all, that a body la, moving with a velocity Ic, and a force If, striking another body la at rest, they will afterwards move on together, each with c and f; which, as I said before, is equal in the whole to lc and lf. If vis inertia, as in this case, neither abates the force nor the velocity of bodies, what does it, or how does it discover itself?

I imagine I may venture to conclude my observations

ou this piece, almost in the words of the author; that, if the doctrines of the immateriality of the soul and the existence of God, and of divine providence, are demonstrable from no plainer principles, the deist (that is, theist) has a desperate cause in hand. I oppose my theist to his atheist, because I think they are diametrically opposite; and not near of kin, as Mr. Whitefield seems to suppose, where (in his Journal) he tells us, "M. B. was a deist, I had almost said an atheist ;" that is, chalk, I had almost said charcoal.

The din of the Market* increases upon me; and that, with frequent interruptions, has, I find, made me say some things twice over; and, I suppose, forget some others I intended to say. It has, however, one good effect, as it obliges me to come to the relief of your patience with

Your humble servant,

B. FRANKLIN.

TO CADWALLADER COLDEN.

Baxter's Book on the Vis Inertia of Matter. - Manufacture of Electrical Apparatus. · Colden's Philosophical Treatise.

SIR,

Philadelphia, 6 August, 1747.

The observations I sent you on Baxter's book were wrote on a sheet or two of paper in folio.† He builds his whole argument on the vis inertia of matter.

* Philadelphia Market, near which Dr. Franklin lived.

Probably the same in substance as the preceding letter to Mr. Hopkinson. Enitor.

I

boldly denied the being of such a property, and endeavoured to demonstrate the contrary. If I succeeded, all his edifice falls of course, unless some other way supported. I desired your sentiments of my argument. You left the book for me at New York, with a few lines containing a short censure upon the author, and that your time had been much taken up in town with business, but you were now about to retire into the country, where you should have leisure to peruse my papers; since which I have heard nothing from you relating to them. I hope you will easily find them, because I have lost my rough draft; but do not give yourself much trouble about them; for if they are lost, it is really no great matter.

I am glad to hear, that some gentlemen with you are inclined to go on with electrical experiments. I am satisfied we have workmen here, who can make the apparatus as well to the full as that from London; and they will do it reasonably. By the next post, I will send you their computation of the expense. If you shall conclude to have it done here, I will oversee the work, and take care that every part be done to perfection, as far as the nature of the thing admits.

Instead of the remainder of my rough minutes on electricity, (which are indeed too rough for your view,) I send you enclosed copies of two letters I lately wrote to Mr. Collinson on that subject. When you have perused them, please to leave them with Mr. Nichols, whom I shall desire to forward them per next post to a friend in Connecticut.

I am glad your Philosophical Treatise meets with so good reception in England. Mr. Collinson writes the same things to Mr. Logan; and Mr. Rose, of Virginia, writes me, that he had received accounts from his correspondents to the same purpose. I perceive by the

papers, that they have also lately reprinted, in London, your "History of the Five Nations" in octavo. If it come to your hands, I should be glad to have a sight of it.

Mr. Logan,* on a second reading of your piece on Fluxions lately, is satisfied, that some of the faults he formerly objected to it were his own, and owing to his too little attention at that time. He desires me to tell you so, and that he asks your pardon. Upon what Mr. Collinson wrote, he again undertook to read and consider your Philosophical Treatise.† I have not seen

* James Logan, who came to America with William Penn, and who was distinguished for his attainments in classical literature, and in almost every branch of science, as well as for his public services for nearly half a century in Pennsylvania. - EDITOR.

The title of this treatise, as originally printed, was as follows; "Explication of the first Causes of Action in Matter; and of the Cause of Gravitation. London, 1746." A second edition enlarged was published five years afterwards with a different title, namely; "The Principles of Action in Matter, the Gravitation of Bodies and the Motion of the Planets explained from those Principles. By Cadwallader Colden, Esquire. London. Printed for Dodsley. 1751." The book was dedicated to the Earl of Macclesfield, then President of the Royal Society. Appended is a chapter entitled, "An Introduction to the Doctrine of Fluxions, or the Arithmetic of Infinities; in order to assist the Imagination in forming Conceptions of the Principles on which that Doctrine is founded." The volume contains eight chapters, besides the one on Fluxions, is printed in quarto, and extends to two hundred and fifteen pages.

Mr. Colden seems not to have been satisfied with the manner in which the first edition found its way to the public. In the Preface to the second edition he says;

"A few copies of the two first chapters of this treatise were published at New York, with design to know the sentiments of the learned on new principles in natural philosophy or physics, which were advanced in that essay. The London edition was without the author's knowledge, and had never been made, could he have prevented it. Since that time, he has been encouraged to go on. In this edition the two first chapters are revised, the matters contained in them follow more consequentially, some obscurities are removed, the sentiments, it is hoped, put in a clearer light, and some new theorems added. In the following chapters, which were not before published, these principles are applied to the explication