To Cadwallader Colden
ALS: New-York Historical Society
Philada. Oct. 25. 1744
I communicated your Piece on Fluxions2 to Mr. Logan, and being at his House a few Days after, he told me, he had read it cursorily, that he thought you had not fully hit the Matter, and (I think) that Berkley’s Objections were well founded:3 but said he would read it over more attentively. Since that, he tells me there are several Mistakes in it, two of which he has mark’d in Page 10. He says, xẋ is by no Means=x+ẋ, nor is the Sq. of 10+1=10:2:01 but=100+20+1 and that the Method of Shewing what Fluxions are, by squaring them, is entirely wrong. I suppose the Mistakes he mention’d, if they are such, may have been Slips of the Pen in transcribing. The other Piece, of the several Species of Matter, he gave me his Opinion of in these Words, “It must necessarily have some further Meaning in it than the Language itself imports, otherwise I can by no means conceive the Service of it.”4 At the same time, he express’d a high regard for you, as the ablest Thinker (so he express’d it) in this part of the World. I purpose to write to you from N York next Week, and till then must defer saying any further on the last mention’d Piece. Enclos’d I send you a Piece of Dr. Mitchel’s (of Virginia) which I caus’d to be transcrib’d while he was here.5 He desires your Sentiments of it, and to be favour’d with any other Observations you have made on the same Distemper (the Yellow Fever). When you have perus’d it, please to return it. I am, Sir Your most humble Servant
Endorsed: B Frankilin
2. The MS of Colden’s “Introduction to the Doctrine of Fluxions, or the Arithmetic of Infinites” was printed in his Principles of Action in Matter (London, 1751), pp. 191–215.
3. [George Berkeley], The Analyst; or, a Discourse Addressed to an Infidel Mathematician (London, 1734). For an introduction to the controversy over fluxions, see Florian Cajori, A History of the Conceptions of Limits and Fluxions in Great Britain (Chicago and London, 1919), pp. 57–64.
4. James Parker printed the essay in New York in 1746, though the title page is dated 1745, as An Explication of the First Causes of Action in Matter, and, of the Cause of Gravitation, and it was reprinted in London and translated into French and German. Colden’s theory, however, was universally rejected by mathematicians. Brooke Hindle, The Pursuit of Science in Revolutionary America, 1735–1789 (Chapel Hill, N.C., 1956), pp. 44–7; Hindle, “Cadwallader Colden’s Extension of the Newtonian Principles,” 3 Wm. ana Mary Quar., XIII (1956), 459–75.
6. On the bottom of this letter Colden has made the following notes: “Suppose x = 10 and ẋ=.1 one tenth not equal to unite as Mr. Logan has it then (10+.1)2=100+2+.01. I do not say any where that xẋ=x+ẋ for on the contrary xẋ I say is infinitely less than x+ẋ or than x for x+ẋ=x the difference being infinitely small.”