Cambridge, Aug. 18th, 1709.
“Sir,
“The earnest desire I have to see a new edition of your Principia makes me somewhat impatient till we receive your copy of it, which you were pleased to promise me about the middle of last month you would send down in about a fortnight’s time. I hope you will pardon me for this uneasiness, from which I cannot free myself, and for giving you this trouble to let you know it. I have been so much obliged by yourself and by your book, that (I desire you to believe me) I think myself bound in gratitude to take all the care I possibly can that it shall be correct.—Your obliged servant,
“Roger Cotes.
“For Sir Isaac Newton, at his house in
Jermyn-street, near St. James’s
Church, Westminster.”
This was the first letter of that celebrated correspondence, consisting of nearly three hundred letters, in which Sir Isaac and Mr. Cotes discussed the various improvements which were thought necessary in a new edition of the Principia. This valuable collection of letters is preserved in the library of Trinity College; and we cannot refrain from repeating the wish expressed by Dr. Monk, “that one of the many accomplished Newtonians who are resident in that society would favour the world by publishing the whole collection.”
When the work was at last printed, Mr. Cotes expressed a wish that Dr. Bentley should write the preface to it, but it was the opinion both of Sir Isaac and Dr. Bentley that the preface should come from the pen of Mr. Cotes himself. This he accordingly undertook; but previous to its execution he addressed the following letter to Dr. Bentley, in order to learn from Sir Isaac the particular view with which it should be written.
March 10th, 1712–13.
“Sir,
“I received what you wrote to me in Sir Isaac’s letter. I will set about the index in a day or two. As for the preface, I should be glad to know from Sir Isaac with what view he thinks proper to have it written. You know the book has been received abroad with some disadvantage, and the cause of it may be easily guessed at. The Commercium Epistolicum, lately published by order of the Royal Society, gives such indubitable proofs of Mr. Leibnitz’s want of candour, that I shall not scruple in the least to speak out the full truth of the matter, if it be thought convenient. There are some pieces of his looking this way which deserve a censure, as his Tentamen de motuum cælestium causis. If Sir Isaac is willing that something of this nature may be done, I should be glad if, while I am making the index, he would consider of it, and put down a few notes of what he thinks most material to be insisted on. This I say upon supposition that I write the preface myself. But I think it will be much more advisable that you, or he, or both of you should write it while you are in town. You may depend upon it I will own it, and defend it as well as I can, if hereafter there be occasion.—I am sir, &c.”
We are not acquainted with the instructions which were given to Mr. Cotes in consequence of this application; but it appears from the preface itself, which contains a long and able summary of the Newtonian philosophy, that Sir Isaac had prohibited any personal reference to the conduct of Leibnitz.
The general preface is dated 12th May, 1713, and in a subsidiary preface of only a few lines, dated March 28th, 1713, Sir Isaac mentions the leading alterations which had been made in this edition. The determination of the forces by which bodies may revolve in given orbits was simplified and enlarged. The theory of the resistance of fluids was more accurately investigated, and confirmed by new experiments. The theory of the moon and the precession of the equinoxes were more fully deduced from their principles; and the theory of comets was confirmed by several examples of their orbits more accurately computed.
In the year 1714, several captains and owners of merchant vessels petitioned the House of Commons to consider the propriety of bringing in a bill to reward inventions for promoting the discovery of the longitude at sea. A committee was appointed to investigate the subject, and Mr. Ditton and Mr. Whiston, having thought of a new method of finding the longitude, submitted it to the committee. Four members of the Royal Society, viz. Sir Isaac Newton, Dr. Halley, Mr. Cotes, and Dr. Clarke, were examined on the subject, along with Mr. Ditton and Mr. Whiston. The last three of these philosophers stated their opinions verbally. Mr. Cotes considered the proposed scheme as correct in theory and on shore, and both he and Dr. Halley were of opinion that expensive experiments would be requisite. Newton, when called upon for his opinion, read the following memorandum, which deserves to be recorded.
“For determining the longitude at sea there have been several projects, true in theory, but difficult to execute.