I had taken no notice of the precaution of making the experiment of the pendulum on the sea shore, because the highest mountain in the United States would not add 1-5000 part to the length of the earth's radius, nor 1-128 of an inch to the length of the pendulum; the highest part of the Andes indeed might add about 1-1000 to the earth's radius, and 1-25 of an inch to the pendulum; as it has been thought worth mention, I will insert it also.
Your letter of April 20th, was duly attended to by me, but I fancy the successor had been decided on before it was known to the public that there would be a vacancy.
I am, with great esteem, my dear Sir, your sincere friend and humble servant.
TO DAVID RITTENHOUSE.
New York, June 20, 1790.
Dear Sir,—I enclosed you on the 17th the alterations I had made in my report in consequence of the Bishop of Autun's proposition, which had come to my hands two days before. On the 18th, I received from Mr. Cutter in London a packet of newspapers, among which were the two enclosed, containing the speech in Parliament of Sir John Riggs Miller, on the subject of weights and measures. I observe, he states the estimate of 39.2 I. for the length of the pendulum as confessedly erroneous. I had adopted it from memory only, and before I had been able to get a single book of any kind, in the first part of the report, wherein I endeavor to ascertain and fix invariably the system of measures and weights now in use with us. But before I proceeded to the second part, proposing a thorough reform, and reducing the whole to the decimal ratio, I had been able to procure here a copy of the Principia, and so to recur to the fountain head for Sir I. Newton's calculations, and then added the note, which you will find page 3 of the report, doubting what could have been the foundation of the common imputation of the estimate of 39.2 to Sir I. Newton, and stating the grounds of that of 39.1682 for the latitude of 51° 31' of 39.1285 for 38°, which I had at first adopted, and 39.14912 for 45°, which I took on receiving the Bishop of Autun's proposition. I have now thought I might venture to take for granted, that the estimate of 39.2 is as erroneous as I had supposed it, and therefore to expunge it from the first branch of the report, and substitute in its stead 39.1682; and to change a passage under the head of "Measures of length" into the following form:
"They furnish no means to persons at a distance of knowing what this standard is. This, however, is supplied by the evidence of the second pendulum, which, according to the authority before quoted, being 39.1682 I. for the latitude of London, and consequently the second rod for the same latitude being 58.7523, we are first to find by actual trial the rod for 45, and to add to that 287/10000 of an inch, or rather 3/10 of a line (which in practice will endanger less error than an attempt at so minute a fraction as 10,000th parts of an inch), this will give us the true measure of 58-3/4 English inches. Or, to shorten the operation, and yet obtain the result we seek, let the standard rod of 45° be divided into 587-1/5 equal parts, and let each of these parts be declared a line, and ten lines an inch," &c.
I propose also to strike out the note (page 3) before mentioned, and to substitute the following in its place:
"The length of the pendulum has been differently estimated by different persons. Knowing no reason to respect any of them more than Sir Isaac Newton for skill, care, or candor, I had adopted his estimate of 39.149 I. for our northern limit of 45°, before I saw the different propositions of the Bishop of Autun, and Sir John Riggs Miller. The first of these gentlemen quotes Mairan's calculation for 48° 50', the latitude of Paris, to wit, 504:257::72: to a 4th proportional, which will be 36.71428=39.1923 inches. The difference between the pendulum for 48° 50' and 45°, as calculated by Sir I. Newton, is .0112 I. so that the pendulum for 45° would be estimated, according to the Bishop of Autun, at 39.1923-.0112=39.1811. Sir John Riggs Miller proposes 39.126, being Graham's determination for 51° 31', the latitude of London. The difference between the pendulum for 51° 31', and 45° by Sir I. Newton, is .019 I., so that the pendulum for 45° should be estimated according to Sir J. R. Miller, at 39.126-.019=39.107 I. Now, dividing our respect between these two results, by taking their mean, to wit, (39.181 + 39.107)/2=39.144, we find ourselves almost exactly with Sir I. Newton, whose estimate of 39.149 we had already adopted."