To David Rittenhouse
New York June 20. 1790.
I inclosed you on the 17th. the alterations I had made in my report in consequence of the Bp. of Autun’s proposition which had come to my hands two days before. On the 18th. I received from Mr. Cutting in London a packet of newspapers, among which were the two inclosed, containing the speech in parliament of Sr. 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 1st. 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 2d. part proposing a thorough reform and the 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 Sr. I. Newton’s calculation: 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 Sr. I. Newton, and stating the grounds of that of 39.1682 for the Lat. 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 Bp. 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 1st. branch of the report and substitute in it’s 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 3/10 of a line (which in practice will endanger less error than an attempt at so minute a fraction as 10000th parts of an inch). This will give us the true measure of 58¾ English inches. Or, to shorten the operation, and yet obtain the result we seek, let the standard rod of 45.° be divided into 587 ⅕ equal parts, and let each of these parts be declared a line, 10 lines an inch.’ &c. I propose also to strike out the note page 3. before mentioned, and to substitute the following in it’s place. ‘The length of the pendulum has been differently estimated by different persons. Knowing no reason to respect any of them more than Sr. Isaac Newton for skill, care, or candour I had adopted his estimate of 39.149 I. for our Northern limit of 45.° before I saw the different propositions of the Bp. of Autun, and of Sr. John Riggs Miller. The first of these gentlemen quotes Mairan’s calculation for 48°—50’ the latitude of Paris towit 504:257::72 pouces: a 4th. proportional which will be 36.71428 pouces = 39.1923 inches. The difference between the pendulum for 48°—50’ and 45.° as calculated by Sr. 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. Sr. 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 Sr. I. Newton is .019 I. so that the pendulum for 45.° should be estimated according to Sr. J. R. Miller at 39.126—.019 = 39.107 I. Now dividing our respect equally between these two results by taking their mean, to wit = 39.1442 we find ourselves almost exactly with Sr. I. Newton whose estimate of 39.149 we had already adopted.’
I propose also to reform a passage under the head of weights in the 1st. branch of the report, to stand thus. ‘Let it then be established that an ounce is of the weight of a cube of rain water of one tenth of a foot, or rather that it is the thousandth part of the weight of a cubic foot of rain water weighed in the standard temperature’ &c.—all which I submit to your judgment, and I will ask you particularly to examine the numbers .0112 and .019 as I have no help here to find them otherwise than by approximation. I have wished much, but in vain, to find Emerson’s and Ferguson’s books here. In short I never was cut off from the resources of my own books and papers at so unlucky a moment. There is a Count Andriani of Milan here who sais there is a work on the subject of weights and measures published by Frisi of Milan. Perhaps you may have it at Philadelphia, and be able to send it to me. Were it not for my confidence in your assistance I should not have ventured to take up this business till I receive my books. I am, my dear Sir with great & sincere esteem Your friend & servt.,