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The distance of 76."8, as nearest to the toise was taken between the microscopes, from + 2" to 78.'8 on the scale as bringing the measure again nearest the middle of the scale.
The value of the micrometer was determined by repeated measurement of the decimal on the scale between 78.7 and 78.8 and found that it measured 0."10053 by the micrometer; the readings here given, will, therefore, be corrected by this value of the micrometer, by which they will represent regular decimals of this individual subdivision.
It was of course also here intended to compare the distance taken on the scale with all the other measures of the same distance which can be measured on the scale, and the value of the micrometer upon a great number of decimal divisions, to obtain a mean value of it. But it being necessary to begin the pyrometrical experiments before the cold weather should cease, I delayed this comparison until after, or to another opportunity, which did not occur before I delivered the whole of these standards, and the scale, with the other instruments. The values here obtained will, therefore, remain individual, unless some future occasion should present to make this necessary trial of the scale on the indicated length, when the results here given may be corrected accordingly.
The microscopes being screwed fast, and the 0.° of the micrometer not agreeing fully with the division of the scale, which, for small dif. ferences it is not proper to correct by the screw of the sliding piece, I used the better method of reading repeatedly the divisions of 78.7 and 78.8 on the micrometer, taking the point of the micrometer so determined, by a mean, for the zero, from which the readings of the micrometer are to be subtracted, as the micrometer read yet by subtraction from 78."8, this point being 78."8001375, all the readings given immediately, are to be subtracted from the number instead of 78."8 only.
I intended of course also to repeat the comparison with the microscope reading directly or onwards, but the same reasons stated prevented the execution of it.
Using again abridged notations for the registering of the results, I called C = the toise of Canivet
letter JA= . Lalande marked A?
A when the marks LB =
- B laid downwards. In the toise of Canivet, three points were observed on the length of the contact, lettered as follows:
i, at 4 of the contact from the inner corner
In the toise of Lenoir only the middle was taken, (which is marked by a line,) like in the comparison at Paris. The same was done with the toises of Lalande. The turning end for end of the toise of Canivet in both cases related was impossible, on account of its breadth. These comparisons present the following table:
The results of the foregoing table are now to be reduced to the standard temperature of 32° by the difference of expansion between iron and brass, for which I shall again use the result of my own experiments. They present thereby the following table of results of toise comparisons :
34.2 76."7427475 + 2.92
+ 6.4 0.00174145
-.74848845 as accepted in the comparison of the original of these toise in 1768, in London, 76.74429393
Having no books about me in which I could see for the details of comparison of toises with English measures, the comparison just quoted is the only one with which I could compare mine, and the in feriority of the two toises of Mr. Lalande in every respect renders it of very little importance.
In the comparison of 1768, the mean adopted as result was IA +IB
P= 76.734 at the temperature of 62°, which is stated to be 0.024 of an inch longer than when determined by Mr. Graham. I have not before me sufficient data to judge of the propriety of the mean adopted, as it does not follow immediately from the two indivi. dual results stated in my notice. In respect to the temperature it seems that both toises and the scale of Bird of equal parts were supposed both at the temperature of 62°. Reducing this result to 32°, by different ratios of expansions, it presents the following result comparable with mine :
Ratio of difference of Amount of Ex-
Value at $2° pansion,
By Borda's expansion 0.00000352 0.0081031 76.7421031 By Troughton's 0.0000039 0.0089779 .7429779 By my experiments 0.000005545495 0.0081618 -.742162
Which are all smaller than mine, and I should suppose to deviate more from truth, as they would give a more erroneous proportion between the metre and toise. But I must again observe, that my results may yet be subject to a small correction by the reduction of the distance used on the scale to its mean value, as has been done with the metres.
The ratio between metre and toise, which may be quoted, as well for curiosity' sake, as also as a kind of trial of my comparison, may here be stated in all combinations which the different stand. ards admit; and I have in doing so the private interest of giving the ratio of the toise of Canivet to an authentic metre; because this toise has served in 1796, to Mr. Tralles and myself, to measure a base line of more than 40,000 feet by an arrangement of toises bars, which were standarded in it.
The ratio of the metre to the toise, or the metre expressed in decimals of the toise, is given by Mr. Delambre.
Captain Kater's comparison of the metre with Bird's scale would give
With sir George Shuckburgh's scale the deviation would be still greater.
F. R. HASSLER. Newark, New Jersey, October, 1819.
Gooernor of New Hampshire to the Secretary of State.
Epping, Vovember 21, 1818. Sir: By the last mail I received your letter of the 4th instant requesting a copy of the law of New Hampshire of 1718, upon the subject of weights and measures, and a statement of each scale beam,