Another excellent instrument, con structed by Mr. Troughton, and shewn at the same time by M. Pictet, was a com parer, calculated to ascertain minute va riations between measures. This instru ment " consists of two microscopes, with cross wires, placed in a vertical situation, the surface of the scale being horizontal, and fixed at proper distances upon a me tallic rod. One of them remains stationa ry at one end of the scale, the other is oc casionally fixed near to the other end ; and its cross wires are moveable by means of a screw, describing in its revolution one 100th part of an inch, and furnished with a circular index, dividing each tura into 100 parts ; so that having two lengths, which differ only one-tenth of an inch from each other, we may determine their difference in ten-thousandths of an The wires are placed obliquely with re spect to the scale, so that the line of di vision must bisect the acute angle which they farm, in order to coincide with their intersection." Au instrument similar to that thus described, and made by Rams den, for measuring the expansion of me tals, was described by General Roy in the seventy-fifth volume of the Royal Trans• actions.
M. Pictet, influenced by a desire of ad vancing science, made an offer to the class of the use of the standard and the micro meter, for the purpose of determining the comparative length of the metre and the English foot : the. offer was gratefully ac cepted by the Society, and Messieurs Le gendre, Machain, and Prony, were ap pointed. to assist in making the proposed comparison of their standard metre of platina and the measure just mentioned. The first assembling of this committee was on the 21st of October, of the same year, at the mansion of M. Le noir. Upon commencing their operations, they found some difficulty arising from the different manner in which the mea sures were defined: the French stan. dards were merely cut off to the length of a metre ; but the English scale was graduated by lines ; consequently, the length of the former could not readily be taken by the microscopes, neither could the English scale be measured by the usual method adopted for making new standard metres, which is accomplished. by one extremity against a firm support, "and bringing the other into contact with the face of a cock, or slider, adjusted so as barely to admit the original standard between it and the fixed sur face." M. Lenoir endeavoured to remove this unfortunate impediment, by taking a piece of brass of the length of a metre, and re ducing the terminations to a thin edge, which was compared by the committee with the standard metre as usual ; when placed on the English scale, the extremi ties of the brass made two parallel lines to those engraved on the scale, and thus the apparatus was capable of being seen through the microscope : by these means the standard metre of platina, and ano ther belonging to the Institute, made of iron, were compared with the English foot ; the two measures each being equal, at the temperature of melting ice, to the ten millionth part of the quadrant of the meridian. " At the temperature of 15.3°
of the decimal thermometer, or 59.5° of Fahrenheit, the metre of platina was equal to 39.3775 English inches, and that of iron to 39.3788, measured on M. Pictet's scale.
It was discovered, however, that the manner employed produced results not quite satisfactory, as an uncertainty oc curred through the difficulty of placing the cross wires exactly at the extreme of the brass plate, where a reflection of light took place which precluded a distinct ob servation, whether the optical axis of the microscope was decidedly a tangent to the surface precisely at the termination. M. Prony, a member of the committee, suggested another arrangement as a reme dy fbr this obstacle, and M. Paul, of Gene va, who was present, carried it into execu tion : this latter gentleman traced a per. pendicular line to its length, on a small metallic ruler, the end of which he placed against a firm resistance, and the cross wires were made to agree with the line ; they then interposed the standard metre between the end of the piece and the re sisting substance, " and the line traced on it, which had now obviously advanced the length of the metre, was subjected to the other microscope. The microscopes, thus fixed, were transferred to the gra duated scale ; one of them was placed ex actly over one of the divisions, and the micrometer screw was turned in order to measure the fraction, expressing the dis tance of the other microscope from ano ther division." A second comparison took place on the 26th of October, at the residence of a member of the committee ; and after se veral satisfactory experiments, it was dis covered, that at the temperature or 55 of Fahrenheit, the standard of pla tina was 39.3781, and that of iron 39.3795 English inches, The different metres be ing intended to be equal at the tempera ture of melting ice, the preceding experi ments may be tried by bringing their re sults to the same temperature. To deter mine this, we have Borda's accurate trials, and the report of the committee of weights and measures on the dilatation of platina, brass, and iron, whence it appears," that for each degree of the decimal thermo meter, platina expands .00000856 ; iron, 00001156 ; and brass, 00001783 : tbr Fah renheit's scale these quantities become 476; 642, and 990 parts in a hundred millions. From these data we find, that, at the freezing point, the standard metre of platina was equal to 39.38280, and that of iron to 39.38265 English inches of M. Pictet's scale. The difference is less than the 500th of a line, or the 200,000th of the whole metre." The facts obtained by all the compari sons amount to this conclusion, taking each of the measures at the temperature of melting ice, the individual standard metres are equal to the 20,000,000th part of the quadrant of the meridian, and to 39.38272 English inches of M. PictEt's scale.