The ' Phil. Trans.' for 1777 contain a description of the method employed by De Luc in the construction of his compensating pendu lums, in order to determine the length of ono metal whose expansion is equal to a given length of another metal. For this purpose he suspended the bar of known length from an arm projecting horizon tally from an upright dud plank. To the lower extremity of this bar was adjusted a small horizontal platform, upon which a bar of the other metal rested in a vertical position. Upon raising the tempe ratures of both bars, every point on the surface of the second bar would obviously become subjected to two motions tending to move it in opposite directions : it would be decreased by the expansion of the first bar, and elevated by the expansion of the second. One point would therefore remain stationary, and this point, being ascertained by raising or lowering a microscope adjusted to the edge of the plank, determined the portion of the second bar, measured from its lower extremity, whose expansion was equal to the whole of the first bar.
The rods employed by Borde in measuring the base-line of the great French Sur•ey consisted of a rule of brass laid upon a somewhat longer rule of platinum and attached at one extremity. The portion of the platinum rule not covered by the one of brags was divided into millionths of the entire length of the rule, and further subdivided by means of a vernier and microscope adjusted to the extremity of the brags rule. The value of each of these divisions having been previously ascertained by first surrounding the compound rule with melting ice, and then immersing it in boiling water, it. was only necessary to observe the indications of the vernier io order to apply the requisite correction for reducing the length of the rod to the standard tempe rature.
For low temperatures, the contrivance of Ramsdell, described in the Phil. Trans.' for 1785, and employed by General by in determining the expansion of the rods used in measuring the base on liounalow Heath for the Trigonometrical Survey, was perhaps unexceptionable. The rod was immersed in a trough of water, and over each extremity was placed a microscope, to which a slow motion could be given in the direction of the length of the rod by means of a fine micrometer screw.
The lines of collimation of the microscopes being thereby adjusted at the commencement of the experiment so as to coincide accurately with two points near the extremities of the rod, the temperature of the water was gradually raised till a thermometer placed in the trough indicated an advance of 10', 20', 30', or any required number of degrees. The consequent elongation of the rod destroyed the coin cidence of its extremities with the lines of collimation of the micro scopes, which was re-established by turning the micrometer screws, and carefully noting the number of turns and fraction of a turn necessary for that purpose; when, the value in parts of an inch of each turn being previously known, a direct measure of the expansion was obtained, free from the errors of a system of levers or of a train of wheels and pinions.
r The property of alumina whereby it undergoes a diminution of bulk when heated, was employed by Wedgwood as a measure of high tempe ratures. Ilia pyrometer consisted of cylinders of fine white clay, and an apparatus for accurately measuring their length. a This apparatus consisted of a metallic plate, upon which were fixed two brass rules slightly inclined to each other. The rules used by Wedgwood were 24 inches long, and divided into 240 equal parts. The distance between the rules at one extremity was 3.10ths and at the other 5.10ths of an inch; consequently the difference between their distances at any two consecutive divisions was the 1200th part of an inch. But It is obvious that these numbers are quite arbitrary, and that by Increasing the length of the rules and diminishing their inclination, the difference between their distances at any two consecutive divisions may be made as small as we please. The clay cylinders were first baked at a red heat, estimated at 947' Fehr., and then reduced to exactly 5-lOths of an inch in length, so as to fit the first division of the wale. When afterwards exposed to a greater heat, they underwent contraction, and the amount of this contraction was determined by observing the division of the scale corresponding to their diminished length. If we then assume, with Wedgwood, that the contraction is proportional to the temperature at which it took place, the latter will likewise be determined ; but independently of the difficulty of pro curing pieces of clay of uniform composition, from which it resulted that two cylinders of equal length when exposed to the same heat seldom underwent the same degree of contraction, it has been found that the duration of the experiment has considerable influence upon the contraction, the longer continuance of a low temperature producing the same contraction as a higher degree of heat continued for a shorter time. As a measure of temperature, therefore, this method cannot be relied on, though as a direct measure of expansion we doubt if it has been surpassed either in the simplicity of its principle or hi the minute ness of the indications of which it is susceptible. A description of the instrument, and of the experiments made with it, will be found in the ' Phil. Trans.' of 1782, 1784, and 1786.