6 The Rev. T. R. Robinson on the Relation between the Temperature of 



be elongated by expansion, the countei'poise will descend, and the index n 

 will describe an arc of the dial proportional to that expansion. A strong pla- 

 tinum wire screwed into the lower part of c dips in the mercury-cup r, and 

 by connecting this and the binding-screw a with a battery, any required cur- 

 rent is passed through the wire w. Since the mass of the cylinder c, and its 

 arbor, is very great in comparison of that part of the wire which is in con- 

 tact with it, besides being connected with the metallic frame of the pyro- 

 meter, it is scarcely heated ; and, therefore, its expansion may be neglected. 

 The effective length of the wire may, therefore, be taken as the distance be- 

 tween the centre of the arbor and the bottom of the clip. Calling this Z, the 

 number of the pyrometer divisions P, and the value of one of them (in units of I ) 

 = e, the machine gives eP equal to the expansion — not of I, — but of a portion 

 of it r, whose length, when expanded, is equal to /. We have, therefore, 



l'=l-eP, 



and obtain the expansion of I itself by the equation 



, ePxl „/, eP 



u — 



l-eP~ V i 



; = gP 1+L +&C. 



In the instrument which I constructed, the length of rf = 3". 00 ; the radius 

 of c = 0'. 208; and the diameters of the arbor i and the dial are respectively 

 0'. 1783 and 3'. 24. As each of the divisions =0'. 17 nearly, the value of e is 



(V 1 7 X *^- X . or 0". 00065 ; and tenths of this are easily estimated. It 

 ^ 3.00 3.24' 



was more exactly determined by lowering the clip an amount measured by a 



micrometer microscope, which gives as a mean of eighteen trials corresponding 



to 147^0.09516, or, 



e = 0.000643. 



The diameter of the counterpoise-pulley =0'. 43 7, and, therefore, any weight 

 applied there causes a tension of the wire 35.3 times as great. The counter- 

 poise consists of a weight hi = 31.3 grains, which equilibrates the arm d and 

 its sector ; and of a piece of cliain o which gives the tension. The use of this 

 arrangement is, that when the wire is heated, and unable to bear much strain, 

 the chain descends and rests on the bottom of the pyrometer, so that as it 



