OF ARTS AND SCIENCES. 167 



the extent of a few millimeters back and forth, according to the vary- 

 ing velocity of the engine. As frequent readings were taken, these 

 clnuigcs were eliminated. In very rare cases the weights had to be 

 changed during the experiment; but this was very seldom. 



The vibration and irregular motion of the calorimeter back and 

 forth served a very useful purpose, inasmuch as it caused the friction 

 of the torsion apparatus to act first in one direction and then in the 

 other, so that it was finally eliminated. The torsion apparatus moved 

 very freely when the calorimeter was not in position, and would keep 

 vibrating for some minutes by itself, but with the calorimeter there 

 was necessarily some binding. But the vibration made it so free that 

 it would return quickly to its exact position of equilibrium when drawn 

 aside, and would also quickly show any small addition to the weights. 

 This was tried in each experiment. 



To measure the heat generated, we require to know the calorific 

 capacity of the whole calorimeter, and the rise of temperature which 

 would have taken place provided no heat had been lost by radiation. 

 The capacity of the calorimeter alone I have discussed elsewhere, 

 finding the total amount equal to .347 k - of water at ordinary tempera- 

 tures. The total capacity of the calorimeter is then A -j- .347, where 

 A is the weight of water. Hence Joule's equivalent in absolute 

 measure is 



102 tt» WD 

 — (4 + .347) (t-t>). 9 > 



where n is the number of revolutions of the chronograph, it making 

 one revolution to 102 of the paddles. 



The corrections needed are as follows : — 



1st. Correction for weighiug in air. This must be made to W, the 

 cast-iron weights, and to A -4- .347, the water and copper of the calo- 

 rimeter. If A is the density of the air under the given conditions, the 

 correction is — .835 A. 



2d. For the weight of the tape by which the weights are hung. 



rp, • • .0006 



lhis is -Try-. 

 n . 



3d. For the expansion of torsion wheel, D' being the diameter at 



20° C. This is .000018 (t" — 20°). Hence, 



J= 102 *g {A+ U ^^ (1 + -000018 (<"-20) +« - .835 A), 



where t — t' is the rise of the temperature corrected for radia- 

 tion. 



