accompany the changes in volume of Solid Bodies. 333 



which corresponds to a partial fall from b to a\ (3) the ampli- 

 tude X g , which corresponds to a partial fall from a 1 to a 2 , (4) the 

 amplitude X 3 , corresponding to a partial fall from a 2 to the end of 

 the lever — we have 



X=X 1 + X 2 + X 3 : 



and this relation is the sure test of the proportionality of effects 

 to causes, that is, of the proportionality of the amplitudes to the 

 quantities of heat. 



When the return of the needle to its original position indi- 

 cated the return of the wire to the surrounding temperature, the 

 weight d was caused to rise to b, and in like manner the eleva- 

 tion of temperature due to the shortening of the wire was noted. 

 A second elongation, equal to the first, was obtained by a second 

 fall of the weight d; but when the equilibrium of temperature 

 was re-established, instead of again making the weight ascend 

 towards the axis, the little steel rod which made the pincer /part 

 of the lever a 1 a? was rapidly withdrawn, the end p of the lever 

 fell upon a support, as seen in the figure, and, the wire returning 

 to its original length, the corresponding elevation of temperature 

 was noted. Thus were observed the two variations of tempera- 

 ture successively produced by an elongation and a contraction, 

 accompanied by external work (positive in the case of the elon- 

 gation, negative in that of a contraction) equal to the product of 

 the weight into the elongation or contraction itself — and of a 

 third variation produced by a contraction equal to the preceding, 

 but which had been accompanied by no external sensible mecha- 

 nical work ; for the work of the gravity corresponding to the very 

 small displacement of the system formed by the wire and the 

 pincer could be neglected as compared with the work of the two 

 first experiments. For the same wire, and in the same series of 

 experiments, these variations of temperature are evidently pro- 

 portional to the quantities of heat disengaged or absorbed ; but 

 if it were desired to determine these quantities of heat themselves, 

 or merely compare the quantities disengaged or absorbed by dif- 

 ferent wires, or by the same wire in different experiments, it 

 would be necessary to take into account a certain number of in- 

 fluences which it is almost impossible to estimate. Thus it is 

 clear that the manner in which heat is communicated from the 

 wire to the pincer depends on the nature of the wire, and the 

 pressure exerted by the pincer on the wire. This pressure even 

 exercises another influence ; it counteracts the changes in length 

 of that part of the wire held between the two branches of the 

 pincers, and consequently diminishes the variations of tempera- 

 ture which take place in this part, and which are precisely those 

 which experiment shows. 



