J. O. Thompson— Law of Elastic Lengthening. 35 



was attached. The frame thus surrounded the vessel without 

 touching it or the board on which it stood. Without some 

 such arrangement there would have been friction between the 

 damper and the sides of the vessel whenever the weight failed 

 to be exactly in the centre of the pan. Furthermore in order 

 to check quickly all motion the wire was passed through a fine 

 hole in a stiff piece of leather, and the side of the frame play- 

 ing between the prongs of a fork was prevented from swinging 

 through a large arc. The weights used had been carefully 

 calibrated so that the average inaccuracy was less than ¥7 



oooo* 

 At first I used as lower mark a fine diamond-mark on the 



wire itself or on a glass bead. Later I used instead a very fine 

 arrow-point printed on paper, and this secured an accuracy of 

 O005 mm. in the setting of the cathetometer. Since in some 

 cases the observed stretching of the wire amounted to more 

 than 66 mm. it is apparent that when one, besides all this, 

 takes mean values of many series of measurements, it is pos- 

 sible to attain a high degree of accuracy. 



Thermal Effects within the' Wire. 



It Was easy to foresee that the chief difficulties in measuring 

 the true elastic lengthening would be those arising from the 

 elastic after-effect and from the thermal effects due to changes 

 in the volume of the wire. These thermal effects according 

 to theory and observation are proportional to the stretching 

 weight, provided that the stretching is not carried beyond the 

 so-called limit of elasticity. By means of special observations 

 with a thermo-pile I was able to prove that in all my experi- 

 ments there was no perceptible deviation from this proportion- 

 ality, and this fact may be taken as evidence that in the 

 experiments the stretching was not carried beyond the proper 

 limit. These thermal effects were in every case of greater 

 influence than the after-effect. 



The formula given by Sir Wm. Thomson for the diminu- 

 tion in temperature At caused by the stretching weight Ap is 



M = dp 



wc 



where A is the heat equivalent of the unit of work, T the 

 absolute temperature, a the coefficient of linear thermal expan- 

 sion, w the mass of the unit of length of the wire, and c 

 the specific heat of the metal by constant pressure. 



Clausius* derives the same equation and states that Joule 

 has corroborated it experimentally. Still the investigation of 

 Joule on this point aimed at and attained merely a rough proof 



* Clausius, Mech. Warmetheorie, 3 Aufl. I, p. 199, 1887. 



