Kinetic Theory of Solids. 39 



4. General Law of the Variation of Rigidity with Temperature. 

 The method of procedure in discovering this law was as 

 follows : — For no single metal was the temperature range 

 large enough to show clearly any simple law, but if the 

 molecules of the different metals behave like similar dynamical 

 systems, then, in passing from the rigidity of rest at absolute 

 zero to the vanishing point of rigidity at the melting-point, 

 the different systems must show close similarity in behaviour. 

 The first thing to do, then, was to find some empirical formula 

 with which to extrapolate for a first approximation to the 

 rigidity at absolute zero. In addition to the experimental 

 data, there' was the valuable fact that in each case the rigidity 

 is known to vanish at the known melting-point, so that, 

 although only a small arc of the whole curve of rigidity and 

 temperature was known in each case, the curve could be pretty 

 safely completed by sentiment down to the point of zero 

 rigidity at the melting-point. The curves thus drawn looked 

 as though they could be fairly represented by the empirical 

 formula 



eg 



1 T-0 



-=a + h 10 ' 

 n 



T being the melting-point. This makes the rigidity vanish 

 at the melting-point, and allows the three constants a, b, c to 

 be determined from three values of the rigidity at different tem- 

 peratures : the formula therefore represented a large stretch 

 of curve, and could with some confidence be used for extrapo- 

 lating over about 300° down to absolute zero. In this manner 

 a preliminary series of values of N, the rigidity at absolute 

 zero of the various metals, was found. Then it was possible 

 to express the value of the rigidity of each metal at all 

 temperatures in terms of the value at absolute zero as unit, 

 and, further, it was promising to express temperature for each 

 metal in terms of its melting-point as unit. When the 

 rigidity ratios so found for the different metals were plotted 

 as ordinates to the temperature ratios as abscisase, the points 

 for all the metals were found to lie on one curve, a parabola 

 with the equation 



j-.-g. ■•••■• w 



The temporary exponential form can now be discarded ; 

 and we will proceed at once to the proof that the simple rela- 

 tion just given is the actual law of the variation of rigidity 

 w T ith temperature. The best way to proceed with the data 



