KINETIC MEASUREMENT OF THE ELASTICITY OF ROCKS. 15 



Now, a and I, being two unknown quantities, we have the relation 



7 Ci 7 



L+ — =1- 



where r = l,2, q. 



By the method of least squares, 4 may be easily found and 

 from it the frequency of the string ria may be calculated by the 

 formula given in the third chapter. 



Wi 712 fi^ — n-j — 71, _i til, 



which are connected by the relation 



?^ + 2??^l'J = /^u where ') = 1,2, t. 



From these values, the frequency of the free vibration of the 

 specimen may be calculated by the method of least squares, n 

 and m^ being two unknown quantities. Thus we have the first 

 value for the frequency, i.e. 



n = n. 

 Now, varying the tension, linear density of string and period 

 of the hammer, i.e. 



we proceed as in the former case and obtain a second value 



n=n . 

 A third series of observations, with TF= TT^, w = Wo and m=m^„ 

 gives a third value 



