418 Mr. C. A. Bell on the Determination 



to be uniform throughout the segment, S being similarly 

 determined for the whole rod. The values o£ the integral 



1 cos -j— - dz 



between the limits z = 0, z = -^ 6 l; 0= T 1 O Z, - = 1 2 ^/ ? and so 

 on, are, to the degree of approximation considered necessary, 



and in order, — multiplied by the fractions 



+ + - +■ + 



•59 -36 -36 -59 -59 -36 -36 -59. 



The total correction thus becomes 



AZ= J_ / •59fS l -So) + '36(S 2 -S )--36(S 4 -S )... + -59(S 1 o-S; 



27T V JS 



the third and eighth sections being omitted. Inspection of 

 the diagrams will show at once if the omission is justified. 



The lists below include three rods in which the subdivision 

 was subsequently made into twenty parts. In tw r o cases the 

 final result was practically unchanged ; in the third the value 

 of a was raised only 3 metres per second. On the whole, 

 further subdivision did not appear to be necessary. 



Finally, we get for the ; * velocity of sound'"' 



a = 2n(l + Al), 



and for Young's Modulus (adiabatic) 



W = a 2 p, 



where p is the density referred to water at 4° C. 



In the tables are given the values of a and E' reduced to 0°. 

 According to Mayer (loc. cit.) Young's Modulus for St. Grobain 

 glass (p = 2*545) diminishes by 1*16 per cent, for a rise of 

 temperature from 0° to 100° C. In a special experiment 

 with the Gallenkamp soft German glass, a diminution of 

 1*12 per cent, from 5° to 100° was observed, closely agreeing 

 with Mayer's determination. With Powell's flint-glass, on 

 the other hand, the curious result was obtained that Young's 

 Modulus is sensibly constant between the same temperature 

 limits, This observation is quite in harmony with the results 

 obtained by Winkelmann and Schott * for glass of the same 

 general character. In fact, if two rods of this glass be 

 " tuned " to the same pitch, one of them may be made very 

 hot by passage through a gas-flame before any distinct altera- 

 tion of its note can be observed. Owing to the brilliance 



* "Ueber die Elasticitat, etc., verschiedener Glaser," Wiedemann's 

 Annalen, Bd. li. p. 697 (1894). 



