Mr. W. Sutherland on a Kinetic Theory of Solids. 215 



can employ either the three-voltmeter method (fig. 1) or 

 either of its analogues, viz. the three-ammeter method (fig. 2), 

 or the one-voltmeter and two-ammeter method (fig. 3). 

 The formulae giving the cosine of the lag angle for the three 

 methods are, respectively, 



V 2 — V 2_V 2 



CO S0:=-^ IS* 1!_ 



C0 2V 1 f 2 > 



cos 



0=^ 



A s " A 1 " 



A 3 2 -A 



V> 2 



Hi) 



COSC7= 



V ' 



2A 1 - 

 r 



^u V 2 , V 3 , A 1? A 2 , A 3 , and Y being the readings of the instru- 

 ments in the different cases. 



XXIX. A Kinetic Theory of Solids, with an Experimental 

 Introduction. By William Sutherland. 



[Continued from p. 43.] 

 Young's Modulus. 



1. The experimental determinations that have hitherto been 

 made of the temperature variations of Young's Modulus have 

 been made for the most part by the static method, the diffi- 

 culties of which detract from its trustworthiness; for example, 

 Wertheim, by the static method, found the Young's Modulus 

 of iron and silver to increase with rising temperature, though 

 we now know that it diminishes. Kupffer (Mem. de V Acad. 

 Imper. des Sc. de St. Pet. 6 ser. t. 6) devised a convenient 

 modification of the kinetic method (by lateral vibrations) 

 which lent itself well to the measurement of the temperature 

 effect, but used an erroneous formula for calculating the 

 modulus from his measurements. Zoppritz (Pogg. Ann. 

 cxxviii.) has recalculated with a correct theory the right values 

 of the modulus of various metals at ordinary temperature 

 from Kupffer's data. I recalculated the values at other tem- 

 peratures, but found the temperature interval of about 30° C. 

 too small to give trustworthy results. Accordingly 1 under- 

 took a series of measurements by Kupffer's method. 



The method consists in causing a rod of the metal to vibrate 

 laterally with one end clamped and the other free, first with the 

 free end vertically above the clamped one, and next under it. 



