104 Professors Ayrton and Perry on 



in the coil, that the great objection to the use of German silver 

 for the internal winding becomes still more striking. For 

 the rate of production of heat in the coil is proportional to 

 C 2 R, which, from (6) and (5), equals 



K 2 i 2 (r!«-r ») * m*o 



Hence to produce the same magnetic effect M in a coil of 

 given length Z, the rate of production of heat is proportional 

 to 



Po ( 10 ) 



( r n_ rQ ny m 



Consequently when a given angular deflection is produced, 

 the rate of wasting electrical energy in heat will be thirteen 

 times as great if German-silver wire be used as it will be if 

 copper is used, no matter what be the gauge of wire employed, 

 that is, whether the voltmeter be wound to measure a maxi- 

 mum potential-difference of 50 or of 500 volts. 

 Eliminating r from (3) and (4) it follows that 



(£-)!--(*■)*, (ii) 



Wo/ w 



where b may have any arbitrary value. Hence if there is a 

 regular change possible in the value of yp such as given in 

 (4), we must have 



c = Fb, 



where P is some constant. Equation (11), therefore, be- 

 comes 



yp = (p\ 



YoPo \Po/ 



(12) 



JOPO \pQ, 



Jf, therefore, our wire in the inside of the coil is of copper 

 and on the outside of German silver, 



13 



yp=-§voPo> 



or p = 13/00. 



Hence from (11) 



or P = 0-143, 



and c = 0'143 b (13) 



It is certain that generally the relationship between 7 and 



