Measurements of Inductance. 533 



cannot possibly occur; and in only three (§§ 9, 10, 13) is 

 the continuous balance dependent upon conditions. More- 

 over, in these three cases it can only be realized by intro- 

 ducing a double adjustment, a thing which is usually regarded 

 as fatal to the practical utility of any method. The advice 

 to " fulfil the condition for a continuous balance when such 

 a condition exists" may well be supplemented by further 

 advice to choose a method (when possible) in which no special 

 condition need be fulfilled (§§ 5, 6, 11). 



§ 15. It only remains to discuss numerically a case in 

 which the balance is merely aggregate. The measurement 

 in § 3 will be selected, and the figures given closely re- 

 semble those obtained in an actual laboratory test. Assume 

 P = 220 ohms, Q = 440, K = 500, S = 1000, G = 1500, s-.= 200; 

 K = 2| mfd.; L = 0*022 henry, g = Q'l. In the equation 

 z = c 1 e at + c 9 e^ t + c z e yt we first determine a, j3, 7 as the roots 

 of the cubic in D, viz. «=-2352-7 sec." 1 , £=-16005'9, 

 7 = —39530*7. We next obtain c b <? 2 , c 3 from the equations 



Ci + c 2 + c d = 0, c 1 a, + c 2 {3 + c 3 y = 0, 

 ,, 02 _l 2 (P + R)(S-s) , 144000. 



the result is 



log/^A = 6-96148, log/- ^ = 5-16024, log/^A = 6*72519. 

 The current 



z = Cl ae at + csPeV + we**, and log/ - °^\ = 2*33304, 



log^W-36452, log(-^=l-3'2212. 



We can then easily show that the current in the galvano- 

 meter is zero (and then reversed) after 1*728 x 10~ 4 sec, 

 and that in this time the flow is 5*19 X 10~ 6 coulomb. At 

 the end of 10" 3 sec. this has been reduced to0*87xl0~ 6 , 

 and after 10~ 2 sec. the aggregate flow (in the direction of 

 the arrow in the figure of § 2) is only 5*5 x 10 ~ 16 . We 

 have here rather exaggerated the inductance of the galvano- 

 meter ; if we take T J henry instead of y\y, we have 



a= -2349-3, /3=- 27076*8, 7= -234011; 

 log(^) = 7-90897, log(- C ') = 7-95799, 



log(^) = 8-98631; 



