U-A =0 



Coefficients of Induction. 337 



expression f 



K/3P(P + Q) 



Differentiating the above expression for q 1 and making 

 </ = 0, we have 



P(Q + S) + (P + Q)(r + G)" 



If we substitute for /3 its value in terms of E, the electro- 

 motive force of the battery and the resistances, we find 



®- = F+KrW- *dil« + *+ i^y^i 



It seems therefore advantageous to make R and P both 

 large, and Q and r both small. Hence the very easy practical 

 method suggested by the formula might not be so sensitive as 

 to obtain first an approximate adjustment, and then to make 

 the final adjustment by varying r. 



The following example of the measurement of the coeffi- 

 cient of self-induction of a coil by this method may be given. 

 The resistance Q being 10 ohms, and P 100 ohms, there was a 

 permanent balance when E. was made 1577 ohms, so that S, 

 the resistance of the coil, was 157*7 ohms. A condenser of 

 1 microfarad capacity was then placed between A and K" and 

 the resistance r adjusted till there was no kick of the galva- 

 nometer-needle. This value of r was found to be 59 ohms, 

 though the sensitiveness was, doubtless, not as great as might 

 have been obtained. Substituting these values, we have 



L = 10 3 x (15770 + 59x1734-7) centim. 

 = •118 henry. 



The same method was also employed to find the coefficient 

 of self-induction of the coil described in (1) of resistance 

 59*51 ohms. P was made 1000 and Q 10 ohms ; and when 

 B, was 5051 an almost perfect balance was obtained. Both a 

 telephone and a galvanometer were used in the final adjust- 

 ment of r, and the value thus found was 3*65 ohms. The 

 coefficient of self-induction is, therefore, 



10 3 x (50510 + 3-65 x 5101-51) centim. 



= •0691 henry, 



which does not differ greatly from the previous result. 



