Coefficients of Mutua I Indu ction . 125 



integrals f xdt and j* ydt respectively, that is, for the total 



currents through the secondary coil and through the galvano- 

 meter. Then, equating the integral values of the electromotive 

 force between A and E derived by considering the paths 

 age and A f E, respectively, we get 



p X-qY = M.~, 



E being here the electromotive force of the battery B. 

 Again, the final charge of the condenser is 



X + Y=CE-^-,. 

 r + r 



Eliminating X from these two equations, 

 Y E 



Cpr—M (r + i J )(p + q) y 

 and this is to be as great as possible. 



The denominator on the right may be written 



pr ( 1 + ?L + <L + <£)., 



\ r p pr J 



the last term inside the bracket is the product of the second 

 and third, and may be taken as constant, since q, the resistance 

 of the galvanometer, and r' , the resistance of the part of the 

 circuit containing the primary coil, are practically determined 

 by the apparatus employed, while pr has the constant value 

 M/C. Hence, Y /(Cpr—M) is greatest when (p + q)(r + r f ) 

 is least, or when p\q — r]r\ which is identical with the con- 

 dition of maximum sensibility given above*. 



In conclusion, I may give a few numerical results as 

 examples of the applicability of the method ; they are derived 

 from experiments made in the laboratory of University College, 

 London, by Mr. F. Womack, B.Sc. 



A. Small Induction- Coil (without iron core). Approximate 

 dimensions : — Primary : length 11 '5 cm. ; mean radius 2 cm.; 

 wire, No. 20 B.W.G. ; resistance 1*65 ohm. Secondary : 

 length 104 cm. ; radius, inside 2*55 cm., outside 3'83 cm. ; 

 wire, No. 30 B.W.G. ; resistance 194 ohms. Battery, 2 

 Groves. Condenser, 4*926 microfarads (by direct measure- 

 ment with ballistic galvanometer) . The secondary coil could 

 slide endways while remaining coaxal with the primary. The 

 first measurements were made with the centres of the primary 

 and secondary as nearly coincident as possible, so as to give a 

 maximum coefficient of induction. The following are the 

 results obtained : — 



* For the mathematical theory of the method, so far as it is given 

 above, I am greatly indebted to my friend Dr. A. H. Fison. 



