of Measuring the Self-Inductance of a.. Coil. 853 



flowing from the time £ = 0. The conditions of the experi- 

 ment require that the galvanometer should give no deflexion 

 after the current has flowed for an appreciable time. This 



condition* can be expressed by I xdt=§, the upper limit 



Jo 



of integration being taken as infinity, since the current will 

 always be zero after a small interval has elapsed. This 

 condition will give 



0=A 1 £- a ^ + A 4 cose *-** 



* cos (Jc 3 t) . dt 



+ A 4 sin € e- k * sin (k s t) . dt ; 



A 4 sin e I e~ k ^ 



Jo 



i.e. — - + A 4 cos € , 2 t % 2 + A 4 sin e * = . 



«1 *2 + #3 #2 + "3 



Also 2£ 2 =« 2 + «3; an( l ^2 2_ !-^3 2 = ^2 a 3- 



Putting in the values of the constants, therefore, we have 



^v + u(ot 2 + Xz)} {«2 a :; + «l( a l — «2~ ^3)} +Aa!W = ; 

 2. e. {v + w(o2 + a 3 )|- {(«! — ««})(«! — a 3 )} +Aa 1 u = 0, 



and, therefore, u + w(a x -H « 2 + ^3) = (H) 



Now from equation (9) above we have, when £—0, 



the term — - being always zero in the case of a constant 



E.M.F. dt 



Also, since (a) =0, we shall have, on putting £ = in the 



. t &BE^ (d,c\ n 

 expression tor a, —. \-p[ -r- \ =U. 



Hence 



i.e. phv+ $L<j-+M.+pr\u=0. 



* Lord Rayleigh, B. A. Report, 1883, p. 444, has drawn attention to- 

 the imperfections of a galvanometer as an instrument for indicating 

 whether the integral sum of the transient currents through it is zero or 

 not. See also a paper by Alex. Russell, M.A., M.I.E.E., Phil. Mag. 

 6th series, vol. xii. No. 69, 1906, where a full investigation and expla- 

 nation of the necessary corrections is given. 



Phil. Mag. S. 6. Vol. 17. No. 102. June J 909. 3 M 



