116 



Lord Rayleigh and Dr. A. Schuster. 



[May 5, 



balance giving promise of results trustworthy within one per cent., 

 we proceeded to apply it with care to the determination of L, but the 

 galvanometer at our command — a single needle Thomson of 2,000 ohms 

 resistance — was not specially suitable for ballistic work. As this 

 method is not explained in any of the usual text-books, it may be 

 convenient here to give a statement of it. 



The arrangement is identical with that adopted to measure the 

 resistance of the coil in the usual way by the bridge. If P be the 

 resistance of the copper coil, Q, R, S, nearly inductionless resistances 

 from resistance-boxes, balance is obtained at the galvanometer when 

 PS = QR. This is a resistance balance, and to observe it the influence 

 of induction must be eliminated by making the battery contact a 

 second or two before making the galvanometer contact. Let us now 

 suppose that P is altered to P + £P. The effect of this change would 

 be annulled by the operation of an electromotive force in branch P of 

 magnitude £P . x, where x denotes the magnitude of the current in this 

 branch before the change. Since electromotive forces act indepen- 

 dently, the effect upon the galvanometer of the change from P to 

 P + £P is the same as would be caused by BP .x acting in branch P, 

 if there be no E.M.F. in the battery branch at all. 



Returning now to resistance P, let us make the galvanometer con- 

 tact before making the battery contact, There is no permanent 

 current through the galvanometer (G), but, at the moment of make, 

 self-induction opposes an obstacle to the development of the current 

 in P, which causes a transient current through G, showing itself by a 

 throw of the needle. The integral magnitude of this opposing E.M.F. 

 is simply L x, and it produces the same effect upon G as if it acted by 

 itself. We have now to compare the effects of a transient and of a 

 permanent E.M.F. upon G. This is merely a question of galvano- 

 metry. If T be the time of half a complete vibration of the needle, 

 6 the permanent deflection due to the steady E.M.F,, a the throw due 

 to the transient E.M.F., then the ratio of the electromotive forces, or 

 of the currents, is 



|T 2sin^ 

 it tan 



If, instead of the permanent deflection 6, we observe the first throw 

 (/?) of the galvanometer needle, this becomes 



T 2sin ^ 

 7r tan jj@ 



In the present case, the ratio in question is, by what has been 

 shown, above £P . x : L x, or £P : L ; so that 



