518 Mr. 0. J. Lodge on a Modification of Mance's 



single strength of current will suffice to determine R after e is 

 known; but in the determination of e another and quite dif- 

 ferent strength of current (viz. zero) was employed. 



A curious illustration of the impossibility of measuring the 

 resistance of an electromotor by means of a constant current 

 was noticed the other day in the physical laboratory at Univer- 

 sity College by Mr. H. F. Morley, who has found that the cur- 

 rent produced by a certain form of gas-battery is, within very 

 wide limits, almost independent of the resistance of its circuit. 

 He endeavoured to measure the internal resistance of this bat- 

 tery by means of its own current, but found it quite imprac- 

 ticable. 



Variation of the Electromotive Force of a Battery. 

 In what precise way the electromotive force of an ordinary 

 cell depends on the current passing through it and on the 

 time that current has lasted, I am not aware of any experi- 

 ments which afford us information. But a law like the fol- 

 lowing seems not improbable. 



E = Ae"K+B ; (1) 



where t is the time the cell has been in action through the re- 

 sistance R ; so that the rate of change of E is proportional to 

 the excess of the strength of current it is producing over the 

 minimum strength to which it will ultimately fall, or 



dE E-B ... 



Tt=-p-sr-- •••••• (2) 



p is a number which may be constant, or it may be a function 

 of the current or of t ; but for a cell making any pretensions 

 to constarcy, it must be small. A and B are constants such 

 that A + B is the initial and B, the final, value of E. 



At any rate we may, I think, reasonably assume that E is 

 not affected instantaneously, however much the resistance of 

 the circuit R is changed, but that it takes a certain time 

 to change its value appreciably ; consequently, if we only 

 change R for an instant of time and then restore it to its ori- 

 ginal value, E may be regarded as constant. It is this fact, I 

 apprehend, which gives Mance's method its practical value, 

 and renders it superior to the somewhat similar methods of 

 Siemens and Thomson, because in it the change of resistance 

 of r can be made very rapidly without disturbing the galva- 

 nometer, and need only last a few seconds. The shortest 

 time, however, is sufficient for some variation to take place in 

 the battery ; and accordingly a kick of the needle is usually 



