October 6, 1905.] 



SCIENCE. 



437 



sistances are in the following proportion. 

 P:Q::R:X. 



It will now be of interest to turn to the 

 original paper by Mance.^ This was com- 

 municated to the Royal Society of London in 

 1871 by Sir Wm. Thomson. Mr. Henry 

 Mance was superintendent of the Mekran 

 Coast and Persian Gulf Telegraph Depart- 

 ment and was especially interested in tele- 

 graph lines and cables and the detection of 

 faults. He considers such a line, well 

 grounded at each end and containing a bat- 

 tery and a galvanometer shunted by a circuit 

 AB. The current through the galvanometer 



/mw 



TTUyw 



Fig. 3. 



can be readily computed. But now let a leak- 

 age be applied to a point on the shunt. In 

 general the deflection of the galvanometer will 

 be changed, but by moving the leakage along 

 AB a point can be found for which the galvan- 

 ometer gives the original deflection. And 

 this deflection will remain the . same for all 

 values of the leakage from ' dead earth ' to 

 infinity. 



Presuming the electromotive ^ in L to remain 

 constant, and taking r = 0, we have the intensity 

 of the current passing through Q represented by 

 the equation 



E 



{X-. 



G\-(A^B)^^] t A-^B 



but after r is connected, the equation becomes 

 E 



As the condition that the galvanometer deflection 

 remains unchanged, the first of these equations 

 must be equal to the second, from which we ob- 

 tain the formula 



A 



L = B 



B 



' Henry Mance, Proc. Roy. Soc. Lond., 1870, Vol. 

 19, p. 248. 



the resistance 6 being immaterial. It will, there- 

 fore, be seen that R always bears the same propor- 

 tion to L that B does to A, the latter bearing 

 some analogy to the proportion coils of a Wheat- 

 stone testing bridge. 



Mance proceeds to point out several applica- 

 tions of this method, concluding, ' lastly, this 

 method may be used to ascertain the internal 

 resistance of a battery.' There is nothing 

 difficult or uncertain in this presentation and 

 it seems strange that this original simplicity 

 should have been so completely lost by later 

 writers. 



The clearest discussion of this method that 

 I have seen in print is that given by Lodge in 

 the paper referred to above, but this is de- 

 scriptive rather than mathematical. However, 

 he introduces a modification of the method 

 which greatly increases the range of its appli- 

 cation. This consists in using a condenser in 

 series with the usual galvanometer, so as to 

 detect variations in difference of potential 

 instead of variations in current. By this 

 means the method becomes a null one, and, 

 moreover, the measurements can be made in 

 a much shorter time as there is no waiting 

 for the needle to come to rest in its defiected 

 position. This is of especial advantage with 

 cells which polarize rapidly. To eliminate 

 the effect of any change in E.M.F. after the 

 circuit is closed, Lodge devised a special key 

 which broke the galvanometer connection im- 

 mediately after the bridge circuit is made. 

 It is better, however, to use a short-circuiting 

 key on the galvanometer as suggested by 

 Guthe.' The key is opened just before the 

 discharge passes through the galvanometer 

 and closed immediately afterwards to avoid 

 any changes due to a variation in the E.M.F. 

 of the cell. 



However, as all cells polarize more or less 

 rapidly, especially just after closing the cir- 



' K. E. Guthe, 'Laboratory Exercises,' 1903. 



