438 



SCIENCE. 



[N. S. Vol. XXII. No. 562. 



cuit, it is not possible to work all the keys by- 

 hand quickly or uniformly enough to obtain 

 the best results. By using a two-pole multi- 

 circuit switch the various keys can be com- 

 bined in one, and a single motion of the hand 

 works them all in the order required. The 

 switch s (Fig. 4) consists of two blades, m 



FiG. 4. 



and n, pivoted at h and d and both moved by 

 the connecting piece, I, over a series of four 

 contact points. Thus, used as a two-pole 

 switch, l) and d can be connected to any one 

 of four different circuits; but in the present 

 case only a few of the contacts are utilized, 

 and these are connected so as to make and 

 break the various connections in the order 

 desired as the switch is quickly moved from 

 one side to the other. 



The arrangement then is as follows : The 

 cell, or other resistance to be measured, is 

 joined in series with three resistances, R, P 

 and Q, Fig. 4. The points A and D are joined 

 to a and d, and are connected whenever n rests 

 upon the third contact point. The galvanom- 

 eter is joined to the points fe and c, while c 

 and e are permanently connected, thus short- 

 circuiting the galvanometer when contact is 

 made on either point, but when m is moved 

 from e to c the short-circuit is raised for an 

 instant. It is during this instant that the 



points a and d are connected by n passing over 

 its third contact. 



The points h and c are also joined to B and 

 C^ the former through the condenser Z. When 

 the key T is closed this condenser is charged 

 to the difference of potential between B and 

 G, the charge passing through the blade m 

 and leaving the galvanometer at rest. When 

 the switch is thrown over to the third point, 

 A and D are connected, which practically cuts 

 P and Q oht of the circuit, leaving only the 

 battery and B. With this shorter circuit the 

 condenser is charged to the difference of po- 

 tential between A and (since D^ B and A 

 are all at the same potential) and if this is 

 the same as that formerly existing between B 

 and there will be no change in the charge 

 and, therefore, no deilection of the galvanom- 

 eter which, for this position of the switch, is 

 not short-circuited. As the switch is moved 

 further the galvanometer is short-circuited 

 again before the connection ad is broken, thus 

 eliminating the back kick of the galvanometer 

 as the charge in the condenser returns to its 

 former value. 



Having set up the apparatus as indicated 

 in the figure, the manipulation is as follows : 

 The key T is closed and the switch quickly 

 moved from e to c. If there is a deflection 

 of the galvanometer the key is opened, the 

 switch set back to its first position, and the 

 values of P and Q changed until zero deflec- 

 tion is obtained when the switch is thrown. 

 The arrangement is then ' balanced ' and 

 X = RQ/P. 



This relation is easily deduced. The po- 

 tential to which the condenser is charged in 

 the first case, viz., that between B and C, is 



e=I{E + P) 



E{B + F) 



B+P^Q+X 



where E is the E.M.F. of the cell and X its 

 resistance. When P and Q are short-cir- 

 cuited the condenser is charged to the differ- 

 ence of potential between A and C, which is 



e' = RF ■- 



'E^X' 



When the galvanometer shows no deflection, 

 e = e' , or 



