RECENT PROGRESS IN PHYSICS. 



441 



Fia. 57. 



In fitijiiro 56 h rei)iesents the battery, t the air thermometer, a a 

 Fig- 5G. j)iece of wire introduced into tlie circuit. 



In tlie two followinf!; fij>;ure8 b and t represent 

 the same things as in tlie other ; i'^is- ^8. 



but in figure 57 we have the wire 

 /? instead of a, and in figure 58 

 both pieces of wire are introduced 

 together, so as to ibrm branches. 



If, now, for a given charge of 

 the battery a certain temperature of the air ther- 

 mometer is produced by the combination in figures 

 56 and 57, the question is, wliat is the temperature 

 for the same charge with the combination of figure 

 58? 



liiess has treated this question in the 63d vol., 



page 486, of Poggendorf's Annalen. 



As we have just seen, the elevation of temperature by the air ther- 

 mometer for unity of charge is represented by the formula — 



l+z 



a indicating the temperature which occurs when only the constant 

 parts of the conducting circle close the battery, 2 the time the dis- 

 charge is retarded by interposing any piece of wire in the circuit, 

 provided the time in which the battery is discharged when the said 

 wire is out of the circuit is taken as unity. 



Having determined by experiment the value of retardation, z for 

 one wire a introduced into the conducting circle, and then, in the 

 same manner, the value z^ for a second wire /9, we are able to deduce 

 theoretically the values of retardation when both wires are introduced 

 together, as shown in figure 58. 



The wire a discharges the unit of electrical charge in the time z ; 



in the unit of time, therefore, it can discharge the quantity -. 



z 



In like manner the second wire ^ in the unit of time can discharge 

 the quantity of electricity -j. 



In the unit of time, then, the two wires introduced together (figure 

 58) into the conducting circle can discharge the quantity ^ + /• 



Hence it follows that with the combination of figure 58 the 

 two wires can discharge the quantity of electricity 1 in the time 



+ 



1 



Now, if — 



a 



^ = . ^--^ 



