330 ELEMENTARY LESSONS ON [CHAP. vn. 



H = C 2 Rt x 0-24 



where C is the current in webers-per-second, R the resist- , 

 ance in ohms, / the time in seconds, and H the heat in 

 the usual unit of heat-quantities, viz. the amount of heat 

 that will raise i gramme of water through iC of 

 temperature (Art. 255). 



Joule's law may be arrived at by the following calculation. 

 The work W done by a current in moving Q units of electricity 

 through a difference of potential V 2 V x is 



W = Q^-Vj); 



and since Q = Ct, and V 2 - V l = E, and W = JH, (where J is 

 Joule's equivalent = 4*2 x lo 7 , and H the heat in water-gramme- 

 centigrade degree units), we have 



JH = CtE (and E - CR). 



= C 2 Rt 



C^Rt j 



whence H = -y-. 



But as C and R are here in "absolute" units, they must be 

 multiplied by 10 2 X io 9 = IO 7 , to reduce to the ordinary case 

 of webers and ohms ; whence 



H = C 2 Rt -j- 4-2 

 = C 2 Rt x 0-24. 



This is equivalent to the statement that a current oj 

 one iveber-per-second flowing through a resistance of one 

 ohm developes therein 0-24 heat-units per second. 



The second of the above laws, that the heat is, cczteris 

 paribus, proportional to the square of the strength of the 

 current, often puzzles young students, who expect the 

 heat to be proportional to the current simply. Such 

 may remember that the consumption of zinc is, cceteris 

 paribus, also proportional to the square of the current ; 

 for, suppose that in working through a high resistance (so 

 as to get all the heat developed outside the battery) we 

 double the current by doubling the number of battery 

 cells, there will be twice as much zinc consumed as before 

 in each cell, and as there are twice as many cells as at 

 first the consumption of zinc is four times as great as 

 before. 



368. Favre's Experiments. Favre made a series of most 

 important experiments on the relation of the energy of a current 



