187 1.] Heat, and Force. 81 



platinum, take two couples of zinc and (say) copper or 



other metal having an electro-motive force = —; take the 



2 

 plates of such a size that the battery resistance of the two 

 couples together shall be exactly equal to the battery- 

 resistance of the former single couple, and use the same 

 conducting wire ; then the quantity of electricity circulating 

 is exactly the same as before, and H becomes — 



f2Rb\ J _ f RH-n* 

 y ) + (rw) 



That is, the heat and circulating electricity are exactly the 

 same as before, and yet as there are two couples instead of 

 one, and the circulating electricity is the same, exactly 

 double the amount of zinc is consumed. 



The theory, then, is here inconsistent with itself. If the 

 zinc consumed be doubled, the heat produced should be 

 double, and the amount of electricity circulating in the 

 circuit should be double. Half the zinc, therefore, is 

 wasted, and the oxidation of a given weight has either pro- 

 duced only half the heat, or if it has produced an equal 

 amount of heat, only half of it has been put into circulation ; 

 and if the magnetical and dynamical effects be proportional 

 to the heat circulating, or to the electricity circulating, or 

 to any power of these, we get from the same quantity of zinc 

 only half of the effect which we got in the first case. 



It is evident, again, that by taking a single couple of zinc 

 and of some other metal whose electro-motive power is half 

 of E (that of zinc and platinum), and halving the total 

 resistance of the circuit, we should get the same quantity of 

 electricity circulating, and an equal quantity of zinc con- 

 sumed as in the first circuit, but only half of the heat 



developed ; for the equation would now become H = P — , 



2 



R being the resistance of the original circuit. So that we 



can construct different batteries in which respectively the 



ratio of the zinc consumed to the heat produced shall be 



the same or shall vary in' any proportion. 



8. Now take another instance of the same kind. First 



take as before a single pair of zinc and platinum. Then we 



get the same equations and results as before ; namely — 



F 2 



H = 



Rb+rw 



Next, insert in the circuit a cell with two plates of zinc, 



VOL. VIII. (O.S.) — VOL. I. (N.S.) M 



