116 On the General Law of the Transformation of Energy, 

 to the heat discharged in unity of time, and 



(11) 



Qi-Qj _ M -Rm 



Q, M ' • • • • 



the proportion of the total energy received which is converted 

 into mechanical power. 



This formula, deduced from an abstract principle by interpre- 

 ting its symbols according to experimental data, agrees with 

 results arrived at by Professor William Thomson and Mr. Joule 

 from the special consideration of electro-chemical and magnetic 

 forces. 



If we take for granted (what is not absolutely certain) that 

 the resistance of the circuit in an electro-magnetic engine is the 

 same whether it is performing work or not, then let Uq be the 

 quantity of the current which would take place if the engine 

 were not working, and we obtain the following value of the 

 electromotive force, 



M = Rwo, 

 which reduces the above formula (11) to the following : 



Q,-Q,^^^-« ^j^^^ 



This is the formula given in a paper " On the CEconomical Pro- 

 duction of Mechanical Effect from Chemical Forces" (Man- 

 chester Transactions, vol. x.), by Mr. Joule, who points out its 

 analogy to the corresponding formula for heat. We have seen 

 that they are particular cases of a universal principle. 



To determine the mean quantity of current u in equation (11), 

 we have the following data. Let v be the mean value of the 



doc 

 function ^^x-rr, and p 



the mean amount of power developed by magnetic force in 

 unity of time ; then, m being a coefficient depending on the 

 length and arrangement of coils round the bar, we have 



P = mw^, 

 and consequently 



is the electric energy converted into mechanical power in unity 

 of time. Adding to this Rm^, the quantity converted into heat, 

 and equating the sum to the total production of electrical energy, 

 we have 



Mw=(R + wiv)m', 



and the quantity of the current is found to be 



M ,^. 



R + mv 



