Powers of Electro-Magnetism, Steam, and Horses. 451 



mechanical power, it would be equal to raise a weight of 158 

 lbs. to the height of a foot*. Hence, if we designate the cur- 

 rent when the engine is at rest by a, and the current when 

 the engine is in motion by b, the heat evolved by the circuit 

 in a given time, will, in the two instances, be as a 2 to & 2 . But 

 the quantities of zinc consumed being as a to &, the heat, per 

 a given consumption of zinc, will be as a to b, or directly as 

 the currents ; a — b will therefore represent the quantity of 

 heat converted by the engine into useful mechanical effect. 

 Therefore, putting x for the mechanical effect in lbs. raised a 

 foot high per the consumption of a grain of zinc, we have 



158 (a-b) 



x = ! -. 



a 



From the above equation it is evident that the ceconomical 

 duty will be a maximum when b vanishes or becomes infinitely 

 small in comparison with a. In this case x = 158, while the 

 power of the engine will become infinitely small with regard 

 to work performed in a given time. We must, however, ob- 

 serve that the equation can only be strictly correct when the 

 current b is uniform, which it never can be exactly, in conse- 

 quence of the resistance of the magnetic induction against the 

 voltaic current varying in the different positions of the revol- 

 ving electro-magnetic armature. Hence the current b is always, 

 to a certain extent, of a pulsatory character, which has the 

 effect of causing it to develope more heat than an uniform cur- 

 rent of the same quantity. From this circumstance, as well 

 as from the unavoidable existence of some slight currents in 

 the substance of the iron of the revolving armature, the actual 

 ceconomical effect will always be somewhat below the duty in- 

 dicated by our formula. 



Applying the formula to our first experiment, we have for 

 the theoretical ceconomical effect, 



158 (2232—920) _ 



2231 ~ 92 ' 9 > 



while the actual ceconomical effect was 

 21100 



205 



= 102-9. 



In our second experiment, the theoretical ceconomical effect 

 will be 



1 58(2232 - 850) _ 



2232 ~ y? ' 8 ' 



* Phil. Mag., vol. xxiii. p. 441. 



