Intelligence and Miscellaneous Articles, 237 



C' = /3+ y c ~ a ) t i n which a and ft are constants. It is a minimum 



(H + .r)" 

 for .t'=0 ; that is, when the external circuit is zero ; it gradually in- 



A a 



creases till it equals——^- for x — 11 + 2a; it decreases to /3 when 



2(R + a) 



x tends towards infinity, which is the case when the circuit is open. 



It follows thence that, if the brake be not touched, the working of 



the machine is progressively retarded as the resistance increases up 



to a value of x equal to R-j-2a, resuming then increasing velocities 



when the external circuit continues to increase. 



These laws may be demonstrated in another way. Experiment 



xA 2 



first measures the quantity C or — ^ ■ , then the increase of work 



4 ' # . (R+*) 2 



T — T' which the motor furnishes to the machine when, the circuit 

 being first open, the resistance x is introduced. T— T v divided by 

 the mechanical equivalent of heat E, represents the heat imparted by 

 the motor ory — (3; we have therefore 



T— T, =c a A 2 



E (R + a;) 2 



By this formula E may be calculated. 



Our experiments have given us more than fifty values for E, which 



agree virtually with those found by other methods. 



(x — cl)A 2 

 The heat taken from the motor /3+ ^ —. — reproduces in the 



circuit a quantity C= — — . According to Joule's law, it should 



(R-f-#)- 



reproduce in the internal circuit a number of thermal units equal to 



A 2 ? 



, whence it follows that the difference between these quan- 



tities, that is, 



represents the quantity of heat uselessly expended. Our experi- 

 ments have shown that it is equal to two-thirds of that borrowed 

 from the motor. 



The discrepancies we have indicated between the laws of the mag- 

 neto-electrical machine and those of the pile may be explained by an 

 hypothesis which appears very probable. One portion of the heat 

 C" which is not utilized will be employed in overcoming passive re- 

 sistances ; it is constant; let us call it M. A second part will be 

 employed in producing a reaction in the fixed magnets which cannot 

 be experimentally valued, but which necessitates an absorption of 

 heat ; it is variable ; let us call it C"; we have 



C "'=> 3 - M - w 



