Intelligence and Miscellaneous Articles. 385 



It is seen that this intensity does not increase indefinitely with the 

 velocity, but tends towards a limit value 



1= 



which is besides very near those obtained for moderate velocities 

 and weak resistances. 



The expression of the total electrodynamic work of the machine, 

 designating by I' the square root of the mean of the squares of the 

 intensities, is 



W=EI' 2 = 5^ 



2^(R 2 IH47r 2 U 2 ) 



This expression tends towards zero when the resistance increases 

 indefinitely, and becomes when the circuit is opened ; experiment 

 shows, in fact, that in this case we have no other work to overcome 

 than that of the passive resistances*. But, contrary to what takes 

 place with a pile, its maximum does not correspond to an external 

 resistance =0. The work at first increases when the resistance is 

 augmented, and passes through a maximum corresponding to the 

 equation 



RT=2ttU. 



The conditions of the maximum of work can always (as is seen) 

 be realized either for a given velocity or a given resistance ; and it 

 is always advantageous to work the machine under those conditions. 

 The equation of the phase then gives 



tan27r0=l, or <p m = i, 



that of the mean intensity 



I - e ° 



m nV27T 2 U' 



and that of the maximum work 



f 2 1 

 W = ° — . 

 m 8»VU T 



Thus, for a given intensity of the field, whatever may be the 

 other conditions under which the machine works, from the moment 

 when it gives the maximum of work 



The retardation is equal to -^ of the entire period ; 

 TJie intensity is constant and equal to the quotient by \J 2 of the 

 absolute maximum of intensity ; 



The electromagnetic work is proportional to the velocity ; 

 The velocity is in a constant proportion to the resistance. 



In the Siemens machine (a machine with four foci) on which 

 my experiments were made, U = 0-104 and n=4. When the in- 

 ductor is excited by a current of 10 webers, e = 22'56 volts: the 

 absolute maximum of intensity is equal to 6*1 webers ; and the 

 intensity corresponding to the maximum of work is equal to 4-31 



* It is not the same if the movable system in the magnetic field in- 

 cludes metallic pieces of some extent, and particularly masses of soft iron. 



