ELEMENTARY THEORY OF ELECTROMAGNETISM. 55 



If we subtract the force 

 which is required to overcome 

 the backward drag of the water 

 (namely, Ri) from the total 

 propelling force E we get the 

 portion of the propelling force 

 which is used to cause the 

 velocity of the boat to increase. 

 Therefore, according to Art. 33, 

 we have: 



E-Ri=L d (i) 



If we subtract the voltage 

 which is required to overcome 

 the resistance of the circuit 

 (namely, Ri) from the total 

 propelling electromotive force 

 E we get the portion of the 

 propelling electromotive force 

 which is used to cause the cur- 

 rent to increase. Therefore, 

 according to Art. 33, we have: 



E Ri = L~T (2) 



2345678 

 hundredths of, a second 



Fig. 43a. 



The general solution of this 

 differential equation,* subject 

 to the condition that the veloc- 

 ity of the boat is zero at the 

 beginning (i = o when t = o), 

 is: 



The general solution of this 

 differential equation,* subject 

 to the condition that the cur- 

 rent in the circuit is zero at the 

 beginning (i = o when t = o), 

 is: 



* See Franklin, MacNutt and Charles's Calculus, pages 168-181 (published by 

 the authors, South Bethlehem, Pa., 1913). 



