ADVANCED ELECTRICITY AND MAGNETISM. 



When a boat moves at veloc- 

 ity 7, the drag of the water 

 opposes the motion of the boat, 

 and this frictional opposition is 

 approximately proportional to 

 /.* Therefore the propelling 

 force E must be equal to RI 

 to maintain the motion of the 

 boat, R being a constant. 



When the velocity of a boat 



dl 

 is increasing at the rate , 



then the propelling force must 

 exceed RI (the backward drag 

 of the water) by an amount 



which is equal to L j-, where 



L is the mass of the boat and 



dl 



is the rate at which the ve- 



dt 



locity of the boat is increasing. 



The backward drag of the 

 water on a canal boat shows 

 itself as a backward pull by the 

 boat on the mule which draws 

 the boat. This backward pull 

 of a boat due to friction may be 

 called the resistance reaction of 

 the boat and it is equal to RI. 



When the speed of a canal 

 boat is increasing at the rate 



When a current / flows 

 through a circuit, something 

 analogous to a frictional re- 

 sistance opposes the flow of 

 current, and to maintain the 

 current an electromotive force 

 equal to RI must act on the 

 circuit according to Ohm's law. 



When a current in a circuit 



dl 



is increasing at the rate -j- f 



then the electromotive force 

 which acts on the circuit must 

 exceed RI by an amount 



which is equal to L, where 

 at 



L is the inductance of the cir- 



1 dl . 



cuit and 3- is the rate at which 

 at 



the current is increasing. 



When a current is pushed 

 through a circuit, the resistance 

 of the circuit shows itself as a 

 resistance reaction which is 

 equal to RI. 



When the value of the cur- 

 rent in a circuit is increasing at 



* The backward drag of the water on the moving boat is by no means propor- 

 tional to the velocity of the boat except when the velocity is quite small. The 

 exact proportional relationship is here assumed for the sake of the analogy. 



