202 THE REALITIES OF MODERN SCIENCE 



with reference to a fixed coil. The former will turn 

 until its motion has reduced the potential energy of 

 the system to a minimum, in which condition the planes 

 of the coils and the currents will be parallel. In 

 general, coils carrying currents, if 

 free to move, will rotate so as to 

 make their currents parallel and 

 will also tractate, the resulting 

 motion of each coil being a com- 

 bination of the two. 



If the coils are not single loops 

 or bunched windings, but are sole- 

 noidal, we have a number of sys- 

 tems of single loops. Of course, 

 each loop of a coil is not free to 

 turn about its own axis, but all 

 must turn about a common axis. 

 The motion of translation is the 

 same for all the loops of the same 

 coil. Each of these systems tends 

 by conversion into kinetic energy 

 to reduce its potential energy, and 

 the space rate at which that of 

 the entire system reduces is the sum of the rates of 

 the component systems ; in other words, the force 

 acting is the sum of the forces due to the several loops' 

 in all the combinations of two at a time which they can 

 form. 



In the solenoids which we have just considered the 

 individual loops are mechanically connected and can- 

 not revolve about axes lying in their own planes. 

 Imagine one solenoid to be replaced by a large number 



FIG. 22. 



