B 



J \j 



A- 



A 



i 



i 



u 



r 



PEIRCE. — CHANGES IN INDUCT.^J«JCES OF ELECTRIC CIRCUITS. 557 



and any impulsive changes in the inductances cause such sudden 

 changes in the current as will keep LiC\+ MCi and ^26*2 + MCx 

 momentarily unchanged. 



Many different working models have been made to illustrate the 

 simple electrical problems which concern two such circuits. Of these 

 some of the best known are due to 

 Maxwell, Rayleigh, J. J. Thomson, 

 Webster, and Boltzmann. 



The original model of Maxwell, 

 now in the Cavendish Laboratory, is 

 represented by Figure 15a, taken 

 from Gray's Absolute Measurements 

 in Electricity and Magnetism, where 

 an excellent account of the appara- 

 tus and its theory may be found. 



In Lord Rayleigh's model, shown 

 in Figure 15b, "two similar pulleys 

 A, B, turn upon a piece of round 

 steel fixed horizontally. Over these 

 is hung an endless cord, and the 

 two bights carry similar pendent 

 pulleys, C, D, from which again hang 

 weights, E, F. . . . In the electrical 

 analogy, the rotary velocity of A 



corresponds to a current in a primary circuit, that of B to a current in 

 the secondary. ... In the absence of friction there is nothing to cor- 

 respond to electrical resistance, so that the conductors must be looked 

 on as perfect. If x and y denote the circumferential velocities, in the 

 same direction, of the pulleys A, B, where the cord is in contact with 

 them, \{x -\- y) is the vertical velocity of the pendent pulleys. Also 

 \{x — y) is the circumferential velocity of C, D, due to rotation, at the 

 place where the cord engages. If the diameter be here 2«, the angu- 

 lar velocity is {x — y) /2a. Thus, if M be the total mass of each 

 pendent pulley and attachment, Mk"^, the moment of inertia of the 

 revolving parts, the whole kinetic energy corresponding to each is 



Figure 15. 



For the energy of the whole system, we should have the double of this, 

 and, if it were necessary to include them, terms proportional to x"^ and 

 y'^, to represent the energy of the fixed pulleys." 



