71] 



CYCLIC SYSTEMS. 



141 



Consequently the kinetic energy of the system consisting of 

 the three masses m l , w 2 , m 3 at distances from the axis r 1} r 2 , r s is 



T = 





if the velocities / can be neglected. The system is cyclic, the r's 

 being positional, the <'s being cyclic coordinates. In order to 

 make the model a more complete representation of two electric 

 currents, Boltzmann modified it so as to have between the co- 

 ordinates r lt r 2 , r s the relation 



r? + rf=yf, r* + r/ = yf, 



where y ly y z are two independent parameters. The two masses 

 m 1} m 2 are chosen equal, being made one-fourth of m 3 . 



The expression for the energy then becomes 



and we may independently change either of the three co- 

 efficients. 



The Pythagorean theorem suggests a geometrical means of 

 imposing the above constraints. To each of the masses m is 

 attached a string, which runs along the rod to the axis of ro- 

 tation, where, after passing round a pulley it is carried vertically 

 downward to be attached to the following device (Fig. 31). A 



FIG. 31. 



pair of rods are articulated at (7, the point of articulation being 

 made to slide in a vertical line CO. The string from m 3 is fastened 

 to the point C. Sliding on a horizontal line AB and in slots 

 in the rods AC, BC, are the points of attachment of the strings 

 from m and m 2 , which are then carried outward and upward 



