558 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Figure 16. 



Here Li = 1^ = 0^ -\- ^^ M = a^ — k\ and, if there were no mag- 

 netic leakage, k would need to be zero. 



Figure 16 represents the model of Professor Sir J. J. Thomson.^ 

 " It consists of- three smooth, parallel, horizontal steel bars on which 



masses nii, m^, m slide, the 



masses being separated from 

 the bars by friction wheels ; 

 the three masses are connected 

 together by a light rigid bar 

 which passes through holes in 

 swivels fixed on the upper part 

 of the masses ; the bar can 

 slide backwards and forwards 

 through these holes, so that 

 the only constraint imposed 



by the bar is to keep the masses in a straight line." 



If x\, x'2 are velocities of mi, m^, in the same direction, the velocity 



of M, if it be midway between m^ and 7^2, is ^ {x'l + ^'2), and the 



kinetic energy is of the form 



\ LiXi"" + Mx\ • ^2 + i UxP, (26) 



where Lx = mx -\- \ m, Li = m^ -\- \m, M—\ m. 



Professor Webster's model is a modification of that of Thomson. 

 " If the middle weight, instead of rolling on a fixed rail, roll on the bar 

 connecting the two other carriages, the coeffi- 

 cients of induction will vary with the position 

 of the middle mass, and moving it along its bar 

 while one of the outer masses is moving will 

 cause the other to move. The centrifugal force 

 tending to make the middle mass roll along its 

 bar will represent the magnetic forces between 

 the currents." 



The very elaborate and ingenious model of 

 Boltzmann is described at length in the first 

 fifty pages of his Vorlesungen iiber Maxwell's 

 Theorie der ElektricitJit und des Lichtes. 



The general features of another simple model illustrative of this 

 electrical problem are shown in Figure 17. The mass of U is Zi — M, 

 that of V is 4il/, and that of W, L^ — M. In Figure 18 the strings 



^ J. J. Thomson, Elements of the INIathematical Theory of Electricity 

 and Magnetism, Chapter XI.; Webster, Science, Dec. 1895; The Theory 

 of Electricity and Magnetism, § 71. 



Figure 



