338 Sir William Thomson on the Motion of 



by an infinitesimal displacement, £\|r, is -j-j-Byj/; and M/tty is the 



work done by the applied forces). It is proved in §§ 724-730 

 of a volume of collected papers on electricity and magnetism soon 



to be published, that jy-s -jj-, &c, are the components of the 



forces experienced by bodies of perfect diamagnetic inductive 

 capacity placed in the magnetic field analogous* to the supposed 

 cyclic irrotational motion. Hence the motive influence of the 

 cyclic motion of the liquid upon the solids in equilibrium is equal 

 and opposite to that of magnetism in the magnetic analogue. 



This is proposition II. of the paper f( On the Forces experi- 

 ienced by Solids immersed in a Moving Liquid/' which relates 

 to the forces required to] keep the movable solids at rest. The 

 present investigation shows Prop. II. of that article to be false. 

 Compare ' Reprint/ § 740. 



9. Equations (16) for the case of a single perforated movable 

 solid undisturbed by others, agree substantially with equations 

 (6) and (14) of my communication f to the Royal Society of 

 Edinburgh of February 1871. The f , t] Q} . . . of the present 



dT dT 

 article correspond to the ~r-) -j-, &c. of the former ; the £, tj, . . . 



mean the same in both. The equations now demonstrated con- 

 stitute an extension of the theory not readily discovered or 

 proved by that simple consideration of the principle of momen- 

 tum, and moment of momentum, on which alone was founded 

 the investigation of my former article. 



10. Going back to the analytical definition of (S in § 3 (5), 

 we see that, when none of the movable solids is perforated, this 

 configurational function is equal to the whole kinetic energy (E) 

 which the polycyclic motion would have were there no movable 

 solid, diminished by the energy (W) which would be given up 

 were the liquid, which on this supposition flows through the 

 space of the movable solid or solids, suddenly rigidified and 

 brought to rest. Putting then 



<a=E-W, ...... (24) 



and remarking that E is independent of the coordinates of the 

 movable solids, we may put — W in place of <2H in the equations 



* Proposition I. of article " On the Forces experienced by Solids im- 

 mersed in a Moving Liquid," Proc. Roy. Soc. Edinb. February 1870, re- 

 printed in Volume of Electric and Magnetic Papers, §§ 733-/40. 



f See Proc. Roy. Soc. Edinb. Session 1870-71, or reprint in Philoso- 

 phical Magazine, November 1871. 



