of Edinburgh, Session 1871-72. 
675* 
published, that 
dij/ 3 d<p 
&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 “ On the Forces experienced 
by Solids immersed in a Moving Liquid,” which relates to the 
forces required to keep the movable solids at rest. The present in- 
vestigation shows Prop. II. of that article to be false. Compare 
“Beprint,” § 740. 
0. 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 Boyal Society of Edinburgh 
of February 1871. The ?? 0 , ... of the present article correspond 
dT «iT 
to the — - , — , &c., of the former; the L », ... mean the same in 
du dv 
both. The equations now demonstrated constitute an extension of 
the theory not readily discovered or proved by that simple considera- 
tion of the principle of momentum, and moment of momentum, on 
which alone was founded the .investigation of my former article. 
10. Going back to the analytical definition of in § 3 (5), we see 
that when none of the movable solids is perforated, this configur- 
ational 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 
48 = E - W . . . (24), ' 
and remarking that E is independent of the co-ordinates of the 
movable solids, we may put — W in place of (fj In the equations 
of motion, which, for this slight modification, need not be written 
* Proposition I. of article on “ The Forces experienced by Solids immersed 
in a Moving Liquid” (Proceedings R. S. E., February 1870, reprinted in 
Volume of Electric and Magnetic papers, §§ 733 ... 740). 
t See Proceedings R. S. E., Session 1870-71, or reprint in Philosophical 
Magazine, Nov. 1871. 
4 u 
VOL. VII. 
