60 
Proceedings of the Royal Society 
3. On the Forces experienced by Solids immersed in a 
Moving Liquid. By Sir William Thomson. 
Cyclic irrotational motion,* [§ 60 (z) ] once established through an 
aperture or apertures, in a movable solid immersed in a liquid, 
continues for ever after with circulation or circulations unchanged, 
[ § 60 (a)] however the solid he moved, or bent, and whatever influ- 
ences experienced from other bodies. The solid, if rigid and left 
at rest, must clearly continue at rest relatively to the fluid sur- 
rounding it to an infinite distance, provided there be no other solid 
within an infinite distance from it. But if there he any other solid or 
solids at rest within any finite distance from the first, there will he 
mutual forces between them, which, if not balanced by proper 
application of force, will cause them to move. The theory of the 
equilibrium of rigid bodies in these circumstances might be called 
Kinetico- statics ; but it is in reality a branch of physical statics 
simply. For we know of no case of true statics in which some if 
not all of the forces are not due to motion ; whether as in the case 
of the hydrostatics of gases, thanks to Clausius and Maxwell, we 
perfectly understand the character of the motion, or, as in the statics 
of liquids and elastic solids, we only know that some kind of mole- 
cular motion is essentially concerned. The theorems which I now 
propose to bring before the Boyal Society regarding the forces ex- 
perienced by bodies mutually influencing one another through the 
mediation of a moving liquid, though they are but theorems of ab- 
stract hydrokinetics, are of some interest in physics as illustrating 
the great question of the 18th and 19th centuries : — Is action at a dis- 
tance a reality, or is gravitation to be explained, as we now believe 
magnetic and electric forces must be, by action of intervening matter? 
I. (Proposition.) Consider first a single fixed body with one or 
more apertures through it ; as a particular example, a piece of 
straight tube open at each end. Let there be irrotational circula- 
tion of the fluid through one or more such apertures. It is readily 
* The references §§ without farther title are to the author’s paper on 
Vortex Motion, recently published in the Transactions (1869), which contains 
definitions of all the new terms used in the present article. Proofs of such 
of the propositions now enunciated as require proof are to be found in a con- 
tinuation of that paper. 
