SIR W. THOMSON ON VORTEX MOTION. 219 



in plane perpendicular to it, according to Poinsot ; or to two impulsive forces in 

 lines not meeting, according to his predecessors. Further, I shall designate by 

 the impulse of the motion at any instant, in our present subject, the system of 

 impulsive forces on the moveable solids which would generate it from rest ; or 

 any other system which would be equivalent to that one if the solids were all 

 rigid and rigidly connected with one another, as, for instance, the Poinsot resultant 

 impulsive force and minimum couple. The line of this resultant impulsive force 

 will be called the resultant axis of the motion, and the moment of the minimum 

 couple (whose plane is perpendicular to this line) will be called the rotational 

 moment of the motion. 



7. But, having thus defined the terms I intend to use, I must, to warn against 

 errors that might be fallen into, remark that the momentum of the whole motions 

 of solids and liquid is not equal to what I have defined as the impulse, but (§ 4) is 

 equal to zero; being the force-resultant of "the impulse" and the impulsive 

 pressure exerted on the liquid by the containing vessel during the generation of the 

 motion : and that the moment of momentum of the whole motion round the centre 

 of inertia of the contents of the vessel is not equal to the rotational moment, as I 

 have defined it, but is equal to the moment of the couple constituted by " the 

 impulse" and the impulsive pressure of the containing vessel on the liquid. It 

 must be borne in mind that however large, and however distant all round from 

 the moveable solids, the containing vessel may be, it exercises a finite influence on 

 the momentum and moment of momentum of the whole motion within it. But if 

 it is infinitely large, and infinitely distant all round from the solids, it does so by 

 infinitely slow motion through an infinitely large mass of fluid, and exercises no 

 finite influence on the finite motion of the solids or of the neighbouring fluid. This 

 will be readily understood, if for an instant we suppose the rigid containing vessel 

 to be not fixed, but quite free to move as a rigid body without mass. The momentum 

 of the whole motion will then be not zero, but exactly equal to the force-resultant 

 of the impulse on the solids; and the moment of momentum of the whole motion 

 round the centre of inertia will be precisely equal to the resultant impulsive 

 couple found by transposing the constituent impulsive forces to this point after 

 the manner of Poinsot. But the finite motion of the immersed solids, and of the 

 fluid in their neighbourhood which we shall call the field of motion, will not be 

 altered by any finite difference, whether the containing vessel be held fixed or 

 left free, provided it be infinitely distant from them all round. It is, therefore, 

 essentially indifferent whether we keep it fixed or let it be free. The former 

 supposition is more convenient in some respects, the latter in others ; but it would 

 be inconvenient to leave any ambiguity, and I shall adhere (§ 1) to the former in 

 all that follows. 



8. To further illustrate the impulse of the motion, and its resultant impulsive 

 force and couple, according to the previous definitions, as distinguished from 



