SIR W. THOMSON ON VORTEX MOTION, 229 



system of impulsive attractions towards the latter, everywhere in the direction of the 

 normal, and amounting to \fq"dt per unit of area. But it must not be forgotten 

 that the term <f> in the expression [§ 31 (5)] for p produces, as shown in § 30 (1), 

 an influence during the collision, the integral effect of which only disappears 

 from the expression [§ 32 (7)] for the impulse after the collision is completed ; that 

 is (§ 29) after the moving system has passed away so far as to leave no sensible 

 fluid motion in the neighbourhood of the fixed body. 



33. Hence, and from § 23, we see that when there is no impact of moving 

 solid against the fixed body, and when the moving solid or group of solids passes 

 altogether on one side of the fixed body, the direction of the translation will be 

 deflected, as if there were, on the whole, an attraction towards the fixed body, or 

 a repulsion from it, according as (§ 25) the translation is in the direction of the 

 impulse or opposite to it. For, in each case, the impulse is altered by the intro- 

 duction of an impulse towards the fixed body upon the moving body or bodies as 

 they pass it ; and (§ 23) the translation before and after the collision is always 

 along the line of the impulse, and is altered in direction accordingly. This will 

 be easily understood from the diagrams, where, in each case B represents the 

 fixed body, the dotted line ITTT, and arrow-heads I F, the directions of the force- 

 resultant of the impulse at successive times, and the full arrow-heads T T, the 

 directions of the translation. 



Fig.l \l' Fig.2, V/fl 



i i \ / 



AT/ l^T 



4 1 



y 



All ordinary cases belong to the class illustrated by fig. 1. The case of a 

 rigid ring, with cyclic motion (§ 25) established round it as core, belongs to the 

 class illustrated by fig. 2, if the ring be projected through the fluid in the direc- 

 tion perpendicular to its own plane, and contrary to the cyclic motion through 

 its centre. 



34. When (§ 66) we substitute vortices for the moving solids, we shall see (§ 67) 

 that the translation is probably always in the direction with the impulse. Hence, 

 as illustrated by fig. 1, there is always the deflection, as if by attraction, when a 

 group of vortices pass all on one side of a fixed body. This is easily observed, for 

 a simple Helmholtz ring, by sending smoke rings on a large scale, according to 



VOL. XX V. PART I. 3 N 



