Solid Bodies through a Liquid. 343 



This corresponds to the formula which I gave twenty-five years 

 ago for the force experienced by a small sphere (whether of fer- 

 romagnetic or diamagnetic non-crystalline substance) in virtue 

 of the inductive influence which it experiences in a magnetic 

 field*. 



14. By taking an infinite straight line for the core a simple 

 but very importaut example is afforded. In this case the undis- 

 turbed motion of the fluid is in circles having their centres in 

 the core (or axis as we may now call it) and their planes perpen- 

 dicular to it. As is well known, the velocity of irrotational 

 revolution round a straight axis is inversely proportional to dis- 

 tance from the axis. Hence the potential function W for the 

 force experienced by an infinitesimal solid sphere in the fluid is 

 inversely as the square of the distance of its centre from the 

 axis; and therefore the force is inversely as the cube of the dis- 

 tance, and is towards the nearest point of the axis. Hence, 

 when the globule moves in a plane perpendicular to the axis, it 

 describes one or other of the forms of Cotesian spirals f. If it 

 be projected obliquely to the axis, the component velocity pa- 

 rallel to the axis will remain constant, and the other component 

 will be unaffected by that one; so that the projection of the 

 globule on the plane perpendicular to the axis will always de- 

 scribe the same Cotesian spiral as would be described were there 

 no motion parallel to the axis. If the globule be left to itself 

 in any position, it will commence moving towards the axis as if 

 attracted by a force varying inversely as the cube of the distance. 

 It is remarkable that it traverses at right angles an increasing 

 liquid current without any applied force to prevent it from being 

 (as we might erroneously at first sight expect it to be) carried 

 sideways with the augmented stream. A properly trained dy- 

 namical intelligence would at once perceive that the constancy 

 of moment of momentum round the axis requires the globule to 

 move directly towards it. 



15. Suppose now the globule to be of the same density as the 

 liquid, If (being infinitely small) it is projected in the direction 

 and with the velocity of the liquid's motion, it will move round 

 the axis in the same circle with the liquid; but this motion 

 would be unstable [and the neglected term w (39) adds to the 



* " On the Forces experienced by small Spheres under Magnetic In- 

 fluence, and some of the Phenomena presented by Diamagnetic Sub- 

 stances," Cambridge and Dublin Mathematical Journal, May 1847 ; and 

 " Remarks on the Forces experienced by Inductively Magnetized Ferro- 

 magnetic or Diamagnetic Non-crystalline Substances," Phil. Mag. October 

 1850. Reprint of papers on Electrostatics and Magnetism, §§ 634-668. 

 Macmillan, 1872. 



t Tait and Steele's * Dynamics of a Particle/ § 149 (15). 



