350 Prof. Challis on the Hydro dynamical Theory of the 



expect a deviation from the experiments described in this paper, 

 we should have only the second explanation to fall back upon. 



The experiments were made in the physical laboratory of the 

 University of Gottingen ; and I have to thank Professor Weber 

 and Professor Riecke for the kindness with which they have 

 placed the necessary apparatus at my disposal. 



XLVIII. The Hydrodynamical Theory of the Action of a Galvanic 

 Coil on an external small Magnet. — Part II. By Professor 

 Challis, M.A., F.R.S. 



[Continued from p. 200.] 



THE discussions of principles and proofs of propositions, con- 

 tained in Part I. in the September Number, have prepared 

 the way for a direct solution on hydrodynamical principles of 

 the problem of the action of a galvanic coil on a small magnetic 

 needle, which I now proceed to give. For the sake of conveni- 

 ence in making references, the articles in this second Part are 

 numbered in continuation of those of the first. 



43. Prom the reasoning contained in arts. 24-88 it has been 

 concluded that the motion of a galvanic current along a uniform 

 conductor whose axis is a complete circle, and whose transverse 

 section is a small circle of given radius, consists of circular 

 motion parallel to the axis and of circular motion about the 

 axis in transverse planes, the result being spiral motion, which, 

 as shown in art. 42, may either be dextrorsum or sinistrorsum. 

 A rectilinear axis being supposed to be drawn at right angles to 

 the plane of the circular axis of the conductor through its centre, 

 let 11 be the distance of any point of the fluid from that axis 

 and r the distance of the same point from the axis of the con- 

 ductor. Then it has been shown in arts. 35-38 that the trans- 



c 

 verse circular velocity is -|, and the circular velocity parallel to 



Q 



the conductor's axis is ■—-, c l and c 2 being arbitrary constants 



indeterminately related to each other. 



44. Now let a small magnet be so mounted that its oscilla- 

 tions about a centre of motion, supposed fixed, shall be con- 

 strained to take place in the plane which passes through that 

 centre and the centre of the conductor's axis, and cuts the plane 

 of this axis at right angles. Prom what is proved in arts. 17- 

 19, to find the direction which the galvanic current gives to the 

 axis of the small magnet we have only to find the direction, at 

 the centre of its motion, of the velocity of the current [resolved 

 in the plane of that motion ; and it is permitted to consider 

 separately the effects of the two motions which the current con- 



