Action of a Galvanic Coil on an external small Magnet. 193 



solar system in space), the determination of the motions whereby 

 the individual parts of the fluid alter their relative positions 

 remains the same. 



29. If while such change of relative position is taking place 

 each rectangular fluid element is also changing form, the lines 

 of motion are necessarily not parallel ; and since, by hypothesis, 

 they are in the directions of normals to continuous curved sur- 

 faces, it follows that for such motions udx + vdy -f wdz is an exact 

 differential. But if each rectangular element retains the same 

 form, the lines of motion must be parallel, the surfaces of dis- 

 placement are planes, and udx + vdy ■+- wdz is integrable by a 

 factor. 



In the course of my many hydrodynamical researches I have 

 had from time to time the benefit of criticisms, and arguments 

 ex adverso, from my mathematical contemporaries ; and I wil- 

 lingly admit that I have thereby been induced in several instances 

 to modify my original views. But hitherto I have not perceived 

 that there is any ground for questioning the truth of the prin- 

 ciples and the reasoning which have conducted me to the equation 

 which I call the third general equation of hydrodynamics, and I 

 have consequently not hesitated to employ the equation (#), 

 which is a logical consequence of that general equation, in lay- 

 ing a foundation for the subjoined hydrodynamical theory of the 

 action of a galvanic coil. 



30. A current of the aether being supposed to flow uniformly 

 along a straight cylindrical conductor, the motion of the fluid 

 at any point may be determined by the following reasoning 

 (given in more detail in the ' Principles of Physics/ pp. 563-565). 

 The motion is plainly a function of the distance from the axis of 

 the cylinder, but cannot be wholly parallel to it ; for if that were 

 the case, since the motion is, by hypothesis, steady, and in such 

 motion the pressure is everywhere less as the velocity is greater, 

 and since in this instance the velocity will evidently be less the 

 greater the distance from the axis, it would follow that on all 

 sides there would be tendency to motion towards the axis, which, 

 if not counteracted, would put a stop to the current. To coun- 

 teract this tendency there must be centrifugal force due to cir- 

 cular motion about the axis ; and according to the hydrodyna- 

 mics of steady motion the rectilinear and circular motions may 

 coexist. Hence, if r be the distance from the axis, and the rec- 

 tilinear and circular motions at that distance be respectively 

 F(r) and/(r), we shall have 



u=^f{r) } t>=- */(!•), w=Y(?>). 



These equations satisfy the condition of constancy of mass ex- 

 Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. 



