Action of a Galvanic Coil on an external small Magnet. 185 



mum velocity in the condensed half of the wave, is towards the 

 rarer end. At the same time, according to the mathematical 

 result obtained in art. 8 of the article in the Philosophical Ma- 

 gazine for June 1872, the impulsive action on the aether, whether 

 the primary vibratory motions be backwards or forwards, is 

 towards the denser end, out of which consequently the generated 

 streams flow. 



11. The next point is to determine the forms of the courses 

 of the magnetic streams generated under the above-described 

 circumstances. To do this it is necessary to begin with admit- 

 ting the truth of the following general hydrodynamical theorem, 

 of which great use will be made in the subsequent investiga- 

 tions. [For proof of the theorem see art. 10 of the communi- 

 cation just cited.] It is not possible that the motion of an un- 

 limited fluid mass can be such as to transfer any portion of the 

 fluid on one side of an unlimited fixed plane to the other side 

 without the transfer of an equal portion from the latter to the 

 former. Thus the motion must be circulating or reentering ; 

 and accordingly a general characteristic of magnetic and gal- 

 vanic currents is accounted for on the principles of hydrody- 

 namics. 



12. This being understood, the forms of the magnetic lines 

 of motion are determinable, at least approximately, by the fol- 

 lowing argument. We have seen that in consequence of the 

 regular gradation of the atomic density of a cylindrical magnet, 

 and the velocities due to the outstanding undulations which by 

 their attractive action maintain this state of density, the fluid is 

 impelled in each transverse section at every instant towards the 

 denser end of the magnet. These impulses operating against 

 the inertia of the surrounding mass of fluid, have the effect of 

 generating streams which, as being due to a steady action, are 

 steady, and, as fulfilling the condition stated in art. 11, are ne- 

 cessarily circulating. To give a first idea of the courses of these 

 streams, at least in the immediate neighbourhood of the mag- 

 net, I cannot do better than refer to the figure in p. 17 of the 

 Astronomer Royal's ' Treatise on Magnetism/ the directions of 

 the axes of the small magnets indicating (as will be shown sub- 

 sequently) the directions of the lines of motion at the positions 

 where they are situated. An approximate analytical expression 

 for the forms of these magnetic curves is derivable from the pre- 

 sent theory by the following investigation. 



13. From what is argued above, the impulses are produced 

 by variations of pressure due to variations of the square of the 

 mean of the velocities within the cylinder estimated in directions 

 parallel to its axis, these variations being caused exclusively by 

 the mean contraction of channel resulting from the increasing 



