Theory of Magnetism. 45 



the opposite direction both on the fluid and the cylinder, the 

 secondary streams would be unaffected, the fluid would be re- 

 duced to rest, and the cylinder would be made to move in it in a 

 given direction with a given velocity. This is the case of nature, 

 a magnetized body being carried through space by the earth's 

 motion, and its magnetism being the result of the generation of 

 secondary streams by the relative motion of the sether and by 

 the interior gradation of density. It is, however, to be observed 

 that the motion which the earth has in common with the solar 

 system, the motion in its orbit, and the rotation about its axis, 

 produce independent magnetic effects, and that the total magne- 

 tism is the sum of the magnetisms which these motions would 

 produce separately. The reasons for this statement are that the 

 resultant of these motions is not a uniform motion in a fixed di- 

 rection, and, as there will be occasion to show subsequently, the 

 secondary motions which they would generate singly are such 

 steady motions as can coexist. 



Reverting now to the case of the magnetic streams of the cy- 

 lindrical magnet, which may be conceived to have a fixed position 

 in space, let C be the middle point of the axis, and let the den- 

 sity increase from the end A to the end B, so that the course of 

 the secondary stream is in the direction from A towards B. Ac- 

 cording to hydrodynamical principles, there can be, on the whole, 

 no transfer of fluid across any plane perpendicular to the direc- 

 tion of the axis, the motions of the fluid within and outside the 

 cylinder being both taken into account. In calculating the ve- 

 locity of the fluid at any point, the effect of the occupation of 

 space by the atoms will be considered only so far as it produces 

 secondary streams by the gradation of density. 



To show how the above-mentioned condition is fulfilled is the 

 object of the following argument. Conceive the axis to be cut 

 perpendicularly by a plane at the distance oc from C in the direc- 

 tion towards B, and draw any straight line from C intersecting 

 the plane in P. Let CP=r, the angle PCB = #, and, y being 

 an unknown function of x, let 2/ 2 + # 2 = R 2 . Since the motion 

 of the fluid is wholly in planes passing through the axis, the 

 velocity at P may be resolved into U along CP and W perpen- 

 dicular to this line. It will now be assumed that for any point 

 in the transverse plane, beyond the distance y from the axis, 



TT VR 3 a w VR 3 . a 



The forms of these expressions have been adopted from a consi- 

 deration of the circumstances of the motion when the fluid is 

 impelled by a moving sphere, in which case, as is known, both V 

 and R are constant, and the expressions apply to all points of 



