Action of a Galvanic Coil on an external small Magnet. 189 

 by the different values of the first term of the formula for ~~ 



. d y 



produce no motion of rotation, because they are equal and in the 

 same direction at equal distances from the axis of rotation on 

 the same side, whether positive or negative, of the axis of the 

 magnet. 



19. But the forces expressed by the second term of the same 

 formula are at a given distance from the axis of motion equal 

 and in the same direction at points equally distant from the axis 

 of the magnet on opposite sides, and at the same time the direc- 

 tions are opposite on the opposite sides of the axis of motion. 

 Accordingly these forces produce motion of rotation, and are 

 the only forces that have this effect. Hence if # be the distance 

 of any atom from the axis of rotation, the whole momentum of 

 rotation is proportional to 



V, sin ^x 22 



d . V sin u 



I—. . dy 



the summation embracing all the atoms on one side of the axis 

 of rotation. It is now to be considered that the accelerative 

 action of the fluid in steady motion on any atom in any direction 

 has a constant ratio to the accelerative force in the same direc- 

 tion of the fluid itself at the position of the atom. [This pro- 

 position is proved in pp. 313-315 of l The Principles of Mathe- 

 matics and Physics. - '] Hence, if H be a constant factor having 

 a certain ratio to the result of the above summation, the directive 

 force of the incident current will be 



KV l sin 0„ 



tending always to place the axis of the small magnet in such a 

 position that its proper current along the axis and the incident 

 current flow in the same direction, in which case 1 = 0. 



20. It follows from the foregoing argument that the longitu- 

 dinal and transversal components of a stream from a large mag- 

 net incident upon a small one are proportional to the directive 

 forces of the stream in the two directions, and that consequently 

 the forces may be supposed to be expressed by the formulae for 

 the velocities obtained in art. 15. 



I take occasion here to remark that the Astronomer Royal 

 has deduced in the Philosophical Transactions (vol. clxii. p. 492) 

 expressions for the same forces wholly different from those in 

 art. 15, by assuming the intensity of the magnetism along the 

 axis of a magnet to vary proportionally to the distance from its 

 centre, and finds that they give numerical results which do not 

 sufficiently agree with experiment. According to the theory I 

 am advocating that assumption is not allowable. 



