358 Prof. Challis on the Hydrodynamical Theory of the 



going communication I have stated that I omitted, from want of 

 leisure, to compare the theory with observation by arithmetical 

 calculations. Part II. was, in fact, finally written out for the 

 press before I took any steps for making such comparison, being 

 deterred from the undertaking mainly by the apprehension that 

 it would require more time and labour than I could spare for 

 it. I have, however, since found that the theory could be 

 sufficiently tested by an amount of calculation much less than 

 that which I thought to be necessary ; and I now propose to give 

 the results of such calculation. 



According to the proposed hydrodynamical theory the action 

 of a cylindrical coil on an external small magnet consists of two 

 parts, which I have named " direct " and " indirect." The for- 

 mulae for calculating the angle of position of the magnet, sup- 

 posing it to depend only on the indirect action, are given in art. 

 15 ; and those for calculating the position as depending only 

 on the direct action are given in arts. 46 and 47. The theory 

 is incapable of furnishing of itself formulae for calculating the 

 effect of the simultaneous action of the two parts \ but it is shown 

 in art. 53 how the calculation may be performed by the aid of 

 experimental data. 



The first set of formulae were derived from the hydrodynamical 

 theory of magnetic force, supposing the form of the magnet to 

 be cylindrical, its transverse section small, and its ends to be flat, 

 on the principle that under these conditions the magnetic action 

 may be supposed to be concentrated in an elementary line of uni- 

 form magnetic intensity along the axis (see arts. 12-14). Then, 

 for the reasons given in arts. 50 and 51, the same supposition is 

 made relative to the galvanic coil ; that is, as far as regards the 

 indirect action, it is supposed to act exactly in the same manner 

 as a magnet of the same length, having the form described above, 

 provided also its transverse dimensions be small compared with its 

 length. This last condition was satisfied in the experiments 

 about to be used for testing the theory, the interior radius of the 

 coil being 0*45 inch, the exterior radius 0*7 inch, and its length 

 13*4 inches. In calculating thus the indirect action the exact 

 transverse dimensions do not come into account. 



It is evident that the action will be the same in all planes 

 passing through the axis of the magnet, or coil ; and since the 

 motion of the aether in any such plane is symmetrical both with 

 respect to this axis and the transverse plane through its middle 

 point, it will suffice to consider the lines of motion of the stream 

 in only one of the quadrants. According to our theory the 

 stream of aether issues from that end of a magnetic needle which 

 is directed southward, which, as represented in the diagram in 

 the Philosophical Transactions, vol. clxii. p. 488, is on the right 



