356 Prof. Challis on the Hydro dynamical Theory of the 



pendicular to that axis, will apparently diverge from a point of 

 the axis more distant from the origin O than the point of appa- 

 rent divergence of those lines of motion of the magnet which 

 pass through the same points P. Analogous considerations, 

 applied to the entering streams at the other end of the coil, 

 would show that the points of apparent convergence of the lines 

 of motion are more distant from O in the case of the coil than 

 in that of the magnet. These inferences from the theory accord 

 with the results of the experiments mentioned in art. 52. 



53. According to what is said in art. 20, the velocities desig- 

 nated by X x , X'u Zj, Z' x are proportional to the directive forces 

 of the coil in the transverse and longitudinal directions. The 



theory has furnished an expression for ==V, which ratio de- 



1 



termines at any point the direction given to the axis of the small 



magnet, either by the streams of a large magnet or by those due 

 to the indirect action of a coil; and it has also furnished the 



71 



value of — 9 which gives the direction that the axis of the small 



magnet would take if acted upon only by the transverse cir- 

 cular movements of the galvanic current. But we require to 

 know the direction of the axis resulting from the total action 

 of the coil, the expression for determining which, on the prin- 

 ciple of the coexistence of velocities, will be 



z,+z\ 



X.+X'f , 



It is here to be remarked that, according to the conditions 

 of the problem, there must be a certain hydrodynamical relation 

 between Z x and Z' v as also between X x and X^; but in the ex- 

 isting state of hydrodynamics it does not appear possible to 

 ascertain these relations exclusively by theoretical investigation. 

 Hence for calculating the above ratio recourse must be had to 

 experimental data. Theory has advanced so far as to prove that 

 Z 1= =CxM, X, = CxM', Z', = C'xN, X'^C'xN', M, M', N, 

 N' being quantities that can be calculated from known formulae, 

 and C, C being unknown constants. If, now, for a certain po- 

 sition of the centre of the small needle the value of the ratio 

 which determines the angular position of its axis be found by 

 experiment to be /3, we shall have 



fl _ Z, + Z , l _ C,M + C/N _ M + C,N 



P X, + X\ ~ CM' + C'N' ~ M' + dN " 



C, being put for — . Consequently C t = N , R ___-£ . By taking 



