50 On the Hijdrodynamical Theory of Magnetism. 



because, while v x retains the same sign, v 2 has equal values with 

 opposite signs for the two arms. 



According to the before-supposed positions of the magnets, 

 the stream from the fixed one will oppose the transverse part of 

 the stream from the moveable one on the east side of the north 

 arm, and conspire with it on the west side, so that the pressure, 

 being greater as the composite velocity is less, will be in excess 

 on the east side. For like reasons the pressures on the atoms 

 of the south arm will be in excess on their west sides. Hence 

 the movement of the needle will be the same as if the pole B of 

 the fixed needle repelled the pole B of the moveable needle and 

 attracted its pole A. 



By this reasoning it is shown that the momentum of rotation 

 of the moveable magnet is proportional to the velocity ?;, ; and 

 from the foregoing mathematical theory it appears that v 1 is in- 

 versely proportional to D 3 , D being the distance between the 

 centres of the magnets, or, presumably, that 



1_ D 3 \ JDV* 



In the second set of experiments the fixed needle was placed 

 either to the north or to the south of the moveable one, so that 

 the latter pointed to its centre, and the direction of its axis was 

 still perpendicular to the plane of the meridian. In these posi- 

 tions the stream of the fixed needle will cut at right angles the 

 axis of the moveable one, and its action on the latter will be very 

 nearly the same in kind as in the former set of experiments, but 

 will differ in the circumstance that the velocity at the distance 

 D is half the velocity in the other case at the same distance. 

 The more exact proportion of the momenta of rotation in the 

 two cases for the same value of D is presumed to be 



These results agree with Gauss's numerical determinations both 

 as regards the law of the inverse cube and the ratio of the mo- 

 menta of rotation. This ratio is shown by the experiments to 

 be nearly equal to 2, and to be less than this value by a greater 

 quantity as the distance D is less; which accords with the above 

 expression, if h 2 be greater than h' 2 . 



The hydrodynamical theory of magnetism has thus given intel- 

 ligible reasons for the facts of these experiments. The provisional 

 assumption that VR 3 = a constant, for the approximate truth of 

 which an antecedent reason was assigned, seems by these results 



