188 Prof. Challis on the Hydrodynamical Theory of the 



of the small magnet's stream at the position of any one of its 

 atoms be V 2 , and be in a direction making the angle a with the 

 axis of the magnet, and let this axis make the angle 2 with the 

 axis of x. Then we have 



w 2 = V 2 cos (0 2 — a), t? 2 = V 2 sin(0 2 — a). 



Hence, by substituting in the above expression for^, 



^ = C-i(Vf + 2V 1 V 2 cos (^-^ + a )+V;). 



The pressure^, so far as it depends onthe term V|, can have 

 no effect in producing either rotation or motion of translation of 

 the small magnet, because the velocities V 2 are symmetrical 

 both with respect to its axis, and to the transverse plane passing 

 through its centre. Hence, omitting this term, we have, since 

 V 1 and ] have been supposed constant, and 2 is a constant 

 angle, 



dp -\t //) a x d.V 2 cosa Tr . /z) £>c?.V 2 sina 



SO 



dp xt ta a N d.V 2 cosa ^.^.Vgsina 

 -|=V lC os^-^)— -f y V l81 n(0,-0 2 )— | 



18. We may now simplify the reasoning, without loss of ge- 

 nerality, by supposing that the axis of oc coincides with the axis 



of the small magnet, or that 0^ = 0. In that case 2 . r = 0, 



0,2 dx 



because by reason of the symmetry of the motion the positive 

 values of — - — J are just counteracted by the negative, and 



the same is the case with respect to the values of * . 



Hence the forces parallel to the axis of the magnet have no ten- 

 dency to produce motion of translation. Neither do they tend 

 to produce rotation, because corresponding to a force at any 

 point on one side of the axis there is an equal force at an equal 

 distance on the other side, and equally distant from the axis of 

 motion. We have thus only to consider the effects of the forces 



do 



f- Now the sum of these forces is zero, because by reason 



dy J 



of the symmetry of the motion, the sums of the positive values 



d.V 2 cosa d.V 2 sina . , , , 



ot -| ana ^ are respectively equal to the sums 



of their negative values. Hence there is no tendency to motion 

 of translation transversely to the axis. Also the forces expressed 



