Prof. Challis on a Theory of Galvanic Force, 435 



tion, — the forces, in each case, being proportional to the rate of 

 change of pressure. 



6. In the " Mathematical Theory of Attractive "Forces/' given 

 in the Philosophical Magazine for November 1859, 1 have shown 

 by the solution of Problems II. and III., that when a small 

 spherical body in a fixed position is submitted to the action of a 

 uniform stream, the pressures on opposite hemispheres are equal, 

 and consequently that the stream would impress no velocity on 

 the sphere supposing it free to move, nor alter any velocity 

 which it may have otherwise acquired. The effect, however, is 

 different if the stream, though steady, be not uniform, that is, 

 if there be change of velocity, and consequently change of den- 

 sity, from point to point in its course. In that case, the mere 

 statical effect of change of density would produce an accelerative 

 force of the body in the direction of the decrement of density. 

 The total effect will, however, be due both to the motion of the 

 fluid and to the variation of its density. I shall not now 

 attempt to solve the problem of calculating this effect mathe- 

 matically, as the following general considerations may suffice for 

 the present purpose. It has already been stated, as a result of 

 mathematical reasoning, that when a small solid sphere moves 

 uniformly in an elastic medium, the pressures on the preceding 

 and following hemispherical surfaces are equal. Hence there is 

 no tendency to acceleration or retardation of the sphere; and 

 the motion of the fluid being the same in successive instants, 

 the total momentum of the fluid and sphere remains the same 

 in successive instants. This permanence of the momentum in 

 cases where no external force acts, may be regarded as a general 

 law of the mutual action between a solid and a fluid. Accord- 

 ingly, since in the case before us the spherical body is accelerated 

 by the fluid, it will impress at each instant on the fluid in the 

 contrary direction by the reaction on its surface, a momentum 

 equal to that which it receives. But the reactions of spheres 

 of different radii are, cateris paribus, proportional to their sur- 

 faces, that is, to the squares of the radii. Hence the instanta- 

 neous increments of momentum of the spheres are in the same 

 proportion, and the accelerations are therefore in the inverse 

 proportion of the radii. Prom this reasoning it follows that 

 when the atoms of any substance are submitted to the action of 

 a steady aetherial current of variable density and velocity, they 

 are accelerated in the direction of the decrement of density in 

 proportion to some function of the decrement, and the less are 

 more accelerated than the greater. 



If the decrement of density be in a direction contrary to that 

 of the stream, the acceleration of the atoms still takes place in 

 the direction of the decrement. 



