of small Spherical Bodies in elastic Mediums. 43 



which if g represent the force of gravity, both the terms are 

 negligible. 



Conceive now a small spherical body to descend vertically 

 in the air by the force of gravity. If it be supposed perfectly 

 smooth, it can impress motion on the fluid only in directions 

 perpendicular to its surface. Thus the motion impressed at 

 each instant by the anterior half of the sphere is directed from 

 a centre. If v be the velocity of the sphere, v cos 9 is the 

 velocity impressed in directions making an angle 6 with the 

 line of its motion. This case of disturbance is therefore si- 

 milar to the last, in that the motion is from a centre; but 

 differs in these respects, — the motion is not the same in all 

 directions from the centre, and the centre is not fixed. But 

 I have elsewhere given reasons for concluding (Cambridge 

 Phil. Trans, vol. iii. part 3.) that the equations we have been 

 using, and the results derived from them, apply at each instant 

 to every elementary portion of fluid disturbed in ariy way, 

 provided the condition of the tendency of the motion at each 

 instant, to or from fixed or moveable centres, be fulfilled. If 

 this be admitted, we may at once conclude that the descend- 

 ing sphere is subject to very little change of pressure on its 

 anterior half; for if g = the density of the fluid in contact 

 with any point of it, we find that, 



XT 1 ^/'{t) ^V 



aNap.logg=--^^^^ ^, 



d v 

 in which y [t) = — ^ — cos 9, a quantity not very different 



from g cos 9, since the resistance of the air is small. The 

 same may be said of the posterior half; for it might be shown 

 that the only difference between the disturbances produced by 

 this half and the other, is that the motion is directed towards 

 a centre. Similar reasoning is applicable to any kind of in- 

 creasing or decreasing motion. From all that precedes we 

 draw this conclusion : — 



When a small spherical body moves in a medium like air 

 with a velocity small compared to the velocity of propagation 

 in the medium, and in any manner except in rapid vibrations, 

 the pressure on its surface is at every point very little different 

 from the pressure of the medium at rest. 



The phitnonienon 1 propose to explain by this result is the 

 spherical form of the drops of rain. That they are spherical 

 is shown by the rainbow. Capillary attraction will account 

 for their assuming in the first instance a sj)herical form ; and 

 from the preceding reasoning it follows that being very small, 

 they do not sufll-r in passing through the air any inequality 

 G2 



