200 Mr CHALLIS's RESEARCHES IN THE THEORY 



At the same time, because a^'N.l.p= — -^ nearly, we shall have 



, T , F'{r-at) ,^, 



«.N.l.p = ^ -(2.) 



The equations (1) and (2), involving but one arbitrary function, can 

 apply only to a single disturbance, which takes place in a direction 

 tending from a centre, as I have elsewhere shewn*. It is important 

 to observe that when r is very small, the term of equation (1) which 

 involves r"- in the denominator may be much greater than that in- 

 volving r. In fact, if we expand the fxmctions, supposing r to be 

 very small. 



&c. 



_ F{-at) _ F'{-at) _ F"{-at) 



When therefore the disturbance is made by a sphere of very small 

 radius r, the motion is transmitted from its surface to other parts of 

 the fluid, nearly as if the fluid were incompressible. 



SECTION V. 



Application of the Principles of the foregoing Section to determine the 

 Resistance of the Air to the Motion of a Sail-Pendulum. 



17. For the sake of simplicity, I will suppose gravity not to act. 

 The ball being spherical and perfectly smooth, the direction of the 

 motion of the aerial particles in contact with its surface tends at every 



* Camh. Phil. Trans. Vol. HI. p. 402. 



