390 Mr. Challis on the general Equations 



If the expanding body cause the particles in contact with it to 

 move with a velocity varying inversely as the square of the 

 distance from the centre, F{t) = a constant, F'{t) = 0; and if 

 at the same time P be the pressure where r is infinitely great, 



P = P-Y- 



The pressure is consequently less as the distance from the centre 

 is less. If the expanding body begin to move with the velocity 

 ,s/2P, and go on moving according to the supposed law, the 

 pressure of the fluid in contact with it, commencing with nothing, 

 will go on increasing: if the initial velocity be greater than 

 ^•2P, the fluid will be made to fly off* from the expanding 

 body, and a vacant space will be produced. 



(2). To take an example of the equation, 



suppose the ventricle of the heart to contract according to a law 



of velocity indicated by sin ^ : then, as the contractions are 



small, the velocity with which the fluid enters the great aorta 



will follow the same law, and may be equal to m sin ^^ . If 



we suppose the arteries to be rigid, and the velocity in them at 

 each point to remain the same in direction while it alters in 

 (fuantity, that is, if the values of a, /3, y, be supposed indepen- 

 dent of the time, which must be very approximately the case, 

 we shall have, 



, , Trat , dm , , . iram irat 



w = <f){s),m sin — - , and -t- = <f>(s}. —— cos — — . 



