392 Mr. Challis on the general Equations 



contains h', it depends on the position of the animal. The total 

 pressure on the surface of the ventricle, when at a maximum, 



varies as I'P; the number of pulsations in a given time is — . 

 Hence, as I'P -l'{n + gh') o^l'.m.^, 



A 



the excess of active force above the least that is requisite for 

 carrying on the pulsations, varies in the same animal, as the 

 greatest velocity impressed on the fluid, multiplied by the num- 

 ber of pulsations in a given time, and in animals of the same 

 construction, as the product of the mass of the fluid, the maxi- 

 mum velocity, and the number of pulsations in a given time. 



3. There is one case of frequent occurrence, in which the 

 equation {D) may be readily applied ; viz. when the motion has 

 arrived at a unifonn state, so that the velocity of every particle 

 passing through the same point, is the same in quantity and 



direction. In this case m is independent of the time, -jr = o. 



dt 



and p = F— ~ + constant*. 



2i 



This equation is applicable to the issuing of water, retained 

 at a constant elevation, in any vessel, through any small orifice, 

 or adjutage fitted to the orifice. Let a be the ratio of the velo- 



* This aud the corresponding equation for clastic fluids, (Art. 9.) may be more 

 simply deduced by combining D'AIenibert's principle with a known property of the 

 equilibrium of fluids : viz. that the pressure at any point of a fluid mass, is obtained by 

 integrating in regard to any line whatever, drawn from the point to the free parts of 

 the fluid. In this way they have been deduced by Mr. Moselcy, in his Treatise on 

 Hydrodynamics lately published ; and he has been the first to observe them. Considering 

 the number of phenomena, at first sight paradoxical, which these equations serve to 

 explain, few things more valuable in the theory of fluid motion have been discovered 

 since the time of D'Alembert. 



