of the Motion of Fluids, 8fc. 391 



-T rr IT am Trat /t , . , &)'.,,. 



Hence, as F= gz, p = gz ^ cos ~^J,p{s)ds --^-f (0- 



Let 2 be measured from a level where the pressure arising from 

 gravity is o ; and let P^ + gh be the pressure where z = h, ft) = w,, 

 f(p{s)ds= —KJ, Ki being a quantity of no linear dimensions: 



mi n . 7 I T^ t Train wUt O),^ _, , , 



Then P,+gh = gh + KJ.-^. cos— f -fW' 



I Ti Tram Trat . J. , n i / \ i > <u— w." 

 and p-P, = gz -— cos —-\K,l+f(p{s)ds\ -^. 



At the entrance of the great aorta let 



z=h', f<p(s)ds=—K.l, p = P., and a) = w. 



Then /' = P,+gA'+ —— cos — — (A:-A,)r 



As it is known that the transverse section of the mean channel 

 of the blood is greater, the greater the distance from tlie heart, 

 K, will be less than K, and w^ less than sr; and the rather so, 

 as A", and w^ refer to a point more distant from the heart. The 

 value of P will be least when sr is greatest. It is possible that 

 the right hand side of the equation above may become negative, 

 in which case the blood might be entirely expelled from the 

 ventricle, as some anatomists suppose it to be. The value of P 

 will be greatest when zr = o, and consequently a), = o. In this 

 case 



r> / r» r^ 7 Tram , ,. j^, Tram 



P = {P,-KJ.-^ + gh) + Kl.-^. 



The quantity in brackets is the least pressure that is requisite 

 for carrying on the pulsations: let it be equal to n + gh'. As it 

 Vol. III. Part III. 3 E 



