114 G. H. KNIBBS. 4 
equivalent in terms of 2,,, k and x, we have for P,, the difference 
of pressures at 2,, and R, 4 
Tv 
In 
P, = 399 ['(R,, + ke) Ade 
0 
Remembering that for x = L,, R,, + kx = Rp, this gives i 
integration and reduction fi 
P, = 229 | In(Bmt Rula+ Pn) _ 8nq Vo Gage 
sh 3 Rm Ry = Ry Rn 4 
V,, being the volume of the frustum ; and similarly for any other 
length of the tube. The formula for a tube forming a series Ls 
conical frusta may consequently be written— 4 
Se oe 
: =* oe 
RR RR 
Tf the quantity in brackets be divided by wL, L being the total 
length of the tube, it will give the reciprocal of the fourth pow — 
of the radius, say R*, of a right circular cylinder of equal length 
and efflux, hence R may be called the ‘mean radius of efflux’ of 
the tube. This value is different to that used by Poiseuille, who @ 
neglecting variations of diameter between the terminals of a 
computation. Putting 
R=3(& - 2,) ande = R, - Rm 
: Ley + Lin 
(23) may be reéxpressed 
3 8nqL Sing L © . 
* : Ger m4 4 ee ig aes Joo* 
DFR eae pe tte 
The former of these is the more convenient expression for 
comparisons. The greatest value of ¢ for any of Poiseuille’s tu? 
is about 1/60—tube D: this produces an error of about 1/1080 
Poiseuille’s method of reduction be followed. 
13. Flow in a frustum ofa right elliptical cone.—The departar 
from a circular form in the transverse section of capillaries 
es 
* Excepting the case of the tube F, see p. 484 of his memoit- 
