118 ‘ G. H. KNIBBS. 
rejection of terms in p and « higher than the square, we obtain 
P, = 8nq i Ln (1 + 2c? + 4p?) approx......... (28) . 
T # ba 
which may be used whenever «* and p* are negligible. This | 
limitation is not so serious as might at first appear, for one would q 
select for the purposes of a viscosity experiment a tube closely — 
approximating in form the right circular cylinder, or, if an oval 
and conical tube must perforce be used, one would be chosen in ' 
which the ratio of the axes was subject only to slight variation, _ 
and in which the axes themselves were of nearly constant magn- 
tude throughout its length. | 
The fall in pressure may also be approximately expressed of : 
terms of the mean of the diameters by substituting the value of 
R; in terms of R},. This gives 
re = 8g ‘ af + 3e2 4p?) (29) 
Rr 
T 4 
Tf the « and p terms be written in the denominator they must 
have the negative sign. This formula will sometimes serve 354 - 
rough check on (26). | 
16. General result.—The equations of Sections 10 to 15 not ’ 
only supply the requisite mathematical material for an accurate 3 
computation of the viscosity from experimental data, but “ i 
furnish also ready means of estimating the consequence of eh 
observed or hypothetical defect of form in a tube proposed t0 s : 
employed for that purpose. And at the same time they indicate ; 
that the method of measuring the mean radius of capillaries only 
by contained volumes of liquid, is unsatisfactory when an ac a 
determination is required, for if the tubes be even slightly elliptical 4 
in section, or conical longitudinally, the volume of efflux pet 4 
of time may sensibly differ from that of a right circular of equal 
length and volume. The degree of precision with which gs : 
"mean radius of efflux’ must be ascertained will always be fou 
Pimes as great as that required in the deduced viscosity, that i8 
say, if the latter is to be exact to say 1 in 1000, the mean radilS 
must be accurate to 1 in 4000. For, if we put é for the ratio of 
me 
Seaitice eo se4 es: rie eRe es 
