xlii. ABSTRACT OF PROCEEDINGS. 
L apart—are measured, B and C are the semiaxes of the ellipse, 
and 7 is the viscosity of the fluid. Tables of the values of viscosity 
and fluidity were given. 
It was pointed out that Prof. Reynolds had, in respect to the 
witnessing of the two régimes in glass tubes, been anticipated in 
1853 by Hagen, who recognised exactly the influence, on the 
velocity of translation parallel to the axis of the pipe, of the 
internal agitation that succeeds the condition of minimum shear— 
the first régime. Reynolds’ factors, in his empirical and supposed 
general formula, were shewn to lead to the same result as the 
formula above given, which is based on rational mechanics. 
That the index 2 in the expression 7? « J, the latter denoting 
H/L, was too great, was proved to have been recognised by DuBuat 
Woltmann and Eytelwein at the end of last and beginning of this 
century, as also by St. Venant, Hagen, and Gauckler, in 1850, 
1853, and 1867, so that Reynolds’ direct statement in 1883, that 
no one had recognised the law U™ « J, was not supported by fact. 
Not only was that so, but St. Venant in 1850 had employed the 
method of logarithmic cobrdinates, as also Hagen in 1853 and 1867. 
Prof. Reynolds’ supposed general empirical formula given in the 
Phil. Trans. in 1883—which might be written 
MPP eth FRO ical (7) 
M and N being constants for all classes of pipe, f the relative 
fluidity, and R and UV the same meanings as usually—was shewn 
not to be experimentally indicated for the second régime, while it 
it might be replaced by the ate rational formula, already givens 
for the first. 
It was shewn that J" « f%, and also that U® « R™, but that 
q and m were not respectively 2—n and 3-—n, as required by 
Reynolds’ formula. For these indices the following were proposed 
as sufficiently interpreting experimental data, viz. 
x 
ee (35) 
= a(n-—1)*+a mf 
in which a = 1, « = 0°18, and z = 2, and 
