96 G. H. KNIBBS. 
which must be received with considerable limitation. Reynolds 3 
proposed correction is evidently based on the results of experi 
ments with sharp-edged cylindrical adjutages of 2 or 3 diameters | 
length applied to orifices, the effect of which is to cause a discharge _ 
of about 0°815 of that theoretically due to the pressure on the | 
supposition that frictional and other resistances may be’ neglected. 
This loss of head, arising from the contraction! at the entrance dt 
the adjutage, and the subsequent expansion to its full diameter, | 
together with the loss from slight frictional resistance and that 
involved in establishing the flow, gives according to treatises 
practical hydraulics U?/[2g (0:815)?] = 1-506 U2/(2g). Tf the 
edges of the cylinder be rounded off at the connection with the 
discharging vessel at Z’, Fig. 1, the value becomes very nearly | 
U? |(2g), the coéfficient 0-815 increasing almost to unity, a according 
therefore to Reynolds, for the condition assumed by Hagenbath, 
m=0-500, or for the reduction of Poiseuille’s work m= 753. 
This statement is not justified hy an analysis of the experiments 
referred to. The objection to unconditionally assuming that ~ 
Square of the mean velocity in the section may be regarded a | 
equivalent to the mean of the squares of the velocities at diferet 
points throughout the section, in estimating the loss of 
necessary to establish flow, is obvious. Couette,” treating the 
problem more exactly, deduced for m the value unity, obse 
that it is just double that obtained by the application of Da 
Bernoulli’s theorem, which attributed to all the molecules of 
fluid a velocity equal to the mean velocity. He proposed tn 
fore the more rigorous formula 
P,=P 5, 
This had eae previously given under another form by Jace 
Bienes Kirchhoff’s Vorlesungen (22nd) for a solution in two dimens 
his treatise on Hydrodynamics, Vol. 1, p. 139. - 
solution of the problem in three dimensions exists so far as he was 8” 
afapand whi —_ by Boussinesq in 1872, see his “‘ Essai sur la™ 
: courantes.”—Mém, des Savants étrangers, t. 23, p- 562, } 
Annal. de Chimie, 6 sér. t. 21, chap. iii., p. 494, 1890. 
