4G 
PR(3FESS0K E. G. C0KE:R AND MR. S. B. CLEMENT ON THE VAPJATION 
fluid ; thus, if we take the general equations of motion for an incompressible fluid 
subject to no external forces, as of type 
t = “ "M * + 7/!; + '^"4 + i + pnw) 
and eliminate the pressures from the equations, we obtain the accelerations in terms 
of diflerent types. Thus, if we take the middle term, viz., — ^ ' ^ { 2 )^. 1 - fl- piiv), and 
p 
for 2->j^.v ^vrite p (4; + ), we get 
I I I _ Now, since dv/dx 
ax d)j j ' 
_ A [ fl: 
dx ' dij I’’ (lij p 
and dujdy have the dimension of a velocity divided by a length and the other term 
has dimension of the square of a velocity, the relative values of these two terms are 
to one anotlier as ju,/cp to v, where c is a length, say the radius of the tube. 
The equations do not show in what way the motion depends upon this relation, 
but it was inferred that the eddying motion must depend on some definite relation 
between v and y/cp, expressible in the form v = hpijcp, where h is some constant. 
The experijuental observations were of t^vo kinds, the earlier depending on the 
device of introducing a colour band into a glass pipe and observing the velocity at 
which break-down of the stream-line motion occurred, and the later method depending 
upon the fact that stream-line motion is associated Avith resistance proportional to 
the velocity, while for eddy motion the resistance is proportional to a higher jDOwer 
of the velocity. 
Both methods showed that the critical velocity at Avhich stream-line motion 
changed to eddy motion varied directly as the viscosity, and inversely as the radius 
of the pipe. 
Object of the Exirndmciits. 
In the experimental verification of the temperature efiect upon the critical velocity 
a satisfactory agreement Avas obtained Avith the formula, but as the range of 
temperature AA^as extremely limited, it Avas pointed out tliat “ it Avould be desirable 
to make experiments, at higher temperature; but there Avere great difficulties about 
this, Avhich caused me, at all events for the time, to defer the attempt.”!' 
It does not appear that such experiments haA^e since been made, and although the 
diificulties Avere not estimated lightly, it seemed Avorth Avhile to attempt experiments 
through a much larger range of tempeiature. 
Scope of the Ex/^erirneats. 
Althougfi it Avould be eminently satisfactory to make experiments througliout the 
whole range of temperature of AAuiter, yet the experimental difficidties of maintaining 
‘Phil. Tram.,’ A, 1895, p. 131. 
t ‘ Phil. Trans.,’ 1883, p. 977 
