80G 
PROFESSOR O. REYNOLDS OR CERTAIN DIMENSIONAL 
Coupled with the conditions for steady density, steady momentum, and steady 
pressure, these equations are, within the limits of our approximation, equivalent to 
and 
d?cr _d-Q? cdcd 
f/,-2 — ( jf — c u ~~ 
(60) 
(61) 
where p the pressure is constant throughout the gas. 
88. The important condition in this investigation is that the tangential force on a 
solid surface shall be zero. 
This condition can only be obtained by the aid of some assumption as to the action 
between the molecules and the surface. An extremely obvious assumption will suffice, 
viz.: that the tangential force on the surface has the same direction as the momentum, 
parallel to the surface, of all the molecules which reach the surface in a unit of time. 
The condition that there shall be no force on the surface is, then, that the momentum 
parallel to the surface which is carried up to the surface shall be zero. 
Thus, if the axial planes be solid surfaces, we have from the values of cr-(Mw), 
?r — 
<T Z (Mr), &c., equations (45) that 
U = V=W = 0.(62) 
at the surface. 
If, further, there is no tangential stress within the gas, it appears from equations 
(59), (60), and (61), that equation (62) must hold throughout the gas. 
The condition that there shall be no tangential stress on a particular solid surface, 
say, the plane of xy, is satisfied if at that surface pod is constant and 
and 
U=0, Y=0 
(63) 
rflT cTV clW dW 
dz dz dx dy 
(64) 
This appears at once from the values of cr.-(Mw), cr.(Mr) obtained as equations (45). 
[The revision of Section VII. necessitated certain alterations in Arts. 87 and 88; 
these articles were therefore revised in the proof, December, 1879.] 
Section IX.— Application to Transpiration through a Tube. 
89. It will be sufficient to consider the simplest cases ; hence it is supposed that the 
gas is transpiring through a tube of uniform section, and further that the tube is of 
unlimited breadth, the surfaces being planes parallel to the plane x y ; the axis of x is 
