834 
PROFESSOR 0. REYNOLDS ON CERTAIN DIMENSIONAL 
And for cylindrical surfaces 
Pc-p 
p 1 
where Apj) and A s s 
2_fl r (°\ c _i\ i 4 ^_1 r /fl % 
2 C 2 ^ 5 \s’ S / ' 77 Cp log e Cj 6 \.s’ S 
Ci Co 
a/ m a/ m 
a/ m 
(141) 
c, —c 
are respectively unity and zero when either - or— 
S V 
Q Q _ Q 
are zero, and respectively zero and unity when both — and —— 1 are infinite. 
s s 
Equations (140) and (141) have been obtained on the assumption that the solid 
surfaces are either concentric spheres or concentric cylinders. But these equations 
indicate what would be the difference of pressure consequent on a difference of 
temperature whatever may be the shape of the surfaces, and particularly so when 
c _ c 
1 and - 2 -—- are finite, which are the most important cases. 
Section XII. —Application to the Experiments with the Fibre of Silk and 
THE BADIOMETER. 
116. Comparing the equations (140) and (141) with the equation of transpiration 
(101), it appears at once that when H is zero these equations are identical in form. 
Hence the curves expressing the relation between the impulsive forces and the density 
of the gas under any given conditions would be of the same character as those 
expressing the relation between the inequalities of pressure and density in the case 
of thermal transpiration through a particular porous plate, and it is not necessary for 
me again to examine this relation. 
Besides which, the experiments on impulsion, elaborate as they have been, furnish 
nothing like the definite results which I have obtained in the experiments on thermal 
transpiration. 
117. The principal results to be deduced from experiments other than those which 
are contained in this paper, are :— 
(1.) That the force and motion are proportional to the difference of temperature, 
which results are seen to follow directly from equations (124) and (140). 
(2.) That with a particular instrument the forces increase with the rarefaction up 
to a certain point, after which they fall off; this result also follows directly from the 
equation (140). 
118. Equations (124) and (140) first revealed to me the fact that the pressure 
of gas at which the force would become appreciable must vary inversely as the size of 
the surface. 
From equation (140) it appears that up to a certain point 
