840 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
by the size of the envelope, so that the larger the envelope the greater the possible 
rate of motion. When the paths of the molecules are limited by the size of the vessel, 
the motion would, if the vanes were perfectly free to move, remain constant for all 
further exhaustion ; but the inequalities of pressure which the gas is capable of exert¬ 
ing diminish with the further rarefaction, and hence, in time, must cease to be suffi¬ 
cient to overcome the resistances to which the motion of the vanes is subject, and 
then the motion ceases. 
124. There are many other points about the phenomena of the radiometer, but with 
most of these I have already dealt in my former papers, the reasoning of which, so far 
as it goes, appears to me to be perfectly consistent with the more complete view of the 
action to which I have now attained. 
My chief object in introducing the phenomena of the radiometer in this paper has 
been to bring out how completely impulsion belongs to the same class of actions as 
thermal transpiration, and the other phenomena depending on the relation which the 
size of the external objects bears to the mean range within the gas. 
The action does not depend on the distance between the hot and cold plates. 
It has been supposed by some writers on the radiometer, that the action depends 
essentially on the distance between the vanes and the sides of the vessel. This dis¬ 
tance, however, is now seen not to be of primary consequence, as no action will result, 
however close the plates may be, unless they are of limited extent—of sizes comparable 
with the mean ranges. 
Section XIII.— Summary and Conclusion. 
125. The several steps in this investigation have now been described in detail. 
They may be summarized as follows :— 
(1.) The primary step from which all the rest may be said to follow is the method of 
obtaining the equations of motion, so as to take into account not only the normal 
stresses which result from the mean motion of the molecules at a point, but also the 
normal and tangential stresses which result from a variation in the condition of the 
gas (assumed to be molecular). This method is given in Sections VI., VII., and VIII. 
(2.) The method of adapting these equations to the case of transpiration through 
tubes or porous plates is given in Section IX. The equations of steady motion being 
reduced to a general equation, expressing the relation between the rate of transpira¬ 
tion, the variation of pressure, the variation of temperature, the condition of the gas, 
and the dimensions of the tube. 
In Section X. is shown the manner in which were revealed the probable existence 
(1) of the phenomena of thermal transpiration, and (2) the law of correspondence 
between all the results of transpiration with different plates, so long as the density of 
the gas is inversely proportional to the lateral linear dimensions of the passage through 
