GASES ARISING FROM INEQUALITIES OF TEMPERATURE. 233 
7. If the bodies are encircled by a ring having its axis in the line joining the 
bodies, then the repulsion between the two bodies, when they are warmer than the 
air in general, may be converted into attraction by heating the ring so as to produce a 
flow of heat inwards towards the axis. 
8. If a body in the form of a cup or bowl is warmer than the air, the distribution 
of temperature in the surrounding gas is similar to the distribution of electric potential 
near a body of the same form, which has been investigated by Sir W. Thomson. Near 
(P6 
the convex surface the value of — is nearly the same as if the body had been a 
complete sphere, namely 2T—, where T is the excess of temperature, and a is the 
radius of the sphere. Near the concave surface the variation of temperature is 
exceedingly small. 
Hence the normal pressure will be greater on the convex surface than on the con¬ 
cave surface, and if we were to neglect the tangential pressures we might think this 
an explanation of the motion of Mr. Crookes’ cups. 
Since the expressions for the stress are linear as regards the temperature, everything 
will be reversed when the cup is colder than the surrounding air. 
9. In a spherical vessel, if the two polar regions are made hotter than the equatorial 
zone, the pressure in the direction of the axis will be greater than that parallel to the 
equatorial plane, and the reverse will be the case if the polar regions are made colder 
than the equatorial zone. 
10. All such explanations of the observed phenomena must be subjected to careful 
criticism. They have been obtained by considering the normal stresses alone, to the 
exclusion of the tangential stresses, and it is much easier to give an elementary 
exposition of the former than of the latter. If, however, we go on to calculate the 
forces acting on any portion of the gas in virtue of the stresses on its surface, we find 
that when the flow of heat is steady, these forces are in equilibrium. Mr. Crookes 
tells us that there is no molar current or wind in his radiometer vessels. It is not 
easy to prove this by experiment, but it is satisfactory to find that the system of 
stresses here described as arising from inequalities of temperature will not, when the 
flow of heat is steady, generate currents. 
11. Consider, then, the case in which there are no currents of gas but a steady flow 
of heat, the condition of which is 
&e (P0 ,cP6_ 
dx~ cly~ dz^ ~ °* 
(In the absence of external forces such as gravity, and if the gas in contact with solid 
bodies does not slide over them, this is always a solution of the equations, and it is 
the only permanent solution.) In this case the equations of motion show that every 
particle of the gas is in equilibrium under the stresses acting on it. Hence, any finite 
portion of the gas is also in equilibrium; also, since the stresses are linear functions of 
MDCCCLXXIX. 2 II 
