ARISING FROM INEQUALITIES OP TEMPERATURE. 683 



the air at a distance from them, then, in any section perpendicular to the 

 axis joining their centres, the point where it cuts this line will have the 

 highest temperature, and there will be a flow of heat outwards from this 

 axis in all directions. 



d'O 

 Hence ^ will be positive for the axis, and it will be a line of maximum 



pressure, so that the bodies will repel each other. 



If both bodies are colder than the air at a distance, everything will be 

 reversed; the axis will be a line of minimum pressure, and the bodies will 

 attract each other. 



If one body is hotter and the other colder than the air at a distance, 

 the effect will be smaller, and it will depend on the relative sizes of the 

 bodies, and on their exact temperatures, whether the action is attractive or 

 repulsive. 



6. If the bodies are two parallel disks very near to each other, the 

 central parts will produce very little effect, because between the disks the 



d~9 

 temperature varies uniformly, and -^ = 0. Only near the edges will there be 



any stress arising from inequality of temperature in the gas. 



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 



d~0 

 by Sir W. Thomson. Near the convex surface the value of -^ is nearly the 



same as if the body had been a complete sphere, namely 2T , where T is 



Cv 



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 concave surface, and if we were to neglect the tangential pressures we 

 might think this an explanation of the motion of Mr Crookes' cups. 



862 



