422 Mr. G. J. Stoney on Polarization Stress in Gases. 



Next, k Q + ki may be plotted down by shifting the centre of 

 this sphere through the small distance B towards positive w, 

 and by then very slightly distorting the form of the sphere. 

 Again, to plot down k + k 2 , we should elongate the sphere in 

 the direction of the axis x by an amount equal to 4C ? and nar- 

 row it equatorially by an amount equal to 2C, without shifting 

 its centre. Finally, k + k x + k 2 would be represented by radii 

 drawn to the surface of this last solid, after it had been slightly 

 distorted and removed through the distance B towards the 

 cooler. Through all these mutations the mean value of the 

 radii drawn from the origin remains unaltered*. 



Comparing these figures with expansion (12), which is the 

 value for IV 2 furnished by Clausius' hypothesis, we find that 

 the form and position of the solid which results from plotting 

 it down are such that (owing to the term containing fi) there 

 is that separation between the origin of radii and the centre of 

 figure which gives a sufficient value to the function k ly but 

 that (the coefficient of /a 2 containing only very small quanti- 

 ties) the solid is not elongated in the way which would allow 

 the function h 2 to attain any considerable value. That the 

 function h 2 is not wholly absent is because of such causes as 

 the slight distortion of figure before mentioned, which give rise 

 to very small f terms of the form k ly k 2 , &c. 



* Since, by the fundamental property of spherical harmonics, 



&c. 



t That k 2 is very small, if we adopt Clausius' hypothesis, may also be 

 seen by comparing equation (18) with experiments on spheroidal drops. 

 Observation shows that, at atmospheric temperatures and pressures, a 

 spheroid of water some millimetres in diameter will be supported at a dis- 

 tance of about a fourth-metre (a metre divided by 10 4 ) from the heater, 

 when the difference of temperatures is about 10° C. In G.C.S. (gramme, 



centimetre, second) systematic measures, the hyper-milligram ( — of the 



gravitation of a milligram, g being gravity measured in metres per second) 

 per square centimetre is the unit of stress. Hence the Crookes's stress 

 which supports this drop must amount to some hundreds of these units. 

 This is the amount indicated by experiment. 



Formula (18) assigns to it a very different value. Clausius estimates 

 the flow of heat across air between a heater and cooler, each a square 

 metre in surface and a metre asunder, and kept at temperatures which 



differ by 1° C, as amounting per second to L2 — of the quantity of 



heat which will warm a kilogram of water 1° C. About ten times this, 

 or M of this calory per second, would be the flow of heat between 



