256 report— 1879. 



from which emission takes place as very small compared with the radii of curvature 

 of the surface, I have deduced the same formula for the increase or diminution of 

 tension as Sir W. Thomson deduced from capillary phenomena. 



7. On the Curve of Polarisation Stress, as determined by Mr. Crookes's 

 Measures with the Radiometer. By G. Johnstone Stonet, M.A., 

 F.B.S., M.B.I.A. 



Mr. Orookes has published in hisBakerian lecture (' Philosophical Transactions,' 

 1878, pp. 300 and 301) a table and curve representing v, the number of revolutions 

 per minute of a radiometer at different tensions of the residual gas when influenced 

 by a candle three inches off. And at pp. 313 to 316 he gives similar values and the 

 curve for p, the coefficient of viscosity of the residual gas at low tensions. From 

 these observations we may obtain information with regard to the polarisation stress 

 which caused the motion. 



The observations of v were made when the radiometer had attained a constant 

 velocity, from which it follows that the retarding forces then balanced the impelling 

 force, and were therefore a measure of it. Now the retarding forces were three : 

 the friction on the peg, an approximately constant force which may be represented 

 by a ; the resistance from viscosity, which may be represented by bfiv (b being 

 another constant), and the force required to drive the residual air out of the path of 

 the advancing vanes, which may be represented approximately by cVv 2 , c being 

 another constant and P the tension. Hence the polarisation stress 



= a + bfiv + cPy 2 , 



the second and third terms of which can be deduced from Mr. Crookes's curves, and 

 separately plotted down, fiv will then furnish a curve resembling Mr. Crookes's 

 curve of velocity in its general shape, but with its maximum at a higher tension. 

 Pd 2 gives a somewhat similar curve, also with a maximum at a higher tension than 

 Mr. Crookes's curve. The friction of the peg will obviously furnish a horizontal 

 line. We do not know the coefficients a, b, and e, but can perceive that the curve 

 representing the impelling force, i.e., the polarisation stress (whose ordinates will be 

 the sum of the ordinates of the foregoing curves, multiplied respectively by the coeffi- 

 cients a, b, c), must have a form somewhat resembling Mr. Crookes's velocity curve, 

 the chief difference to be noted being that the maximum stress occurs at a higher 

 tension than the maximum velocity. 



The form of the curve thus deduced from the observations is in harmony with 

 the approximate curve which results from the theory of polarisation stress put 

 forward by the author of the present communication (see ' Scientific Transactions of 

 the Royal Society of Dublin,' New Series, vol. i. ; or ' Philosophical Magazine,' for 

 December, 1878). It is also consistent with the complete expansions for the polari- 

 sation stress given in the next communication. 



8. On Complete Expansions for the Conduction of Heat and the Polarisation 

 Stress in Gases. By G. Johnstone Stonet, M.A., F.B.S., M.B.I.A. 



Clausius obtained for the flow or conduction of heat across a layer of gas, the 

 expression, 



and by the extension of Clausius's investigation, which Mr. George F. Fitzgerald 

 suggested in a letter to ' Nature', the present author obtained for the accompany- 

 ing polarisation stress, the expression, 



K = \ mn I 1^(3^ - Y)d,x. 



