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



the shape of the remainder of the curve must be one which is 

 independent of the particular value of P which we have used. 

 Hence, if k is the maximum value of k in that curve, it follows 

 that k and k must remain proportional to one another when 

 P is changed. Hence equation (10) furnishes 



kocP.(AT) 2 -(D) 



We learn from this inquiry that the maximum polarization 

 stress which can be elicited between a given heater and cooler 

 by varying the distance between them will, if the tension of 

 the gas is altered, change in the same ratio as that tension, 

 and that it will occur at intervals between heater and cooler 

 which vary inversely as that tension. This fully accounts for 

 the powerful Crookes's force which presents itself in experi- 

 ments at ordinary atmospheric tensions as compared with the 

 feeble force exhibited in radiometers. It accounts also for 

 the very short interval at which the heater and cooler must be 

 placed when the gas is dense. 



Part II. Investigation of a Complete Expression for the Stress. 



19. As it has been asserted (' Nature,' vol. xvii. p. 122) that 

 the views of the present writer are at variance with the results 

 established by previous investigators, I will proceed to show 

 that the theory of unequal stresses which I have put forward 

 is, on the contrary, the necessary sequel of them. I will show 

 this by continuing the method of investigation commenced by 

 Professor Clausius in his memoir on " the Conduction of Heat 

 by Gases," in the way which was pointed out by Mr. George 

 F. Fitzgerald in ' Nature/ vol. xvii. p. 200. This inquiry will 

 have the further advantage of furnishing a complete expression 

 for Crookes's stress. 



Clausius (Phil. Mag. vol. xxiii. p. 514) has given the 

 following expression for the stress across a layer of gas con- 

 ducting heat, in the direction normal to a heater and cooler, 

 the opposed surfaces of which are parallel and extensive, 

 P^l^ + X^ 2 , 



e being a small quantity of the same order as the striking- 

 distance of the molecules, and X x being a coefficient of which 

 Clausius did not compute the value, as the scope of his inves- 

 tigation only required him to go as far as the first order of 

 small quantities. Now Mr. Fitzgerald, in his letter to ' Nature/ 

 and more fully in conversation with the writer, pointed out 

 that if an expression for P y , the stress parallel to the surfaces 

 of the heater and cooler, were calculated by a method similar 

 to Clausius', the coefficient of e 2 in this expression could not 



