Mr. G. J. Stoney on Polarization Stress in Gases. 415 



above, section 8). The curve b c d is therefore known ; and 

 if by equation (B) we plot down from it the values of k (the 

 polarization stress), we find them approximately represented by 

 the ordinates of a curve of the form ace, the portion to the 

 right of c being coincident with an equilateral hyperbola, 

 while to the left of c the ordinates fall short of the hyperbola, 

 rising to a maximum and then falling off to zero. The posi- 

 tion of this maximum cannot be obtained with certainty, 

 because equation (B) is less to be depended on at very low 

 tensions. Bearing this in mind, the accordance of the theoretic 

 values with those determined experimentally by Mr. Crookes 

 and Mr. Moss is satisfactory. 



17. From equation (B) we may obtain another useful for- 

 mula which expresses the approximate law according to which 

 polarization stress depends upon the interval between heater 

 and cooler, whenever this interval exceeds the limit determined 

 by the condition that there shall be a sufficient number of mo- 

 lecules in the unit tube to allow heat to pass by conduction. 



In this case we know the equation of the gradient of tem- 

 perature (see Clausius' equation (54), Phil. Mag. vol. xxiii. 

 p. 527), and that it is approximately represented by a straight 



AT . 

 line when, as we have assumed, -^- is small, using AT for the 



difference between the temperatures of the heater and cooler. 

 Hence, and from Clausius' equation (56), it appears that 



G 2 (AT) 2 



using X for the distance between the heater and cooler. 

 Introducing this value into equation (B), we find 



K a px 2 ; ^ 



a result which agrees satisfactorily with Mr. Moss's experi- 

 ments. 



18. If we use X for that interval between heater and cooler 

 which would make the number of molecules in the unit tube 

 equal to N, and if we use k for the corresponding value of the 

 Crookes's stress, then equation (C), and the obvious equation 



X oc p, furnish us with the following : — 



* ocP.(AT) 2 (10) 



Now equation (C) enables us to plot down a part of the curve 

 representing the relation between k and X when AT and P 

 are kept constant; and although equation (C) cannot be relied 

 upon when X is less than X , it is nevertheless evident that 



