50 G. Jounstonse Stoney On Polarization Stress in Gases. 
17. From equation (B), we may obtain another useful formula 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 molecules in the unit tube 
to allow heat to pass by conduction. 
In this case we know the equation of the gradient of temperature (see Clausius’s 
equation 54, Phil. Mag. vol. 23, p. 527), and that it is approximately represented by 
6 : NI . OR 
a straight line when, as we have assumed, “7 is small, using AT for the difference 
between the temperatures of the heater and cooler. Hence, and from Clausius’s 
equation 56, it appears that— 
G2, (AT)? 
at xe 
using X for the distance between the heater and cooler. Introducing this value 
into equation (B), we find— 
Sua () 
a result which agrees satisfactorily with Mr. Moss’s experiments. 
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, andif we use «, for the cor- 
responding value of the Crookes’s stress, then equ. (C), and the obvious equation 
IX “ furnish us with the following— 
moo PYAT)? . . 2» (10) 
, Now equation (C) enables us to plot down a part of the curve representing the 
relation between « 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 the form of the remainder of the curve must be one which is inde- 
pendent of the particular value of P which we have used. Hence if « is the 
maximum value of, in that curve, it follows that ~ and «, must remain pro- 
portional to one another when P ischanged. Hence equation (16), furnishes— 
ince P{(AT)2 . . 5 (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 cocler must be placed when the gas is dense. 
