G. Jounstonz Stoney On Polarization Stress in Gases. 51 
Part 2.—INVESTIGATION OF A ComPLETE EXPRESSION FOR THE STRESS. 
18. As it has been asserted (‘‘ Nature,” vol. 17, 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 for- 
ward is, on the contrary, the necessary sequel of them. I will show this by con- 
tinuing 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. 17, p. 200. This inquiry will have 
the further advantage of furnishing a complete expression for Crookes’s stress. 
19. Clausius (Phil. Mag., vol. 23, p. 514) has given the following expression for 
the stress across a layer of gas conducting heat, in the direction normal to a heater 
and cooler, the opposed surfaces of which are parallel and extensive— 
P,—19v,2-+ Ke 
« being a small quantity of the same order as the striking distance of the mole- 
cules, and X, being a coefficient of which Clausius did not compute the value, as 
the scope of his investigation 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, poited out that if an expression for P,, the stress 
parallel to the surfaces of the heater and cooler, were calculated by a method 
similar to Clausius’s, the coefficient of «* in this expression could not be the same 
as X,, and that hence there must be a difference between the two stresses, in other 
words a polarization stress. 
20. Clausius (loc. cit.) gives the following general expression for the normal 
stress 
Pe= of 1V%.2dp Nos (hy 
where I is the coefficient expressing the proportion of molecules travelling in the 
directions which make an angle with the normal or axis of « of which the cosine 
is » ; and where V’ is the mean of the squares of their velocities. 
Now if, employing a process exactly similar to that pursued by Clausius on pp. 
512 and 513 of his memoir, we use N for the number of molecules in a unit of 
volume, then will Ndr be the number of molecules within a slice of unit area and 
thickness dr, which we may suppose to be placed perpendicular to the vector 7. Then 
| = Nidrde 
will be the number of molecules moving within the slice in directions which lie 
_ within an element of solid angle de, which we will suppose makes the angle ¥ with 
the vector 7, so that the time they take to cross the slice will be 
dr .sec 
ee 
