Mr. Gr. J. Stoney on Polarization Stress in Gases. 417 



be the same as X 1? 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 expres- 

 sion for the normal stress — 



P,=ip( 'vPpHfi, (11) 



where I is the coefficient expressing the proportion of mole- 

 cules travelling in the directions which make an angle with 

 the normal or axis of x of which the cosine is jju, and where 

 V 2 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 r. Then 



— mdrda 



will be the number of molecules moving within the slice in 

 directions which lie within an element of solid angle da, which 

 we will suppose makes the angle ty with the vector r ; so that 

 the time they take to cross the slice will be 



dr . sec -v/r 

 V ' 

 V being their velocity. Hence the number traversing the 

 slice in the specified direction within a unit of time is 



j- . NIV cos \|r . da. 



Multiplying this by mY cos i/r we get the resolved part of 

 their momenta along r. The sum of all such components of 

 the momenta, all estimated as positive, is P r , the stress in the 

 direction of r. Whence, and writing p for niN, we find 



* Al) 



IV 2 cos 2 yjrda. 



the integration being extended over the unit sphere. 



Hence the stresses in the directions of three rectangular 



axes are 



Phil. Mag. S. 5. Vol. G. No. 39. Dee. 1878. 2 E 



