ARISING FROM INEQUALITIES OP TEMPERATURE. 



709 



those of a line, and its ratio to I, the mean free path of a molecule, is given 

 by the equation 



*-i(H< < 7 >- 



Kundt and Warburg found that for air in contact with glass, G = 2l, 

 whence we find f=\, or the surface acts as if it were half perfectly reflecting 

 and half perfectly absorbent. If it were wholly absorbent, G = f I. 



It is easy to write down the surface conditions for a surface of any form. 

 Let the direction-cosines of the normal v be I, m, n, and let us write 



d e , d 

 -T- lor i-j- 

 dv dx 



We then find as the surface conditions 



u-G~[(l-f)u-lmv - 

 " 



d 



^- 

 ay 



d 



-j-. 



dz 



p6 \dx 



vG ~r f(l m 1 ) v mnw mlu~\ + - ^( ^ m-p ) (d + iG^- | = i 

 dv LV 4 pd \dy dv] \ dv) 



wG-r\(\n*)w nlu nmv~\ + - /t (-r- 

 dv 1 ^ J 4 pO \dz 



- r 

 dv 



^ r 

 dv 



...(71). 



In each of these equations the first term is one of the velocity-components 

 of the gas in contact with the surface, which is supposed fixed; the second 

 term depends on the slipping of the gas over the surface, and the third term 

 indicates the effect of inequalities of temperature of the gas close to the 

 surface, and shows that in general there will be a force urging the gas from 

 colder to hotter parts of the surface. 



Let us take as an illustration the case of a capillary tube of circular 

 section, and for the sake of easy calculation we shall suppose that the motion 

 is so slow, and the temperature varies so gradually along the tube that we 

 may suppose the temperature uniform throughout any one section of the tube. 



Taking the axis of the tube for that of z, we have for the condition of 

 steady motion parallel to the axis 



dp _ /d'w d?w\ 



