450 Mr James, The Theoretical Value of Sutherland's 



Now, if p is the radius of curvature at any point of the path, and /x 

 the inchnation of the radius vector to the tangent, 



-^ ^ ' p sm fji TD^p PV [ ^ 



or to the first order 



1^ Vfi'r) 

 p 7V • 



If s is the arc of the path this is 



# ^ _ Vfi'r) 

 ds V^r ' 



leading to rjj = - ^^ j J-Sp- £ dr. 



Also, from the equation 



1 /dr\^ 2r^ 



we obtain 



r^ \auj f 

 ds ( {72+2<D(f)}r 



dr {r^{V^+2^{r)}-2)^V^ 

 which to the first order is 



ds _ r 



dr (f2_ ^2\i' 



whence ifj (g) = ~ I -^ ^ ' — 



72.^ (,-2_ ^2) 



It will be observed that / (r) may be of any order of magnitude, 

 provided only O (r) remains small. 



§ 5. The Viscosity of a Single Gas. General Analysis. On 

 reference to the papers cited* it will be seen that we have now to 

 evaluate 



Q"(7)-777 {'"''sm^'Ixpd]), 

 Jo 



where p^ is the greatest value of p for orbits involving colhsion, 



so that ^^ =- ct{1 + 20 (ct)/7-}2. To our order we may put p^ = a. 



Putting X = x'~ 'Aj ^i^d expanding in ifj to the first power only, 



AQ" (7) = - 777 l^ijj sin '2x' cos 2x'pd'p. 

 Jo 



* First Paper, p. 453 : fi" ( V) is denoted there by 9s\^ ( Fo). See also pp. 457, 458. 



