Mr. J. C. Maxwell on the Dynamical Theory of Gases. 209 



whence 



2p fdu 1 (du dv dw\\ , g 



If we make 



1 J_p _ 



3M 2 p"^ 



fj, will be the coefficient of viscosity, and we shall have, by equa- 

 tion (120), 



~> n fdu 1 fdu dv dw\\ 



(125) 



„ fVy 1 fda dv , ^wA~l 



pP^-^is - 3 (S + # + It). I ' 



and by transformation of coordinates we obtain 

 (dv dw\ \ 



(126) 



& — ^s + aft [ 



p^=-^T y + %y j 



(127) 



These are the values of the normal and tangential stresses in 

 a simple gas when the variation of motion is not very rapid, and 

 when fi, the coefficient of viscosity, is so small that its square 

 may be neglected. 



Equations of Motion corrected for Viscosity. 



Substituting these values in the equation of motion (76), we 

 find 



"du dp 



rd c "u 



+ dz*j 

 1 d /du dv dw\ ^ 

 -^TAdx + d-y + diJ-^'J 



P ~dt + dx ^\dx* + dy 



(128) 



with two other equations which may be written down from sym- 

 metry. The form of these equations is identical with that of those 

 deduced by Poisson * from the theory of elasticity, by supposing 

 the strain to be continually relaxed at a rate proportional to its 



* Journal de VEcole Poly technique, 1829, vol. xiii. chap. xx. p. 139. 

 Phil. Mag. S. 4. Vol. 35. No. 236. March 1868. P 



