, STRESSES IK RAKUTKD OASES 



(13) Equation of Temperature. 



Adding the three equations of the form (44), and omitting terms con- 

 uining Bff*" quantities of two dimensions, and also products of differential 



such as /* , we find 

 ax cij" 



, . 



The first term of the second member represents the rate of increase of 

 temperature due to conduction of heat, as in Fourier's Theory, and the second 

 term represents the increase of temperature due to increase of density. We 

 must remember that the gas here considered is one for which the ratio of 

 the specific beats is 1'6. 



(14) Stresses in the Gas. 



Subtracting one-third of the sum of the three equations from (44), we 

 obtain 



2 fdu dv dw\ 



+ ^) W 



This equation gives the excess of the normal pressure in x above the 

 mean hydrostatic pressure p. The first two terms of the second member 

 represent the effect of viscosity in a moving fluid, and are identical with those 



u by Professor Stokes (Cambridge Transactions, Vol. vin., 1845, p. 297). 

 The last two terms represent the part of the stress which arises from inequality 

 of temperature, which is the special subject of this paper. 



There are two other equations of similar form for the normal stresses in 

 y and :. 



The tangential stress in the plane xy is given by the equation 



fdu dv\ . u 5 d* 



Fhero are two other equations of similar form for the tangential stresses 

 in the planes of yz and zx. 



