CHAPTER VII. 



PHYSICAL PROPERTIES OF A GAS (CONTINUED). 



MASS MOTION AND CALORIMETRY. 

 General hydrodynamical Equations of Motion. 



171. LET us consider the small element of volume dxdydz supposed 

 entirely inside the gas, of which the centre is at , 77, and which is 

 bounded by the six planes, parallel to the coordinate planes, of which the 

 equations are : 



f , dx dy ., dz 



* = f-2> y = v-f> 2 = t-2- 



At any point let the molecular density be denoted by v. Strictly 

 speaking, the quantity required is the " effective molecular density" v 1} 

 defined in Chapter IV., but it will tend to clearness to suppose for the 

 present that the molecules are vanishingly small, so that the distinction 

 between v and ^ disappears. In either case v (or Vj) is a function of 

 x, y, z, and when it is necessary to specify the point at which v (or v^) is 

 measured we shall write it in the form v Xi y> z . 



Let the law of distribution at any point be f(u, v, w), it no longer being 

 supposed that the law of distribution is the same throughout the gas, so 

 that f(u, v, w) is a function of as, y, z as well as of u, v, w. When it is 

 necessary to express this we shall be able to replace 



f(u, v, w) by f(u, v, w, x, y, z). 



As before, let us say that a molecule belongs to class A, when its velocity 

 components lie within the limits 



u and u + du, v and v + dv, w and w + dw. 



