Prof. Clausius on the Conduction of Heat by Gases. 527 



is obtained, 



T^Cff + C,, . . . ... (54) 



where C and C x are constants. 



The quantity of gas enclosed betweeen two surfaces of given 

 temperatures does not, therefore, as might perhaps be supposed 

 at first glance, assume such a condition that the temperature is 

 a linear function of the abscissa ; but the alteration of tempera- 

 ture from one limiting surface to the other takes place according 

 to a somewhat more complicated law, inasmuch as the power 



T* is represented by a linear function of the abscissa. 



When the constants C and C x in equation (54) are deter- 

 mined 'by aid of the given temperatures of the limiting sur- 

 faces, the temperature can be calculated for every other point of 

 the gas. And since, further, the product of temperature into 

 density must remain constant within the gas if the density be 

 given for any one point, it can be calculated from the tempera- 

 ture for every other point. Accordingly, the condition of the 

 gas is fully Xnown. so far as regards temperature, density, and 

 pressure. 



§ 24. By introducing into equation (VIII.) the value that has 

 been found for q, we obtain the following equation for G, the 

 conduction of heat within the gas : 



G=~^kmN u*^ e *. . . . (XIII.) 



, * Maxwell (Phil. Mag. S. 4. vol. xx. p. 32) gives the following express 

 sion for the vis viva which passes in the positive direction through a super- 

 ficial unit of a plane perpendicular to the axis of x during a unit of time, 



\ : G =-5sS WM > < A > 



where I denotes the mean length of excursion of the molecules which cor- 

 responds to the density of the gas at the place under consideration. Sub- 

 stituting for I its value 





we have 



a— is^*)"" }«*£ 



This expression differs from that given above only by containing | in place 

 of T V But if we trace the way in which Maxwell arrives at equation (A), 

 we shall find that this near accordance of his result with mine is only 

 apparent. 



Denoting the mass of gas which passes in a positive direction through 

 the unit of surface during a unit of time by E, Maxwell establishes the 



