316 Mr. S. H. Burbury on some Problems 



^U 7 7 



Informing ■=- - we have now the factor Po>-— , instead of 



du . 3 



<» — as in diffusion. Also k= — ,if t be the absolute tempera- 



ture and 



cZ& _ 3 dr _ 2 , 2 dr 



dx ^r 2 dx 3 <i#' 



We have now to compare two systems in each of which P is 

 constant throughout the tube, but has not necessarily the same 

 constant value in both systems, and h has different values in 

 the two systems. 



We may make 



N 



(1) P the same, that is y- the same, in both systems. 



tc 



(2) N the same in both systems. 



In case (1) ^-,asa function of k, has dimensions k 2 ^M 



In case (2) it has dimensions k^—~. 



Now the flow of heat per unit of time through a section of 

 the tube, that is the rate of conduction, is 



N(-Vf dcoe-^co'x^co^kco' 2 ), 



\7T/ J 



and therefore varies 



in case (1) as */k, or as —y=- } 



V T 



in case (2) as —=. or as a/t- 

 V h 



We have then the following result. Assuming that the 



molecules may be treated, as regards their mutual encounters, 



as elastic spheres, the rate of conduction of heat between 



points of equal pressure but unequal temperature varies, as 



between two systems with the same pressure, inversely, and 



as between two systems with the same density directly, as the 



square root of the absolute temperature. 



23. When the disturbance is of the second order, as in the 



problem of viscosity, the mean value of \fi, given E, is (see 



figure, § 6) 



3 2 nnD 1 3/V-RcosEy 1 



In order in this case to prevent the appearance of negative 



