420 Prof. Clausula on the Conduction of Heat by Gases, 



entitled " Illustrations of the Dynamical Theory of Gases," in 

 which also the question of the conduction of heat is considered. 

 In this memoir, which is remarkable for the elegance of its mathe- 

 matical developments, the motion of small bodies is regarded 

 from very general points of view, and many valuable results are 

 arrived at in it ; nevertheless I do not believe that its contents 

 are correct in every point. I am more particularly of opinion 

 that the author has treated the conduction of heat too incom- 

 pletely ; and although his formula differs but little from that 

 which we shall deduce, important differences nevertheless occur 

 in respect to other matters, to which I shall refer in their proper 

 places, and which make it appear that the close agreement of the 

 ultimate formula is merely accidental. 



The general importance of the phenomenon of the conduction 

 of heat, and the slight attempts that have hitherto been made to 

 ascertain the real nature of the process upon which it depends, 

 induce me to think that I shall be justified in submitting this 

 process, and the entire condition of gaseous bodies by w T hich it 

 is accompanied, to a closer mathematical treatment upon the 

 foundation of the hypothesis which I have hitherto advocated, 

 and in thus endeavouring to deduce the laws of the conduction 

 of heat by gases. I venture also at the same time to point out 

 that the principles which will be followed in this investigation 

 are capable of being applied, with certain modifications, to many 

 other cases where the problem is to determine the internal pro- 

 cesses going on in a quantity of gas, and that the developments 

 which follow may lay claim in this respect to a more general 

 significance than the problem treated in the first instance. 



I. Definition of the case to be considered. 



§ 1. We will suppose a quantity of gas between two parallel 

 plane surfaces of infinite size, each of which is maintained at a 

 constant temperature. If the temperature of one surface is 

 higher than that of the other, a transference of heat from one 

 surface to the other will take place, through the medium of the 

 gas, by the continual passage of heat from the warmer surface 

 into the gas, its advance from one layer to the next within the 

 gas itself, and its being at last given up by the gas to the colder 

 surface. As it is our object to consider here only that movement 

 of heat which is caused by conduction, and not that which might 

 be occasioned by currents of gas produced by the warmer por- 

 tions being specifically lighter than the colder, we will suppose 

 the action of gravity entirely excluded : this is approximately 

 the case when the two surfaces are horizontal and the hotter is 

 above, for then no currents can arise. 



