Prof. Clausius on the Conduction of Heat by Gases. 421 



If both surfaces are kept for a considerable time at constant 

 temperatures, a state of equilibrium is at length established in 

 the gas, of such a kind that the temperature remains invariable 

 at each point within it, but is different at different points — the 

 heat being so distributed that, in any plane parallel to the two 

 limiting surfaces, the temperature is the same at every point, but 

 that it continually decreases according to a definite law in the 

 direction from the warmer to the colder surface. A definite and 

 constant flow of heat through the gas then takes place. 



It is this stationary condition of the gas that we have to con- 

 sider, and to endeavour to determine the amount of the flow of 

 heat which goes on owing to the conductive property of the 

 gas. 



§ 2. We will suppose a straight line drawn between the two 

 surfaces and perpendicular to them, and we will assume this as 

 the axis of abscissas : the temperature within the gas is then a 

 function of the abscissa x ; and if, in order to be able at once to 

 form a definite conception, we assume that the first surface, where 

 the abscissa has its smallest value, is the warmest, the tempera- 

 ture diminishes within the gas as the value of x increases. With 

 the density of the gas the case is reversed, for in a state of equi- 

 librium the density of the gas must be higher in proportion as 

 the temperature of the gas is lower ; it is therefore a function of 

 x whose value increases with that of x. 



We will assume at starting that the gaseous molecules fly 

 about irregularly in all directions, and accordingly strike and 

 rebound from each other, now in one place, now in another, and 

 also that the velocity of their motion is greater the higher the 

 temperature. Let us now suppose a plane cutting the space 

 filled with gas, and parallel to the surfaces by which this space 

 is bounded ; then during a unit of time a great number of mole- 

 cules will pass from the negative to the positive side of this plane, 

 and vice versa. The molecules which pass from the negative to 

 the positive side have a greater average velocity than those which 

 pass from the positive to the negative side, since, according to 

 our assumption, the temperature is higher, and therefore the 

 moving velocity of the molecules greater, on the negative side of 

 the plane than on the positive side. The total vis viva which 

 traverses the plane in a unit of time in the positive direction is 

 therefore greater than that which traverses it in the negative 

 direction ; and if we strike out, as compensating each other, 

 equal quantities which traverse it in opposite directions, we still 

 obtain a certain excess of vis viva traversing the plane in the 

 positive direction. Vis viva and heat being regarded as synony- 

 mous, the amount of vis viva thus passing through the plane 

 constitutes the heat-stream mentioned in the last section, which 



