148 Thermal Transpiration and Radiometer Motion. 



niously attributed as an inherent property to gas conducting- 

 heat is exactly the velocity which would result from the action 

 of the walls of the tube if the motion of the gas were unre- 

 stricted, and hence the danger that the error in Mr. Suther- 

 land's theory might pass unnoticed. 



That in adopting this erroneous foundation Mr. Sutherland 

 is not quite satisfied is shown in the last paragraph, p. 374. 

 This begins : — " The most convenient starting-point is the laws 

 discovered by Clausius (Pogg. Ann. cxv. 1862) for the con- 

 duction of heat in gases. In a vertical cylinder of gas, 

 bounded by a solid wall impermeable to heat and two con- 

 ducting plane ends, the lower at a temperature 6 X the higher 

 at the temperature 2 , when the flow of heat has become 

 steady and the pressure throughout the cylinder is con- 

 stant, &c" Clausius expressly excludes solid walls. 



Then, again, in the next sentence : — " Now in the establish- 

 ment of the law of temperature it was shown by Clausius 

 that in a mass of gas which is not uniform in temperature 

 there is motion of the gas in the direction of variability ; but 

 it is assumed (as can easily be proved) that under ordinary 

 circumstances this motion can never produce an appreciable 

 departure from uniformity of pressure, &c. ; ' 



This is a complete misstatement. Clausius showed that 

 the velocity which would otherwise arise from the excess of 

 the rate of variation of density over the opposite rate of 

 variation of the velocity of the molecules is balanced by the 

 difference in the opposite velocities of the molecules emerging 

 from the hot and cold sides of an element of the varying gas 

 respectively, the excess being in the direction of the colder 

 side ; but he never mentions a velocity of the gas except as 

 zero. And Mr. Sutherland does not notice that the velocity 

 resulting from the difference just mentioned is towards the 

 colder side, and is opposite to that which he has found, which 

 is towards the hotter side. 



In pointing out these errors, although my chief object has 

 been to prevent unnecessary confusion in this abstruse subject, 

 it has also been done with a view to assist Mr. Sutherland in 

 his effort (with which I sympathise). And I hope he will 

 now see that the difficulties of the subject do not exist in 

 mathematical form, but in the conception of the mechanical 

 actions involved ; and after mastering these, that he may be 

 able to produce a translation from the general analysis into a 

 group of particular examples treated in one dimension. For 

 1 have no doubt that the great difficulty which many find in 

 this subject arises from unfamiliarity with the expressions in 

 the analysis in three dimensions — a difficulty which is not 

 likely to be removed.. 



