Conduction of Heat by Rarefied Gases. 201 



difference is probably due, apart from the inexactness of such 

 a rough calculation, to the fact that the surface of Mr. Brush's 

 thermometer was coated with shellac, which of course may 

 produce another value of 7 than glass. 



I should like to say some words concerning another point. 

 Mr. Brush proves that Newton's law of cooling is not 

 strictly true, since the curves representing the cooling down 

 from 1 5° to 10°, from 9° to 6°, &c. do not coincide, as would 

 be required by an exponential formula. The cooling is going 

 on faster with increasing difference of temperature than would 

 follow from Newton's law. 



I think this is not surprising at all, since it is known that 

 the coefficient of conductivity, and also the radiation, are 

 increasing with rise of temperature. By assuming Stefan's 

 law of radiation to be true, according to which the quantity 

 of heat radiated away from a body is proportional to the 

 fourth power of its absolute temperature, and by assuming the 

 coefficient of conductivity to increase by about 0*2 per cent, 

 for one degree (according to Winkelmann, Wied. Ann. xliv. 

 pp. 177, 429), we find just about such differences as exhibited 

 by the air-curves and, at the lowest pressures, by the hydro- 

 gen C curves. 



The great value of these differences in the higher parts of 

 the C curves, however, seems to suggest that 7 is decreasing 

 with rise of temperature. 



A remarkable fact, too, seems to be the great influence of 

 temperature-difference on the intensity of convection-currents, 

 as shown especially by the air curves A in the larger bulb, 

 which may be compared with a theoretical formula put 

 forward by Lorenz * — for a less complicated case, though — 

 according to which convection-currents produce an effect 

 proportional to the J power of temperature-difference. 



But these phenomena are not in immediate connexion with 

 the subject here discussed ; for our purpose it is sufficient to 

 note that Mr. Brush's experiments are quite in accordance 

 with our theory, supposing the existence of discontinuity of 

 temperature proportional to the free path of the molecules. 



Explanation by Kinetic Theory of Gases. 



9. Now the question arises how this remarkable pheno- 

 menon is to be explained. 



It cannot be reduced to any effects of radiation (in the 

 sense now used), in Poisson's way, as has been mentioned 

 at the beginning of this paper ; this is also excluded by the 



* Wied. Ann. xiii. p. 582. 



