206 Dr. 0. J. Lodge on the Variation of the Thermal 



point have established the following expression for the velocity 

 of cooling of a body whose absolute temperature is v, in an 

 enclosure of absolute temperature v , containing gas at the 

 pressure or, 



v = P(a» - a v °) + Q«*(v - v ) 1,232 ? 



which may also be written in terms of the excess of tempera- 

 ture 6 = v — v Q , thus, 



d = Va^(a 9 -l) + Q^e i ' 23 K .... (5) 



The first term is the rate of cooling by radiation ; the second 

 term is the rate of cooling by convection. In other words, Q = 

 in a vacuum ; and P is small if the surface of the body is sil- 

 vered, but great if it be lampblacked. The constant g depends 

 on the nature of the gas ; for air it is '45 ; but a is said to be 

 a universal constant, and equal to 1*0077. Although this is an 

 empirical formula, it is perhaps the most perfect example of 

 such a formula that we have, and it expresses Dulong's results 

 thoroughly well. The necessity of such an elaborate expres- 

 sion has been called in question by Narr ; but his experiments, 

 so far as they go, seem rather to confirm than to upset this ex- 

 pression ; and it has been in the main verified by Provostaye 

 and Desains. 



11. Some caution, however, seems advisable with respect to 

 the second term, which expresses the loss by convection as 

 constant power of the excess of temperature ; because it was 

 found by Principal Forbes that when the excess of tempera- 

 ture was very small, the loss by convection was almost inap- 

 preciable ; and he suggested the viscosity of the air to account 

 for this — some finite excess of temperature being required to 

 set convection-currents going. The point of inflection, more- 

 over, which Forbes found on the curve 0, 6 at a high tempe- 

 rature (see § 4) is wholly unaccounted for by Dulong's expres- 

 sion ; but it is probable that here the experiments of Dulong 

 are the most accurate, and that the contrary flexure of Forbes's 

 curve was due to waves of heat in the elongated mass whose 

 cooling he investigated*. Experiments on the rate of cooling 

 of bodies at the ordinary pressure of the atmosphere have been 

 made by Mr. Macfarlane and by Mr. Nichol ; but their excesses 

 of temperature only went as high as 60° (see Everett, i On 

 C.Gr.S. Units,' p. 50). I believe ProfessorsAyrton and Perry 

 have some results not yet published. 



On another ground also caution seems to be rendered ne- 

 cessary by the kinetic theory of gases, as illustrated in the 



* Or see Professor Tait's explanation given to the .Royal Society of 

 Edinburgh on the 20th of last January (' Nature/ No. 486, p. 379). 



