400 
PROF. LOIJIS VESSOT KING ON THE CONVECTION OF 
shown very satisfactorily in the last column of Table VI. and in fig. 7 where no 
systematic variation with the radius can be detected. The mean value of the ratio 
Bj \ / at) as the final result of the entire series of observations is given by 
/3j\/a 0 — 1'432 x 10 -3 ,.(68) 
heat units being measured in watts. 
In the numerical calculation of the theoretical factor 2v 7r.s 0 o- 0 /c 0 we take cr 0 = (F001293, 
k 0 = 5‘66xl0~ 5 calories( 38 ) and s 0 = O' 171 calories( 3il ), the specific heat at constant 
volume being that appropriate to the problem since no external work is done by the 
expansion of the heated air. We find 2\/ 7rS 0 <x 0 /r 0 = 3'96 x 10 -4 expressed in calories ; 
on multiplying by 4T8 to reduce to watts we have finally 
2\/ 7ts 0 <t 0 k 0 = 1*66 x 10~ 3 . (69) 
The agreement with the experimental factor in equation (68) must be considered 
fair in view of the uncertainty attached to the value of the heat conductivity, and also 
in that the theoretical investigation does not take into account the variation of this 
and the other factors with the temperature gradient in the neighbourhood of the 
wire. 
(ii.) Analysis of the Convection Constant C. 
The rational interpretation of the convection constant C in the light of the theory 
of Section 6 requires us to separate out the energy losses due to radiation. The 
characteristic form of the equation giving the total radiation from metallic surfaces is 
e = O - 0 *,.( 70 ) 
where 0 represents the absolute temperature and a and (3 are constants depending on 
the nature of the metal forming the surface. From the observations of Lummer and 
Kurlbaum ( 40 ) it can be shown that the radiation loss for polished platinum is given 
in watts per cm. 2 by the relation 
e = 0‘514 ( 0 / 1000) 5 ' 2 .( 71 ) 
Assuming the total radiation loss of a small wire to be proportional to its 
circumference, the loss per unit length is calculated for a wire of diameter O'OIO cm., 
( 3S ) Recent determinations of the thermal conductivity of air are— 
4'76 x 10 -5 at 24° C. (O. J. Stafford, ‘ Ztschr. f. Physik. Chemie,’ 77, p. 67, 1911.) 
5 - 22 x 10 -5 at 0° C. Mean of five observers (Kaye and Laby, ‘ Tables,’ p. 52). 
5-66 x IO - 5 at 0° C. (Eucken, A., ‘ Physik. Zeit.,’ 12, 1101, 1911.) 
5 - 69 x 10 -; \ Mean value adopted by Chapman, ‘ Phil. Trans.,’ A, vol. 211, p. 465, 1912, where 
further references to recent determinations are given. 
(39) There is little variation in the experimental determinations of the specific heat at constant volume. 
The above value is taken from Kaye and Laby’s ‘ Tables,’ p. 58. 
( 40 ) Lummer and Kurlbaum, ‘ Verh. Phys. Ges.,’ Berlin, 17, p. 106, 1898. 
