244 
MR. J. E. PETAVEL ON THE HEAT DISSIPATED BY A 
Simultaneously with conduction (he., the dissipation of heat by molecular motion) 
we have convection, by which the heat is carried off by the general upward flow of 
the gas. 
With an infinitely small radiator each molecule comes in contact with the radiator 
at the temperature of the enclosure. With a radiator ot large area a certain propor¬ 
tion of the molecules wdiich strike its upper surface have already become heated by 
previous contact. The heat lost by convection decreases therefore as the diameter 
of the radiator increases ; it is obvious, however, that it can never become zero, hut 
must tend tow^ards a constant quantity. 
Such experimental observations as are available point to the same conclusion, the 
loss by convection being best represented by an expression of the form Co + 
The loss by radiation is independent of the size of the radiator and may be put equal 
to a constant, The variation of emissivity with the size of the radiator is there¬ 
fore expressed by the following formula :— 
Emissivity = c 2 , (c^ + c^)r~^ = C -E 0'r~^ .... (vi.). 
This is the same expression as was established empirically by Ayrton and Kilgour."^ 
Within the range of their experiments {r = O'OlaZ to 7' = 0T78 millim.) both C 
and C' w^ere constants. 
In an investigation on the effect of the size of the enclosure, formula (iii.) is not 
suitable. It w^as established that the length of the cylinder was sufficiently great 
in comparisoii with its diameter to render the end effects negligible. We therefore 
cannot put II = oc . If, how'ever, we take the simple case of a spherical enclosure 
and radiator, and reason by analogy, w^e can easily obtain the information we 
desire. 
Proceeding as on page 240, the thermal resistance of the elementary spherical 
shell is 
1 dr 
THK ^ • 
Integrating w'e get for the total resistance 
1/1 1 \ _ 1 - /• 
4nKVr “ 11 / "" 411K ^ ' R/- 
The part of the emissivity due to conduction is therefore 
Ayrton and KiLGOril (‘Phil. Trans.,’A, vol. 183, p. 371, 1892) have shown that an expression of 
this form holds good for the smallest diameters that can practically be used. It M ould, hou'ever, be uiuvise 
to extend the formula much lieyond the limit M'ithin -which it has been experimentally jjroved. It is 
evident that for r = 0 the expression is at fault, for the value of the emissivity cannot exceed E = NC 
where N is the number of molecular impacts and C the molecular specific heat. 
