240 
mi. J. E. PETAVEL OX THE HEAT DISSIPATED P.Y A 
Let us divide this space into a number of concentric cylinders, having a length I 
equal to the distance between the potential terminals of the wire and a thickness Ar. 
The thermal resistance of each of these cylinders will be 
_ Ar 1 
“ mir ^ K ’ 
where r is the radius of the cylinder and K the conductivity of the gas under 
consideration, in this case air. 
The total thermal resistance will therefore he 
1 r dr 
~ 2n/K J 7 • 
Integrating between the limits r = It = ladius of tlie enclosure and r = = 
radius of the radiator, we have 
Total resistance = 
or the conductance = 
1 
, (log, R - log, 
2n/K 
K2m 
, T. , = Total flow of heat per decree Centio'rade of 
log,fl — log,ri . ^ ^ 
temperature Interval per second. 
Now tlje emlssivity is defined as the flow of heat per unit surface of radiator per 
degree Centigrade per second, and the above expression divided by the superficial 
area of the wire will thus be equal to the part of the emissivity due to conduction 
alone. 
y ^ K2m ^ 
2n/-fl(log,P-log,rb (log,P - l..g,ri)q. 
where E, is the part of the emissivity due to conduction alone. In the present case 
= 0'0553, R = 1'03, thus: 
E,= 
(>1617 ■ 
Inversely, if the convection is zero and the radiation = R, 
0'1617 (E — R) — K = conductivity. 
By measuring the emissivity at low tenq)eratures and pressures, we can reduce, 
though not entirely suppress convection, and, l)y subtracting the heat lost lyy radia¬ 
tion, obtain a comparison Avith tlie standard determinations of the conductivity of 
gases. Tlie value tlius calculated will always he in excess of the true conducti\dty of 
the gas liy an amount proportional to the heat lost by cimvection. 
In the following table E is the emissivity at 100° ft, and 0‘1 atmosphere ; R the 
radiabion calculated from J. T. Bottomley’s experiments,"'^ and is the conduc¬ 
tivity at 100° C. according to Winkelmann :— 
* ‘ Itoy. Sor. Pruc-.,’ vol 66, p. 276, 1900. 
