THERMAL EMISSIVITY OF THIN WIRES IN AIR. 
399 
x/j ( t) be the emissivity at a temperature t for a wire of diameter d. 
K ,, number of calories corresponding with one watt-second. 
A ,, current in amperes flowing through the wire ; 
then following the method of reasoning employed with such problems, we have 
7 TtP d 
4 dx 
+ 
ApKA=/(0 = nd(t- t 0 )i(t) 
( 8 ). 
</j (t) is in reality the reciprocal of the amount of heat in calories that would flow 
per second across one cubic centimetre of the material for 1° C. difference of tempera¬ 
ture between the opposite faces and for a mean temperature of the material of f. 
xjj (t) is the number of calories lost per second on account of radiation and con¬ 
vection for 1° C. excess temperature from a square centimetre of the platinum wire 
of diameter d and at a temperature t. 
In the preceding equation d is strictly the diameter of each part of the wire at the 
particular temperature it is at. As, however, an increase of the temperature from 
0° C. up to 300° C. only increases the linear dimensions of platinum by about 
0'26 per cent., d may be taken as the diameter of the wire at 15° C. 
fit) and xjf (t) are known from the various curves connecting resistance with 
temperature and emissivity with temperature for each of the various wires experi¬ 
mented on. The variation of the thermal resistance of platinum with temperature 
has not, as far as we can learn, been experimentally examined, nor does it appear to 
be even known whether the thermal resistance of platinum increases with tempe¬ 
rature, as does the thermal resistance of iron, or diminishes with the rise of 
temperature, as does the thermal resistance of copper and German silver. Under 
these circumstances we decided to assume that the thermal resistance of platinum 
was a constant, and had the value it is known to possess at ordinary temperatures, 
and to see what sort of result a mathematical assumption based on this result would 
lead to. 
As a matter of fact, even the thermal conductivity of platinum at ordinary tempera¬ 
tures is not stated explicitly in hooks, but it can be easily arrived at indirectly. For 
we find that Wiedemann and Franz determined that 
Thermal conductivity of platinum 8'2 
Thermal conductivity of copper 77'2 
and in the article “ Heat ” in the ‘ Encyclopaedia Britannica,’ the value of the thermal 
conductivity of copper, 0‘96 as determined by Angstrom, is stated to be trustworthy. 
From these numbers we deduce that the thermal resistance of platinum, at ordinary 
temperatures, is 9’858, which is the value we have taken for <f> ( t). 
Equation (8) can then be written in the form 
