THERMAL EMISSIVITY' OF THIN WIRES IN AIR. 
395 
assume that the three formulae (5), (6), (7) given above for e may be used not merely 
for the platinum wires when fine, but also as giving at any rate a rough approximation 
of the value of e when the wire is as much as 4 or 5 millims. thick, we may conclude 
that for a temperature of 100° C. the value of d in the formula 
e = 0-001036 + 0-012078 
must be something of the order 220 mils, or 5"6 millims., so that the neglect of the 
second term may not make an error in e of more than 5 per cent., and something of 
the order 1"15 inch, or 29"3 millims., if the error is not to exceed 1 per cent.; that for 
a temperature of 200° C., the value of d in the formula 
e = 0-001111 + 0-014303 d~ l 
must be something of the order 244 mils, or 6"2 millims., so that the neglect of the 
second term may not make an error in e of more than 5 per cent., and something of 
the order 1-28 inch, or 32"5 millims., if the error is not to exceed 1 per cent. ; and that 
for a temperature of 300° C., the value of d in the formula 
e — 0-001135 + 0-016084 d~ l 
must be something of the order 267 mils, or 6*8 millims., so that the neglect of the 
second term may not make an error in e of more than 5 per cent , and something of 
the order 1 *39 inch, or 35"3 millims., if the error is not to exceed 1 per cent. 
Generally, then, although it may be possible to obtain only very rough approxima¬ 
tions of the values of the emissivities of thick wires by using the three formulae that 
we have deduced from the experiments on thin wires, still it follows that to assume 
that the emissivity is a constant for wires whose diameters vary from a small value 
up to 1 inch is to make a large error in the case of the greater number of the wires, 
and an error of hundreds per cent, in the case of some of them. 
The formulae (5), (6), (7) given above have been calculated from the results of 
experiments made on wires varying from 1"2 to 14 mils, and the method of calculation 
employed makes the percentage difference between the observed and calculated 
emissivity very small at each end of the range as well as in the middle. We may, 
therefore, use the formula to obtain some idea of what the emissivity is likely to be for 
a wire somewhat smaller than that used in the experiments, say, of 0"75 mil in diameter. 
Using formula (7) to obtain the emissivity at 300° C., we find it to be 0"02258. We 
can now make an approximate estimate of the current density, or amperes per square 
centimetre, it would be necessary to employ with a platinum wire of 0"75 mil in order 
to keep it at a temperature of 300° C., when the enclosure was, say, at 15° C. 
From the tables that we have given of the resistance of platinum wire at different 
temperatures, we see that the resistance of 17 centims. of wire 0"152 millim. in 
3 e 2 
