i68 
Electric Lighting by Incandescence . [February, 
could be obtained from the balloon : when he was half a 
mile over London he could see Margate and Brighton, and 
on to the Norfolk coast. This showed how much may be 
seen from a comparatively small elevation. From the 
height of a mile he could see nearly 90 miles, and even when 
a few hundred feet high one was in a position to see over 
the country for several miles ahead. In any case he hoped 
that in the next Expedition, from whatever country it may 
proceed, not only one balloon but several balloons would be 
taken out. 
V. ELECTRIC LIGHTING BY INCANDESCENCE. 
To determine the Electromotive Force required to maintain a rod 
of a given material , of given dimensions , at a given tem- 
perature , when loss of heat by radiation , convection , and 
conduction are taken into account. 
By Prof. W. E. Ayrton. 
S AVING found it necessary to solve the above question 
in connection with the possibility of economically 
illuminating, by a material rendered incandescent 
with the eleCtric arc (the system employed by Edison, 
Wedermann, Sawyer-Man, &c., and first patented in England 
by De Moleyns in 1841, and not, as commonly supposed, by 
King, since his patent bears the date of 1845), I have 
thought that the results obtained maybe generally interesting. 
The problem of the flow of heat through a bar from which 
there is loss of heat by radiation and convection has, since 
the time of Fourier, been often treated; the mathematical 
investigation was employed by Forbes in his experiments 
made to determine whether the heat conductivity of iron, 
like the eleCtric conductivity, varied with the temperature, 
and exactly similar equations have been made use of in 
studying the passage of an eleCtric current- through a wire 
from all points of which there is leakage, as in an ordinary 
submarine cable, and especially in a submarine cable made 
of inferior gutta-percha. The problem, however, we have 
on the present occasion to deal with differs from the pre- 
ceding in that there is, at every point, not only loss of heat 
by conduction, radiation, and conveCtion, but, in addition, 
