106 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Pressure in the Vacuum Space of the 3-Litre Flask, and 
Emissiyity of the Metal Surfaces. 
The results stated in Table VI allow the emissivity of the reflecting 
surfaces of the flask and the degree of tenuity of the vacuum to be 
obtained. 
Before emissivity can be calculated it is necessary to inquire into the 
manner of heat-exchange, by radiation, of two reflecting surfaces facing 
each other. The following demonstration is due to J. A. Harker : — 
Let the emissivity of either of the two similar surfaces be E. Suppose 
E units of heat to be emitted by the hotter surface ; of these E 2 will be 
absorbed and E(1 — E) will be reflected by the second or cooler surface. 
The first surface will then reflect E(1 — E) 2 units, of which the second 
surface will absorb E 2 (l — E) 2 . Proceeding thus, it appears that when the 
hotter surface emits E units the cooler surface gains an amount which is 
the sum of an infinite G.P. whose first term is E 2 and whose common ratio 
is (1 — E) 2 , and that summation is 
E 
2 - E' 
Applying Barker’s result to Stefan’s Law ; taking the constant of that 
law as L385 x 1CT 12 (calorie units) ; taking the latent heat of a half-and-half 
mixture of liquid nitrogen and liquid oxygen as 502 cals, per grm. ; and 
making use of the dimensions of the flask, the emissivity of the gilding- 
metal surfaces was found to be O’OSO. That for pure copper polished to the 
highest degree is 0016. The fact that the makers of the flask have only 
succeeded in getting an emissivity amounting to thrice that of copper is 
important. In studying to reduce the tranquil evaporation rate in these 
particular flasks it is evidently on the radiation loss that most attention 
should be focussed. A small increase upon the value for the emissivity of 
copper might have been expected owing to the gilding metal containing 
tin, and a further slight increase is no doubt due to the smear of solder 
running equatorially round the inner sphere ; but the main reason for the 
enhanced radiation is probably that water vapour condensed on the inner 
sphere and spoilt the surface. It is a most difficult matter, with the 
method of evacuation used at present for soft-soldered metal flasks, to rid 
the charcoal and vacuum space entirely of water vapour. 
With pressures as low as those in the vacuum spaces of liquid-air 
bottles, the heat-transfer by conduction across such a space is proportional 
to the difference of temperature, (d x — d 2 )> to the pressure, y>, and to the area 
of the surface, A, and is independent of the distance. 
That is to say : — 
Heat transferred by conduction across the vacuum = c(6 1 — 0 2 )p A . (6) 
