100 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the polished pure metal, it is justifiable to assume that the variation in 
emissivity, over the range of X m in question, will be similar to that of 
copper. The data available indicate that the emissivity of copper is very 
nearly constant between A w = 10 4/x and A m = 7'9/x ; and that, if it be taken 
as 0 016, it will be correct over the whole range to the third place of 
decimals. The emissivity of gilding metal has accordingly been regarded 
as constant for the temperatures used in the tests described below. 
The first of the analyses here attempted is based upon figures given by 
Dewar for a glass flask in which the inner vessel was “ silvered ” with 
mercury, the outer one being untreated. The evaporation loss of the flask 
was ascertained over a temperature-range (of extending between 158° abs. 
and 338° abs. Information does not appear to be available regarding the 
change of emissivity of glass and mercury surfaces over such a wide range 
of X m as is here involved, and it has been necessary to assume the emissivity 
of these surfaces to be constant between the stated extremes of temperature. 
Owing to the uncertainty resulting from the incompleteness of the physical 
data, the results obtained for the glass flask must be regarded as rough 
approximations. When emissivity is constant, the heat radiation may 
be expressed as 
Ls^W-9/) (1) 
in which a is a coefficient depending upon the emissivity of the surfaces 
and upon their dimensions. The unit may be calories per second, or, as is 
here more convenient, grams of liquid air evaporated per hour. 
(2) Conduction across the Vacuum Space. — With the highly refined 
vacua with which we are concerned, the mean free path of the gas 
molecules is greater than the distance (about 1 cm.) between the hot and 
cold surfaces ; hence, if conductivity had been independent of temperature, 
the heat carried by conduction across the vacuum would be proportional to 
($i — 0 2 )- In a gas, however, the conductivity varies as the square root of 
the absolute temperature, and, as the mean temperature across the vacuum 
space is 0 - 5(d 1 + 0 2 ), the expression representing the evaporation loss due 
to this cause is, in grams of liquid air evaporated per hour : 
• • • • ( 2 ) 
where b is constant for a given bottle. 
(3) Neck Conduction. — The amount of liquid evaporated because of heat 
conducted along the inner neck, C, of the flask cannot be evaluated even 
roughly by direct computation based upon the dimensions of the neck and 
the conductivity of the metal, owing to the fact that the tube forms the 
