293 
of Edinburgh, Sessio7i 1867 - 68 . 
Hence it appears that the volume increases and the surface con- 
tracts, or vice versd, for they cannot both remain unaltered. And 
the physical circumstances show at once that the former is the case. 
The formula just written shows that the volume increases by 
as much as that of a bubble, whose surface is equal to the diminu- 
tion of surface, would change when it is so increased that the air it 
contains is at the pressure of the atmosphere. 
It is obvious that the same process of physical reasoning may 
be applied to any number of soap-bubbles when made to unite ; so 
that we may thus, without any analysis, conclude that for any 
number of positive quantities x, y, z, &c., we have always 
x 2 + y 1 + z°- + > (x^ + y ! + z' + ) 3 . 
For if R be the radius of the bubble formed by the union of others 
of radii x, y, z, &c., we must have 
E 2 < x 1 + y 1 + z 1 + 
and R ? > x 3 + f" + z 3 + ..... 
from which the above result is evident. 
Professor Tait exhibited to the Society a very easy mode of de- 
monstrating some of Stewart’s results regarding equality of absorp- 
tion and radiation. Letters drawn with ink on a slip of platinum 
foil appeared brighter than the ground when the foil was heated 
in a large blowpipe flame, but darker than the ground on the other 
side of the foil. Thus, though glowing more brightly, the iron 
spots are really at a lower temperature than the foil beside them. 
The spectra of the two portions were described and their lengths 
compared, with the view of strengthening the proof ; and the ex- 
periment was applied to suggest an explanation of the singular 
observation by which Secchi was led to conclude that iron is trans- 
parent at a red heat. 
