of Edinburgh^ Session 1865-66. 
563 
3. Note on the Compression of Air in an Air-bnbble 
under Water. By Professor Tait. 
In an air-bubble of moderate dimensions the pressure is very little 
greater than that of the atmosphere ; but, as the difference of 
pressures within and without a bubble is proportional to its curvature, 
it appeared to me possible that the so-called solution of air in water 
might be due in some degree to the extreme compression of the 
air when divided into small bubbles invisible perhaps even under 
the microscope. 
For a rough attempt at a solution, let us assume air to follow 
Boyle’s law for all pressures, and suppose the common formula 
to hold for the smallest bubble. 
Both of these assumptions are probably far from correct — the first, 
when the condensation of the air is great ; and the second, when the 
dimensions of the bubble are so small as to be comparable with the 
greatest distance at which molecular forces are sensible. 
If E be the radius of the sphere which the contained air would 
occupy at the pressure of the atmosphere ; r the radius of the 
bubble, and p the pressure inside, 
Now, by experiments on the rise of water in capillary tubes, it 
2T 
is found that the value of — is, roughly, -0001 inch, if T be 
Po 
the tension per linear inch, p^ the pressure per square inch. From 
the smallness of this quantity it appears that unless E be very 
small, the second term of the above cubic is of little consequence, 
and therefore the dimensions of the bubble are little altered. 
' 2T 
P-Po= — 
Eliminating p by the help of the first equation. 
