642 
PROFESSORS A. W. REIN OLD AND A. W. RUCKER 
Thus a slight increase in the principal ordinate of a spherical film converts it into a 
nocloid the mean curvature of which is greater or less than that of the sphere according 
as the distance between the rings is less or greater than the circumference of a ring 
X 0-4803. 
If this distance between the rings is exceeded, an arrangement consisting of two 
spherical films, the interiors of which are in communication, will be unstable. 
We have next to investigate the sensitiveness of our experiment. 
If two films, which are in communication, are in equilibrium, the pressure exerted 
on the internal air must be the same. Hence 
4T _ 4T / 
^ u + /3 a.' +/3' 
If the equilibrium is maintained after a change in any or all of these quantities, 
clT T (d* + d{3) _ dV T \d*' + dp) n _ A 
«+/3 (a+>) 2 “«'+/3' («' + /T) 2 .' 
The six quantities da, d/3, d^> x , and dec, d/3', d$ x can be determined from the six 
conditions that the values of X and Y shall in each case remain unaltered, that the 
changes of volume shall be equal in magnitude and opposite in sign, and that the 
change of pressure shall be the same for each film. 
If the two films are similar the condition dV = —dV' leads in general to the result 
da= — da.' and d/3= — d/3'. 
In the case of two cylinders an expansion of the one is accompanied by a contraction 
of the other. If both were initially similar in all respects it is easy to show that 
da= — d/3', where the latter symbol refers to the film which has undergone a 
contraction. 
For, since the lengths of the cylinders were the same, and in the case of the 
cylinder 
a=/3=Y and E = F =(/>, 
we have 
X=aE+/3F=2Ytf, 1 =2Y .( 13 ) 
and from (10), since cZV=— dV', 
da{(f> x (cot </> L —tun </>// — 1 }/tan fa-dp' — -^(cot <f>i — tan<£/) — 1 j/cot </>/, 
which, by (13), gives da.— — d/3', and in like manner da — — d/3. 
Hence, from (12), if we put cZT' = 0, 
2{da+d/3)T=(a+/3)dT=2YdT, 
