488 



Prof. W. A. Osborne and Mr. W. Sutherland. [July 5, 



equal dimensions are tied to two limbs of a T-tube and inflated by the third 

 limb, which can be closed by a tap. As a rule one of the balloons inflates 

 well, the other remaining small. On closing the tap in the inflating tube 

 the contents of one balloon can be discharged into the other by squeezing 

 with the hand. If the air be worked backwards and forwards a few times 

 to equalise the "history" of each, it will be found that if the balloons are 

 approximately equal in volume they will remain so for a few seconds, in 

 a state of unstable equilibrium, and then one of the balloons will partially 

 deflate itself into the other. The balloon which is now the larger, if 

 squeezed until its volume is slightly less than that of the other and then 

 let go, will continue to deflate until equilibrium is reached. 



These experimental results appeared to be utterly at variance with what 

 was deducible from the theory of a perfectly elastic balloon. Amongst 

 the many articles dealing with the elasticity of rubber to which I had 

 access, I found one which promised to throw some light on my results. 

 0. Frank* assumes a somewhat modified Hooke's law. According to him 

 the pressure dF in a sample of section q and length x associated with a 

 shortening dx is given by the formula 



fZP/g = ILdx/x, 



in which unit initial length and unit initial cross sectional area are not con- 

 sidered, but length and area such as they are when the change dx is produced. 

 If x is the original length and x x the final, he calls A = (xi—x )/x the 

 specific extension. For the total tension in a strip of unit width and of 

 initial thickness z his final result on p. 608 can be written 



T = 2 EA 



(1 + A) 2 " 



Substituting this value of T in equation (1), we get 



4EAzp 

 Pl " + A) 2 ' 



But in the case of the balloon the specific extension A = (n — r )/r , 

 therefore 



i?1 = 4Evo r -S^- 



According to this equation the pressure in an inflating balloon will rise 

 to a maximum when o\ = f r , and will approach asymptotically to zero when 

 ?'! increases indefinitely. But I may say at once that this approach to zero 

 pressure is never given in balloon experiments, so that Frank's analysis 

 fails to explain the results obtained. One may indeed state a priori that as 

 * ' Annalen der Physik,' vol. 21, p. 602, 1906. 



