485 



The Elasticity of Rubber Balloons and Hollow Viscera* 

 By Prof. W. A. Osborne, with a Note by W. Sutherland. 



(Communicated by Prof. J. N. Langley, F.R.S. Eeceived July 5, 1909.) 

 (From the Physiological Laboratory, University of Melbourne.) 



Introductory Theory. 



In an elastic balloon the relation between the internal excess pressure and 

 the tension of the wall can be readily calculated if we assume that the 

 balloon is spherical and that the material is homogeneous and of negligible 

 weight. If we suppose the balloon divided into two hemispheres by a plane 

 horizontal partition, the area of this partition will be 7rr 2 and the downward 

 force on the upper surface due to the excess pressure p will be irr 2 p. The 

 balloon wall meets the partition at right angles along a length 2irr. Hence 

 if T is the tension in the wall, the upward force exerted by this tension on 

 the partition is 27rrT. But as these two forces must be equal we have 



7rr 2 p = 2 TrTr, so that p = 2T/r. (1) 



When such a balloon is filled without stretching the wall the pressure 

 inside is equal to the prevailing atmospheric, and the radius r may be 

 termed the initial radius. If we assume that the balloon is perfectly 

 obedient to Hooke's law, then 



Ti = K(n-r )/r ; 



but from (1) we learn that 



hence, by substitution, pi = 2 K/r — 2 K/ri, 



or n (^i)=2K. (2) 



That is to say, the pressure will increase with radius asymptotically to 

 2 K /r , and if we plot radius against pressure we shall obtain a rectangular 

 hyperbola. 



The original object of the following research was to investigate the elastic 

 behaviour of various hollow viscera. Before doing so I decided, however, to 

 carry out a number of experiments with rubber balloons, using the pressures 

 found with varying radii as fundamental data. 



* This research was completed before I became aware, from a reference in Boruttau's 

 ' Lehrbuch der Medizinischen Physik,' that a similar investigation had been carried out 

 by E. du Bois-Reymond, and the results published in the ' Festschrift f iir Rosenthal.' On 

 obtaining the latter, I found sufficient difference in the treatment of the subject to 

 warrant publication of this. [See also A. Mallock, ' Roy. Soc. Proc.,' vol. 49, p. 458.] 



VOL. LXXXI. — B. 2 N 



