1909.] Elasticity of Rubber Balloons and Hollow Viscera. 499 



corresponding error for (5) being 17 per cent. But it is probable that in 

 neither case are these really errors of formula, because with the smaller 

 weights there is liability to considerable experimental uncertainty while 

 " taking up the slack " of the specimen. 



It is interesting to see how the type of formula (6) applies to 

 Prof. Osborne's experiments on the bladder of a dog. We must treat the 

 .experimental facts so that they are as similar as possible to those of muscle. 

 If we return to (1) we see that wpr 2 corresponds with w the weight used to 

 stretch muscle, although it stretches the bladder wall in two directions at 

 right angles to one another. The chief effect of this stretching in two 

 directions is to replace E as measured on a strip cut from the bladder wall 

 and stretched only in one direction by 2 E. From the experiments we get 



= 0-00121 -0-000318 (r-r ), (7) 

 irpir v ' 



with the following comparison : — 



r 1-336 1-680 1-927 2121 2-285 2-429 2'672 2-878 



_pexper. ... 14 40 55 63 68 77 87 

 p calc 35 50 58 64 68 76 82 



r 3-220 3-637 3-959 4-252 4493 4-655 4-856 



^exper. ... 95 107 117 217 410 560 620 

 p calc 95 116 142 182 243 318 533 



At the two lowest pressures after the discrepancy between calculation 

 and experiment is large, but can plainly be ascribed to the taking up of 

 slack in the experiments. The formula fits the facts satisfactorily over the 

 very great elongation from r = 2421 to r = 3-220. Beyond that the 

 formula ceases to give the connection between p and r in a useful manner, 

 but on that account it by no means loses its physical significance. If we 

 write (7) in the form 



p = (r-?- )/7rr 2 {0-00121 -0-000318 (r-?- )}, (8) 



we see that for values of r—r greater than 3 the difference 0-00121 — 

 0-000318 (r— r ) becomes small compared with either 0-00121 or 

 0000318 (r— ?- ). Hence a small error in r produces a much larger relative 

 error in p. With this fact in view it appears that (7) gives a good account 

 of the physical happenings in the wall of the bladder during the large 

 elongations up to r = 4 - 856. 



The form (7) can be applied to the experiments on a deflated rubber 

 balloon, but not to those on an inflated. 



