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



In the experiments with the dog's bladder, a is nearly 0, so that this 



takes the simpler form E = ^ — ~, s — , which is still too awkward for 



1 2z (r— r )r ' 



interpretation. But to connect the results for the tissue of dog's bladder 



with those for other tissues the modulus of elasticity E can be regarded from 



a different point of view. In experiments on dead muscle, for instance, the 



muscle is stretched by different weights, the amount of stretching produced 



by each being recorded. As the muscle is lengthened its cross-section is 



diminished, but, as a rule, no account is taken of this fact. This is because 



more interest is taken in the behaviour of the muscle as a whole, or of a 



single representative muscle fibre, than in the intensity of the tension or 



the tension per cm. 2 of cross-section of the muscle. For the gastrocnemius of 



the frog stretched by amounts I — 1 , by weights w up to 95 grammes, 0. Henry 



has shown* that the following formula holds : 



l-l = 6-55 log (l+w/6\L0), (5) 



l — U being expressed in mm. and w in grammes weight. For other tissues 



with a wide range of elastic properties, A. Goyf finds the same formula to 



apply with appropriate values in place of 6 - 55 and 6"10. But the physical 



explanation given for (5) by Henry is not sound, as he interprets l + w/6'10 



in the form (6 , 10 + w)/6 - 10 to mean that there is at the beginning a tonus of 



the muscle equivalent to a weight 6*1 grammes. If there is stress in the 



muscle at the beginning it must be self-equilibrating, and it is not correct 



mechanics to fix upon one part of this internal stress, called the tonus, and 



treat it as a sign of a not otherwise demonstrable external force denoted 



above by 6*1. But, guided by the success of (5), we can arrive at a simpler 



formula which is capable of legitimate and easy physical explanation. Let 



us suppose that the elongation I— 1 caused by w is related to w by the following 



equation : 



(l-l )/w = a-b(l-l ), (6) 



where a and b are constants for a given tissue. 



This means that the average elongation caused by unit weight, that is to 



say (l—l Q )/tv, diminishes with increasing w in such a way that the diminution 



is linear in the total elongation produced by w. When 5=0, we have the 



usual Hooke's law for small strains. It is possible to give a theoretical 



molecular explanation of (6), though it would not be appropriate here. In 



the case of the frog's gastrocnemius, for values of w from 30 to 95 grammes, 



it gives the elongation l — I , with a maximum error of 1*6 per cent., and 



from to 30 grammes with a maximum error of 16 per cent., the 



* 'Compt. Eend.,' vol. 162, 1906, p. 729. 

 t Ibid., p. 1158. 



