XV] OF BLOOD-VESSELS 949 



area, but the thickness of the wall varies very considerably. For 

 instance, in the left ventricle the apex is by much the thinnest por- 

 tion, as it is also that with the greatest curvature. We may assume, 

 therefore (or at least suspect), that the formula, ^ (1/r + 1/r') = C, 

 holds good ; that is to say, that the thickness {tj of the wall varies 

 inversely as the mean curvature. This may be tested experimentally, 

 by dilating a heart with alcohol under a known pressure, and then 

 measuring the thickness of the walls in various parts after the whole 

 organ has become hardened. By this means it is found that, for 

 each of the cavities, the law holds good with great accuracy*. 

 Moreover, if we begin by dilating the right ventricle and then dilate 

 the left in like manner, until the whole heart is equally and sym- 

 metrically dilated, we find (1) that we have had to use a pressure 

 in the left ventricle from six to seven times as great as in the right 

 ventricle, and (2) that the thickness of the walls i» just in the same 

 proportion f. 



Many problems of a hydrodynamical kind arise in connection 

 with the flow of blood through the blood-vessels; and while these 

 are of primary importance to the physiologist they interest the 

 morphologist in so far as they bear on questions of structure and form. 

 As an example of such mechanical problems we may take the con- 

 ditions which go to determine the manner of branching of an artery, 

 or the angle at which its branches are given off; for, as John Hunter 

 said J, "To keep up a circulation sufficient for the part, and no more, 

 Nature has varied the angle of the origin of the arteries accordingly." 

 This is a vastly important theme, and leads us a deal farther than 

 does the problem, petty in comparison, of the shape of an egg. For 

 the theorem which John Hunter has set forth in these simple words 

 is no other than thaf " principle of minimal work" which is funda- 

 mental in physiology, and which some have deemed the very criterion 



* R. H. Woods, On a physical theorem applied to tense membranes, Journ. 

 of Anat. and Phys. xxvi, pp. 362-371, 1892. A similar investigation of the 

 tensions in the uterine wall, and of the varying thickness of its muscles, was 

 attempted by Haughton in his Animal Mechanics, 1873, pp. 151-158. 



t This corresponds with a determination of the normal pressures (in systole) 

 by Knohl, as being in the ratio of 1 : 6-8. 



% Essays, edited by Owen, i, p. 134, 1861. The subject greatly interested Keats. 

 See his Notebook, edited by M. B. Forman, 1932, p, 7; and cf. Keats as a Medical 

 Student, by Sir Wm Hale- White, in Guy's Hospital Reports, lxxiii, pp. 249-262, 

 1925. 



