666 ON THE FORM AND BRANCHING [ch. 



of the small arteries, and still more of the capillaries, become 

 exceedingly thin, and more so than in strict proportion to the 

 narrowing of the tube. 



In the case of the heart we have, within each of its cavities, a 

 pressure which, at any given moment, is constant over the whole 

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

 For instance, in the left ventricle, the apex is by much the thinnest 

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

 assume, therefore (or at least suspect), that the formula, 

 t{l/r + 1/r') = C, holds good; that is to say, that the thickness (t) 

 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 symmetrically 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 is just in the same proportion j*. 



A great many other problems of a mechanical or hydro- 

 dynamical kind arise in connection with the blood-vessels J, and 

 while these are chiefly interesting to the physiologist they have 

 also their interest for the morphologist in so far as they bear upon 

 structure and form. As an example of such mechanical problems 



* Woods, R. H., On a Physical Theorem applied to tense Membranes, Jotirn. 

 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, pp. 151-158, 1873. 



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

 by Krohl, as being in the ratio of 1 : 6*8. 



X Cf. Schwalbe, G., Ueber Wechselbeziehungen imd ihr Einfluss auf die 

 Gestaltung des Arteriensystem, Jen. Zeitschr. xn, p. 267, 1878 , Roux, Ueber die 

 Verzweigungen der Blutgefassen des Menschen, ibid, xn, p. 205, 1878; Ueber die 

 Bedeutung der Ablenkung des Arterienstammen bei der Astaufgabe, ibid, xm, 

 p. 301, 1879; Hess, Walter, Eine mechanisch bedingte Gesetzmassigkeit im Bau 

 des Blutgefasssystems, A. f. Entw. Me.ch. xvi, p. 632, 1903; Thoma, R., Ueber die 

 Histogenese und Histomechanik des Blutgefasssystems, 1893. 



