XV] OF BLOOD-VESSELS 951 



growth and evolution an efficient mode of transport has been attained. 

 To prove that it is the very best of all possible modes of transport 

 may be beyond our powers and beyond our needs; but to assume 

 that it is perfectly economical is a sound working hypothesis*. And 

 by this working hypothesis we seek to understand the form and 

 dimensions of this structure or that, in terms of the work which it 

 has to do. 



The general principle, then, is that the form and arrangement 

 of the blood-vessels is such that the circulation proceeds with a 

 minimum of effort, and with a minimum of wall-surface, the latter 

 condition leading to a minimum of friction and being therefore 

 included in the first. What, then, should be the angle of branching, 

 such that there shall be the least possible loss of energy in the course 

 of the circulation? In order to solve this problem in any particular 

 case we should obviously require to know (1) how the loss of energy 

 depends upon the distance travelled, and (2) how the loss of energy 

 varies with the diameter of the vessel. The 

 loss of energy is evidently greater in a 

 narrow tube than in a wide one, and greater, 

 obviously, in a long journey than a short. 

 If the large artery, AB, gives off a com- 

 paratively narrow branch leading to P 

 (such as CP, or DP), the route ACP is 

 evidently shorter than ADP, but on the 

 other hand, by the latter path, the blood has 

 tarried longer in the wide vessel ^B, and has '^ ^. ^g 



had a shorter course in the narrow branch. 



The relative advantage of the two paths will depend on the loss 

 of energy in the portion CD, as compared with that in the alternative 

 portion CD', the one being short and narrow, the other long and 

 wide. If we ask, then, which factor is the more important, length 



* Cf. A. W. Volkmann, Die Haemodynamik nach Verauchen, Leipzig, 1850 

 (a work of great originality); G. Schwalbe, Ueber. . .die Gestaltung des Arterien- 

 systems, Jen. Zeitschr. xii, p. 267, 1878; W. Hess, Eine mechanischbedingte Gesetz- 

 massigkeit im Bau des Blutgefasssystems, A.f. Entw. Me'ch. xvi, p. 632, 1903 ; Ueber 

 die peripherische Reguiierung der Blutzirkulation, Pfluger's Archiv, CLXvm, pp. 

 439-490, 1917; R. Thoma, Die mittlere Durchflussmengen der Arteriert des 

 Menschen ais Funktion des Gefassradius, ibid, clxxxix, pp. 282-310, cxcra, 

 pp. 385-406, 1921-22; E. Blum, Querschnittsbeziehungen zwischen Stamm u. Asten 

 im Arteriensystem, ibid, clxxv, pp. 1-19, 1919. 



