954 ON THE FORM AND BRANCHING [ch. 



But the increasing surface of the branches soon means increased 

 friction, and a slower pace of the blood travelling through; and 

 therefore the branches must be more capacious than at first appears. 

 It becomes a question not of capacity but of resistance; and in 

 general terms the answer is that the ratio of resistance to cross- 

 section shall be equal in every part of the system, before and after 

 bifurcation, as a condition of least possible resistance in the whole 

 system; the total cross-section of the branches, therefore, must be 

 greater than that of the trunk in proportion to the increased 

 resistance. 



An approximate result, familiar to students of hydrodynamics, is 

 that the resistance is a minimum, and the condition an optimum, when 

 the cross-section of the main stem is to the sum of the cross-sections 

 of the branches as 1 : ^2, or 1 : 1-26. Accordingly, in the case of 

 a blood-vessel bifurcating into two equal branches, the diameter 

 of each should be to that of the main stem (approximately) as 



J 



1-26 



-^-il, or (say) 8: 10. 



While these statements are so far true, and while they undoubtedly 

 cover a great number of observed facts, yet it is plain that, as in 

 all such cases, we must regard them not as a complete explanation, 

 but as factors in a complicated phenomenon : not forgetting that 

 (as one of the most learned of all students of the heart and arteries, 

 Dr Thomas Young, said in his Croonian lecture*) all such questions 

 as these, and all matters connected with the muscular and elastic 

 powers of the blood-vessels, "belong to the most refined departments 

 of hydrauhcs"; and Euler himself had commented on the "in- 



* On the functions of the heart and arteries, Phil. Trans. 1809, pp. 1-31, 

 of. 1808, pp. 164-186; Collected Works, i, pp. 511-534, 1855. The same lesson is 

 conveyed by all such work as that of Volkmann, E. H. Weber and Poiseuille. 

 Cf. Stephen Hales's Statical Essays, ii, Introduction: "Especially considering 

 that they [i.e. animal Bodies] are in a manner framed of one continued Maze of 

 innumerable Canals, in which Fluids are incessantly circulating, some with great 

 Force and Rapidity, others with very different Degrees of rebated Velocity: 

 Hence, etc." Even Leonardo had brought his knowledge of hydrodynamics to 

 bear on the valves of the heart and the vortex-like eddies of the blood. Cf. 

 J. Playfair McMurrich, L. da Vinci, the Anatomist, 1930, p. 165; etc. How com- 

 plicated the physiological aspect of the case becomes may be judged by Thoma's 

 papers quoted above. 



