XV] OF BLOOD-VESSELS 957 



they must not be too large, or they will hold more blood than is 

 needed — and blood is a costly thing. We rely once more on 

 Poiseuille's Law*, which tells us the amount of work done in causing 

 so much fluid to flow through a tube against resistance, the said 

 resistance being measured by the viscosity of the fluid, the coefficient 

 of friction and the dimensions of the tube; but we have also to 

 account for the blood itself, whose maintenance requires a share 

 of the bodily fuel, and whose cost per c.c. may (in theory at least) 

 be expressed in calories, or in ergs per day. The total cost, then, 

 of operating a given section of artery will be measured by (1) the 

 work done in overcoming its resistance, and (2) the work, done 

 in providing blood to fill it; we have come again to a differential 

 equation, leading to an equation of maximal -efficiency. The general 

 result! is as follows: it can be made a quantitative one by intro- 

 ducing known experimental values. Were blood a cheaper thing 

 than it is we might expect all arteries to be uniformly larger than 

 they are,, for thereby the burden on the heart (the flow remaining 

 equal) would be greatly reduced — thus if the blood-vessels were 

 doubled in diameter, and their volume thereby quadrupled, the 

 work of the heart would be reduced to one-sixteenth. On the other 

 hand, were blood a scarcer and still costlier fluid, narrower blood- 

 vessels would hold the available supply; but a larger and stronger 

 heart would be needed to overcome the increased resistance. 



* Owing to faulty determination of the fall of pressure in the capillaries, 

 Poiseuille's equation used to be deemed inapplicable to them ; but Krogh's recent 

 work removes, or tends to remove, the inconsistency {Anatomy and Physiology of 

 the Capillaries, Yale University Press, 1922). 



t Cf. C. D. Murray, op. cit. p. 211. 



