950 ON THE FORM AND BRANCHING [ch. 



of "organisation*." For the principle of Lagrange, the "principle 

 of virtual work," is the key to physiological equilibrium, and 

 physiology itself has been called a problem in maxima and minima f. 



This principle, overflowing into morphology, helps to bring the 

 morphological and the physiological concepts together. We have 

 dealt with problems of maxima and minima in many simple con- 

 figurations, where form alone seemed to be in question; and we 

 meet with the same principle again wherever work has to be done 

 and mechanism is at hand to do it. That this mechanism is the 

 best possible under all the circumstaaces of the case, that its work 

 is done with a maximum of efiiciency and at a minimum of cost, 

 may not always lie within oui; range of quantitative demonstration, 

 but to believe it to be so is part of our common faith in the perfection 

 of Nature's harndiwork. All the experience and the very instinct of 

 the physiologist tells him it is true ; he comes to use it as a postulate, 

 or meihodus inveniendi, and it does not lead him astray. The dis- 

 covery of the circulation of the blood was implicit in, or followed 

 quickly after, the recognition of the fact that the valves of heart 

 and veins are adapted to a one-way circulation ; anA we may begin 

 likewise by assuming a perfect fitness or adaptation in all the minor 

 details of the circulation. 



As part of our concept of organisation we assume that the cost 

 of operating a physiological system is a minimum, what we mean 

 by cost being measurable in calories and ergs, units whose dimensions 

 are equivalent to those of work. The circulation teems with illustra- 

 tions of thi^ great and cardinal principle. " To keep up a circulation 

 sufiicient for the part and no more" Nature has not only varied the 

 angle of branching of the blood-vessels to suit her purpose, she has 

 regulated the dimensions of every branch and stem and twig and 

 capillary; the normal operation of the heart is perfection itself, 

 even the amount of oxygen which enters and leaves the capillaries 

 is such that the work involved in its exchange and transport is 

 a minimum. In short, oxygen transport is the main object of the 

 circulation, and it seems that through all the trials and errors of 



* Cf. Cecil D. Murray, The physiological principle of minimal work, in the vascular 

 system, and the cost of blood-volume, Proc. Acad. Nat. Sci. xii, pp. 207-214, 1926; 

 The angle of branching of the arteJries, Journ. Gen. Physiol, ix, pp. 835-841, 1926; 

 On the branching-angles of trees, ibid, x, p. 72;'), 1927. 



t By Dr F. H. Pike, quoted by C. D. Murray. 



