668 



ON THE FORM AND BRANCHING 



[CH. 



elusions which we have just arrived at. The most important of 

 these are as follows: (1) If an artery bifurcate into two equal 

 branches, these branches come off at equal angles to the main 

 stem. (2) If one of the two branches be smaller than the other, 

 then the main branch, or continuation of the original artery, 

 makes with the latter a smaller angle than does the smaller or 

 '"lateral" branch. And (3) all branches which are so small that 

 they scarcely seem to weaken or diminish the main stem come off 

 from it at a large angle, from about 70° to 90°. 



We may follow Hess in a further investigation of this pheno- 

 menon. Let AB be an artery, from which a branch has to be 

 given off so as to reach P, and let ACP, ABP, etc., be alternative 



courses which the branch may follow : 

 CD, DE, etc., in the diagram, being 

 equal distances (= I) along AB. Let 

 us call the angles PCD, PCE, x^, x^, 

 etc. : and the distances CD', DE', by 

 which each branch exceeds the next in 

 length, we shall call Z^, Zg, etc. Now it 

 is evident that, of the courses shewn, 

 ACP is the shortest which the blood 

 can take, but it is also that by which 

 its transit through the narrow branch 

 is the longest. We may reduce its 

 transit through the narrow branch more 

 and more, till we come to CGP, or 

 rather to a point where the branch 

 comes off at right angles to the main 

 stem; but in so doing we very con- 

 siderably increase the whole distance 

 travelled. We may take it that there will be some intermediate 

 point which will strike the balance of advantage. 



Now it is easy to shew that if, in Fig. 330, the route ADP and 

 AEP (two contiguous routes) be equally favourable, then any 

 other route on either side of these, such as ACP or AFP, must 

 be less favourable than either. Let ADP and AEP, then, be 

 equally favourable; that is to say, let the loss of energy which 

 the blood suffers in its passage along these two routes be equal. 



Fig. 330. 



