952 



ON THE FORM AND BRANCHING 



[CH. 



or width, we may safely take it that the question is one of degree ; 

 and that the factor of width will become the more important of 

 the two wherever artery and branch are markedly unequal in size. 

 In other words, it would seem that for small branches a large angle 

 of bifurcation, and for large branches a small one, is always the 

 better. Roux has laid down certain rules in regard to the branching 

 of arteries, which cojrespond with the general conclusions which we 

 have just arrived at. The most important of these are as follows: 

 (1) If an artery bifurcates 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 the phenomenon. 

 Let AB be an artery, from which a branch has to be given off so 



as to reach P, and let ACP, ADP, 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, 

 PDE, Xi, X2, etc.: and the distances 

 CD', DE', by which each branch exceeds 

 the next in length, we shall call li,l2, 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 considerably increase the whole distance 

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

 which will strike the balance of advantage. 



Fig. 456. 



