948 ON THE FORM AND BRANCHING [ch. 



tendency would also be manifested by the presence in the upper 

 part of the shell of any accumulation of substance Hghter than water, 

 such as is actually present in the masses of fatty, oily eggs. 



On the form and branching of blood-vessels 



Passing to what may seem a very different subject, we may 

 investigate a number of interesting points in connection with the 

 form and structure of the blood-vessels, and we shall find ourselves 

 helped, at least in the outset, by the same equations as those we 

 have used in studying the egg-shell. 



We know that the fluid pressure (P) within the vessel is balanced 

 by (1) the tension (T) of the wall, divided by the radius of curvature, 

 and (2) the external pressure (pn), normal to the wall: according to 

 our formula 



P = y„+r(l/r+l//). 



If. we neglect the external pressure, that is to say any support 

 which may be given to the vessel by the surrounding tissues, and 

 if we deal only with a cylindrical vein or artery, this formula 

 becomes simpUfied to the form P = T/R. That is to say, under 

 constant pressure, the tension varies as the radius. But the tension, 

 per unit area of the vessel, depends upon the thickness of the wall, 

 that is to say on the amount of membranous and especially of 

 muscular tissue of which it is Qomposed. Therefore, so long as the 

 pressure is constant, the thickness of the wall should vary as the 

 radius, or as the diameter, of the blood-vessel. 



But it is not the case that the pressure is constant, for it 

 gradually falls off, by loss through friction, as we pass from the 

 large arteries to the small; and accordingly we find that while, for 

 a time, the cross-sections of the larger and smaller vessels are 

 symmetrical figures, with the wall-thickness proportional to the size 

 of the tube, this proportion is gradually lost, and the walls of the 

 small arteries, and still more of the capillaries, become exceedingly 

 thin, and more so than in strict proportion to the narrowing of the 

 tube. 



In the case of the heart we have, within each of its cavities, a 

 pressure which, at any given moment, is constant over the whole wall- 



I 



