XV] AND OF SEA URCHINS 665 



to elevate, rather than to depress the shell. Mr Darling tells me 

 that these forms "are nearly identical in shape with globules I 

 have frequently obtained, in which, on standing, bubbles of gas 

 rose to the summit and pressed the skin upwards, without being 

 able to escape." The same condition may be at work in the 

 sea-urchin; but a similar tendency would also be manifested by 

 the presence in the upper part of the shell of any accuniulation 

 of substance lighter 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, on the same principle 

 and by help of the same equations as those we have used, for 

 instance, 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 = p,, + T{l/r+l/r'). 



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 cyhndrical vein or artery, this formula 

 becomes simplified 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 composed. 



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 



