218 AREAS OF ARTERIAL TRUNKS AND BRANCHES. 
so vastly, as we proceed from their origin towards their termi¬ 
nation, yet their capacity does not, at least in any considerable 
degree;—that is, the first or main trunk will allow as much 
fluid to pass through it in a certain time, as will the whole of 
the first set of branches into which it divides, or the still more 
numerous subordinate branches into which these diverge. Or, 
to put this fact in another form, if we cut across the main 
trunk, and compare the area , or space included within its 
circular walls, with the sum of the areas of all the branches it 
supplies at a certain distance—say a foot—from the heart, we 
shall find them precisely equal ; and the same will hold good, 
if the comparison be made with the sum of the areas of the 
more numerous but smaller branches at a greater distance from 
the main trunk. It is quite true that, when an artery divides 
into branches, the combined size of these seems to be greater 
than that of the trunk; but this is only because the compa¬ 
rison is made, not between the areas of their circles, but their 
diameters . Thus, an artery of 10T lines in diameter, may 
divide into three branches, two of them having a diameter of 
7 lines, and the third a diameter of 2 lines;—and yet these 
will convey no more blood than the .single trunk. For, 
according to a simple rule in geometry, the areas of circles are 
to each other as the squares of their diameters. The area of 
the trunk is expressed, therefore, by the square of 10T, 
which is almost exactly 102. The area of each of the two 
large branches, in like manner, is expressed by the number 
49, which is the square of 7 ; and that of the smaller one by 
4, the square of 2 ; and the sum of these (49+49+4) is ex¬ 
actly 102, making the combined areas of the branches the same 
as that of the trunk. In like manner, one of the branches of 7 
lines diameter might subdivide into two branches of a little 
less than 5 lines each ; for, as the square of 5 is 25, and twice 
that number is equal to 50, the combined areas of the two 
branches of 5 lines each, exceed by very little the area of the 
trunk of 7 lines.—Hence it results, that the pressure of the 
blood upon the walls of the arteries will be everywhere 
almost exactly the same;—a conclusion which is confirmed 
by experiment. 
248. There are certain differences in the structure and dis¬ 
tribution of the Arteries and Veins, which it is desirable to 
mention. The Arteries receive the blood pressed out from 
