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 1O1 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. Fof, 

 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 10-1, 

 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 



