6 Dr. Young’s Lecture on the Functions 
which was one ninetieth part of an inch only. It is true, that 
Haller is disposed to question the accuracy of this observa- 
tion, and to attribute a much greater velocity to the blood 
flowing through the capillary vessels, but he did not attempt 
either to measure the velocity, or to determine it by calcula- 
tion : nor is this the only instance in which Haller has been 
led to reason erroneously, from a want of mathematical know- 
ledge : he may, however, have observed the particles of blood 
moving in the axis of a vessel with a velocity much exceed- 
ing the mean velocity of its whole contents. If we calculate 
upon these foundations, from the formula which I have already 
laid before the Society, it will appear that the resistance which 
the friction of the arteries would occasion, if water circulated 
in them instead of blood, with an equal velocity, must amount 
to a force equivalent to the pressure of a column of fifteen 
inches and a half : to this we may add about a fourth for the 
resistance of the capillary veins, and we may estimate the 
whole friction for water, at twenty inches. The only consi- 
derable part of this force is derived from the term 2 y^~r in 
the value of f: this term increases for each successive seg- 
ment in the ratio 1 : 1.49425 = 1 : n, and the sum of the 
series is to the first term, as n ~~- to 1. It appears also, that 
a very small portion only of the resistance is created in the 
larger vessels : thus, as far as the twentieth division, at the 
distance of an inch and a quarter only from the extreme capil- 
lary arteries, the pressure of a column of one twentieth of an 
inch only is required for overcoming the whole friction, and 
at the twenty fifth division, where the artery does not much 
exceed the diameter of a human hair, the height to which the 
