VELOCITY AND PRESSURE OF BLOOD-FLOW. 489 



veins may be expressed, therefore, by a curve such as is shown 

 in Fig. 191. 



Explanation of the Variations in Velocity. The general rela- 

 tionship between the velocities in the different parts of the vascular 

 system is explained by the difference in the width of the bed in 

 which the blood flows. In the systemic circulation the main stem, 

 the aorta, branches into arteries which, taken individually, are smaller 

 and smaller as we approach the capillaries. But each time that 

 an artery branches the sum of the areas of the two branches is 

 greater than that of the main stem. The arterial system may be 

 compared, in fact, to a tree, the sum of the cross-areas of all the 

 twigs is greater than that of the main trunk. It follows, there- 

 fore, that the blood as it passes to the capillaries flows in a bed 

 or is distributed in a bed which becomes wider and wider, and as it 

 returns to the heart in the veins it is collected into a bed that be- 

 comes smaller as we approach the heart. Vierordt estimates that 

 the combined calibers of all the capillaries in the systemic circula- 

 tion would make a tube with a cross-area about 800 times as large as 

 the aorta. If the circulation is proceeding uniformly it follows 

 that for any given unit of time the same volume of blood must 

 pass through any given cross-section of the system, that is, at 

 a given point in the aorta or vena cava as much blood must flow 

 by in a second as passes through the capillary region and that 

 consequently where the cross-section or bed is widest the velocity 

 is correspondingly diminished. If the capillary bed is 800 times 

 that of the aorta, then the velocity in the capillaries is -g^-g- of that 

 in the aorta, say, -g-J-g- of 320 mms. or 0.4 mm. Just as a stream 

 of water flowing under a constant head reaches its greatest velocity 

 where its bed is narrowest and flows more slowly where the bed 

 widens to the dimensions of a pool or lake. 



Variations in Velocity with Changes in the Heart-beat or 

 the Size of the Vessels. While the above statement holds true as 

 an explanation of the general relationship between the velocities in 

 the arteries, veins, and capillaries at any given moment, the absolute 

 velocities in the different parts of the system will, of course, vary 

 whenever any of the conditions acting upon the blood-flow vary. 

 In the large arteries, as has been said, there are extreme fluctua- 

 tions in velocity at each heart beat; but if we consider only the 

 average velocities it may be said that these will vary throughout 

 the system with the force and rate of the heart beat, or with the 

 variations in size of the small arteries and the resulting changes in 

 blood-pressure in the arteries. Marey* gives the two following 

 laws: (1) Whatever increases or diminishes the force with which 

 the blood is driven from the heart toward the periphery will cause 

 the velocity of the blood and the pressure in the arteries to vary in 

 * "La Circulation du Sang/' Paris, 1881, p. 321. 



