236 PHYSIOLOGY CHAP. 



current, unites again into a single outflow tube in which the 

 sectional area is once more reduced, we obtain a system of canals 

 which schematically represents the circulatory system. Under 

 these complex conditions the same fundamental laws hold good 

 that we have been discussing for the preceding simple cases. 



The rate of flow to the different parts of the system is inversely 

 proportional* to the sum of the cross-sections, i.e. to the width of 

 the current bed. Since the same amount of fluid enters the 

 system by the inflow tube, and leaves the system by the outflow 

 tube, in the time-unit, so the same amount of fluid must pass 

 through every section of the system in the same time, with a 

 correspondingly greater velocity where the sectional area is 

 narrower, with less velocity where it is wider. 



The pressure at every point of the system must be proportional 

 to the sum of the resistances which the fluid has to overcome 

 before reaching the outflow. Since the section of each tube 

 decreases as the system branches, while the total sectional area 

 increases, so the sum of the resistances must increase with the 

 former and decrease with the latter. Which of these two condi- 

 tions has the preponderating influence ? Experience shows that 

 when the branching of the system goes as far as the production of 

 capillary tubes, the sum of the resistances increases in these to 

 such an extent that it cannot be compensated by the widening, 

 however great, of the bed of the stream. In a system of capillary 

 vessels the velocity of outflow is, according to Poiseuille, propor- 

 tional, not, as in tubes of larger diameter, to the square, but to the 

 fourth power of the radius. 



II. All these laws, in so far as they concern pressure, velocity, 

 and outflow, are perfectly applicable to the vascular blood system, 

 since this consists of canals which ramify until they are reduced 

 into a capillary network with a vast extension of the bed of the 

 current, and then gradually form into canals again, each of which 

 has individually a wider cross-section, but which as a whole make 

 up a narrower channel. Setting aside for the moment the differ- 

 ences between the circulatory system and the system of conducting 

 tubes which we have just been considering, it is possible to formu- 

 late three general laws which are at the base of the circulatory 

 phenomena. 



(a) Laws of Current. Under normal circulatory conditions, 

 the amount of blood that flows out of the heart through the arteries 

 in the time-unit is exactly equal to that which flows into the 

 heart by the veins ; the amount of blood which enters or leaves 

 the right or left heart is exactly equal to that which leaves or 

 enters the left or right heart ; in more general terms, the amount 

 of blood which passes through any total cross-section of the circu- 

 latory system is exactly equal to that which passes in the same 

 time through any other total cross-section of the same system. 



