MECHANICS OF THE CIRCULATION IN THE VESSELS n 9 



as we have seen, exists in a moving liquid in two forms, potential and 

 kinetic, the former being measured by the lateral pressure, the latter 

 varying directly as the square of the velocity. Whenever the velocity, 

 and therefore the kinetic energy, of a given mass of the blood is 

 diminished without a corresponding increase in the potential energy, 

 some of the total stock of energy must have been used up to overcome 

 resistance (p. 84). 



In a uniform, rigid, horizontal tube, as has been already remarked, 

 the velocity (and consequently the kinetic energy) is the same at 

 every cross-section of the tube, while the potential energy, re presented 

 by the lateral pressure, diminishes regularly along the tube. When 

 the calibre of the tube varies, it is different. Suppose, for instance, 

 that the liquid passes from a narrower to a wider part, the velocity 

 must diminish in the latter. The kinetic energy of visible motion 

 which has disappeared must have left something in its room. Here 

 there are three possibilities: (i) The kinetic energy that has disappeared 

 may be just enough to overcome the extra friction in the wider part of 

 the tube due to eddies and consequent change of direction of the lines 

 of flow ; in this case the potential energy of a given mass of the liquid 

 will be the same at the beginning of the wider part as in the narrower 

 part. The lost kinetic energy will have been transformed into heat. 

 (2) The kinetic energy which has disappeared may be greater than is 

 enough to overcome the extra resistance ; a portion of it must, therefore, 

 have gone to increase the potential energy, and the lateral pressure will 

 be greater in the wide than in the narrow part. (3) The lost kinetic 

 energy may be less than enough to overcome the extra resistance; in 

 this case both the lateral pressure and the velocity will be less in the 

 wide than in the narrow part. It has been experimentally shown that 

 when a narrow portion of a tube is succeeded by a considerably wider 

 portion, and this again by a narrow part, case (2) holds; and the liquid 

 may, under these conditions, actually flow from a place of lower to a 

 place of higher lateral pressure. 



In the vascular system the conditions are not the same. The 

 widening of the bed which takes place as we proceed in the direction 

 of the arterial current is not due to the widening of a single trunk, 

 but to the branching of the channel into smaller and smaller tubes. 

 In the larger arteries the increase of resistance is so gradual that both 

 the potential and the kinetic energy diminish only slowly, and the 

 lateral pressure and velocity are not much less in the femoral artery 

 than in the aorta or carotid. But in the arterioles the friction 

 increases so greatly that although the velocity, and therefore the 

 kinetic energy, in the capillary region is much less than in the 

 arteries, the amount of kinetic energy lost is not upon the whole 

 equivalent to the energy consumed in overcoming the extra resis- 

 tance ; the potential energy of the blood is also drawn upon, and the 

 lateral pressure falls sharply in the capillary region, as well as the 

 velocity. Where the capillaries open into the veins, the lateral pres- 

 sure again sinks abruptly, while the velocity begins to increase, till in 

 the largest veins it is probably about half as great as in the aorta. 

 Where does the extra kinetic energy of the blood in the veins come 

 from ? To say that the vascular channel again contracts as the 

 blood passes from the capillaries into the veins, and that, since the 



