THE CIRCULATION OF THE BLOOD AND LYMPH 75 



.The problems of the circulation are partly physical, partly 

 vital. Some of the phenomena observed in the blood-stream 

 of a living animal can be reproduced on an artificial model ; 

 and they may justly be called the physical phenomena of the 

 circulation. Others are essentially bound up with the pro- 

 perties of living tissues ; and these may be classified as the 

 vital or physiological phenomena of the circulation. The dis- 

 tinction, although by no means sharp and absolute, is a con- 

 venient one at least, for purposes of description ; and as such 

 we shall use it. But it must not be forgotten that the physio- 

 logical factors play into the sphere of the physical, and the 

 physical factors modify the physiological. Considered in its 

 physical relations, the circulation of the blood is the flow of a 

 liquid along a system of elastic tubes, the bloodvessels, under 

 the influence of an intermittent pressure produced by the action 

 of a central pump, the heart. But the branch of dynamics 

 which treats of the movement of liquids, or hydrodynamics, is 

 one of the most difficult parts of physics, and, in spite of the 

 labours of many eminent men, is as yet so little advanced that 

 even in the physical portion of our subject we are forced to rely 

 chiefly on empirical methods. It would, therefore, not be pro- 

 fitable to enter here into mathematical theory, but it may be 

 well to recall to the mind of the reader one or two of the simplest 

 dat& connected with the flow of liquids through tubes : 



Torricelli's Theorem. Suppose a vessel filled with water, the level 

 of which is kept constant ; the velocity with which the water will 

 escape from a hole in the side of the vessel at a vertical depth h 

 below the surface will be v= \/2gh, where g is the acceleration pro- 

 duced by gravity.* In other words, the velocity is that which the 

 water would have acquired in falling in vacua through the distance h. 

 This formula was deduced experimentally by Torricelli, and holds 

 only when the resistance to the outflow is so small as to be negligible. 

 The reason of this restriction will be easily seen, if we consider that 

 when a mass m of water has flowed out of the opening, and an equal 

 mass m has flowed in at the top to maintain the old level, everything 

 is the same as before, except that energy of position equal to that 

 possessed by a mass m at a height h has disappeared. If this has all 

 been changed into kinetic energy E, in the form of visible motion 

 of the escaping water, then E = ^mv 2 = mgh, i.e., v= */2gh. If, how- 

 ever, there has been any sensible resistance to the outflow, any 

 sensible friction, some of the potential energy (energy of position), 

 will have been spent in overcoming this, and will have ultimately 

 been transformed into the kinetic energy of molecular motion, or heat. 



Flow of a Liquid through Tubes. Next let a horizontal tube of 

 uniform cross-section be fitted on to the orifice. The velocity of 

 outflow will be diminished, for resistances now come into play. 

 When the liquid flowing through a tube wets it, the layer next the 

 wall of the tube is prevented by adhesion from moving on. The 



* I.e., the amount added per second to the velocity of a falling body 

 (g = 32 feet). , 



