THE CIRCULATION OF THE BLOOD AND LYMPH 71 



distinction, although by no means sharp and absolute, is a 

 convenient one at least, for purposes of description; and as 

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

 physiological factors play into the sphere of the physical, 

 and the physical factors modify the physiological. Con- 

 sidered 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 profitable 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 

 data 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 vacuo 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 negligable. 

 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 = J;/z# 2 = #//#, i.e. t v= */2gh. If, 

 however, 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 particles next 



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

 Gr=32 feet). 



