ANATOMICAL AND PHYSICAL DATA 83 



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 or mechanical phenomena of the circulation. 

 Others are essentially bound up with the properties of living tissues ; 

 and these may be classified as the vital or physiological phenomena of 

 the circulation. The 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. 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 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 thejside of the vessel at a vertical depth h below 

 the surface will be v= *Jtgh, where g is the acceleration produced by 

 gravity.* In other words, the velocity is -that which the water would 

 have acquired in falling in vacua through the distance A. 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 

 ra 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 w 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 = j2gh. 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 over- 

 coming 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 uni- 

 form 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 

 this stationary layer rub on it, so to speak, and are retarded, although 

 not stopped altogether. The next layer rubs on the comparatively 

 slowly moving particles outside it, and is also delayed, although not 

 so much as that in contact with the immovable layer on the walls of 



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

 (g = 32 feet). 



