98 THE MECHANISM OF THE CIRCULATION. 



very long in comparison with the diameter of the tube. Thus, according to 

 Moens, the velocity of the wave varies inversely as the square root of the 

 diameter of the tube and the density of the fluid, and directly as the square 

 root of the thickness and elastic coefficient of the wall. 



As a wave travels down an elastic tube it is altered in form, owing 

 to the viscosity of the fluid. Thus it becomes smaller, less steep, and 

 more drawn out the further it travels from its source. 



If water be rhythmically pumped into an elastic tube, a positive 

 wave starts with each input and travels through the tube ; and similarly, 

 with each cessation of the input, there starts a negative wave. If the 

 tube be sufficiently long, these waves are entirely spent ; but if the tube 

 be short, the waves may be reflected and run to and fro several times. 

 Thus there may arise 



1. The primary positive or input wave ; 



2. The first centripetal reflected wave ; 



3. The second centrifugal reflected wave ; 



4. The second centripetal reflected wave ; 

 and so on until the input wave is entirely spent. 



Similarly, on the cessation of input there may arise 



1. The primary negative wave ; 



2. The first centripetal reflected wave ; 



3. The first centrifugal reflected wave ; 

 and so on until the wave is spent. 



If the end of the elastic tube be shut, the wave is completely re- 

 flected, and without change of sign. If the end be fully open, the wave 

 is completely reflected with change of sign. 



In the case of a wave travelling up and down a tube, one end of 

 which is open and the other shut, the change of sign takes place at the 

 open end only. If one end of a tube be partly open and partly closed, 

 then the sign of the wave when reflected will be partly changed and 

 partly unchanged. Thus reflected waves of opposite sign arise, and 

 these, according to their comparative size, may more or less interfere 

 with one another. It follows that with a certain size of opening 

 the reflected waves will completely interfere, and thus they will 

 disappear. 



It has been experimentally determined by v. Kries that if an elastic 

 tube be of sufficient width, and no reflection of the wave takes place, 

 the seat of maximal and minimal velocity in the tube will be found to 

 be the same as the seat of maximal and minimal pressure. Thus, if the 

 pressure be found to increase in an artery, where the velocity decreases, 

 a significant proof of reflection is obtained. 



In addition to the waves which travel through the fluid in an elastic 

 tube, the wall of the tube is itself thrown into vibration with each throb 

 of the pump, just as a rubber band vibrates when it is suddenly and 

 momentarily thrown into tension. These vibrations, according to v. 

 Kries, are of such frequency as to be extraordinarily difficult to observe, 

 and they cannot be considered to have any effect on the main features 

 of the pulse curve. 



Thus far we have considered the simplest possible conditions, the 

 production of waves in an elastic tube of uniform bore and of uniform 

 structure. In the circulatory system the conditions are, on the other 

 hand, of considerable complexity. The arteries continually change, their 

 walls become more or less elastic, the lumen wider or narrower, and finally 



