THE PULSE. 97 



of impact, the rate with which the impact travels from truck to truck 

 will be quite independent of the constant velocity of the train, while 

 the impact will momentarily increase the velocity of each truck .and 

 translate it forwards. That a wave must be considered mainly as the 

 propagation of a change of form, is shown by the consideration of the 

 following case. Suppose a long trough to be filled with water, and 

 the water be pumped rhythmically out of it, then the water, with each 

 stroke of the pump, will move towards the exit, but a negative wave at 

 the same time, and in a contrary direction, will travel along the trough. 

 The negative wave will slightly retard the velocity of flow towards the 

 exit, but in itself it is a propagation of a change of form, which is 

 entirely independent of the velocity of the fluid. 



From mathematical consideration of a wave in an artery, where the blood 

 and the vessel wall are held to be constants, the motion of the blood is assumed 

 to be irrotational, and, to avoid the complication of gravity, the portion of 

 the artery is supposed to be horizontal, Nicolls draws the following conclu- 

 sions : 



1. That all particles of blood which lie on any cross-section continue to 

 lie on the same cross-section during the passage of a wave ; that is to say, each 

 cross-section moves forward as a whole, and thus each particle, when the 

 wave has passed, is left in advance of its original position. 



2. The distance to which each particle is advanced is equal to the total 

 increase in volume, divided by the area of the cross-section. Thus the passage 

 of a positive wave slightly increases the velocity of the blood. 



3. That the square of the velocity of the wave varies inversely as the 

 density of the fluid and the radius of the tube. 



4. That the less elastic the vessel the greater the velocity. 



5. That the amplitude of the wave varies directly as the radius. In 

 vessels of very small diameter the pulse becomes imperceptible, since, for a 

 given wave length, the artery must have a certain diameter before pulsation be 

 possible. 



6. That the effect of the viscosity of the blood on the pulse is too small 

 to be of any importance. 



7. That normally the pulse wave is mainly the effect of lateral vibration, 

 but in conditions where the range of pressure is very great, as in aortic 

 regurgitation, longitudinal vibrations, which become visible as capillary pulsa- 

 tions, may occur. 



Some of these deductions are in close agreement with the experimental 

 determination of Moens. 



The wave of expansion, according to Moens, 1 travels through such a tube 

 as an artery with a constant velocity, which is expressed by the following 

 formula : 



where v = the velocity per second. 



g = the acceleration due to gravity. 

 e = the elastic coefficient of the wall. 

 a = the thickness of the wall. 

 d = the diameter of the tube. 

 D = the density of the fluid. 

 k = a constant. 



It is postulated that the thickness of the wall is small, and the wave length 



1 "Die Pulscurve," Leyden, 1878, S. 87, cf. Grunmach, Arch. f. Physiol., Leipzig, 

 1888, S. 129 ; v. Kries, "Stud, zur Pulslehre," Freiburg, 1892, S. 7. 

 VOL. ii. 7 



