204 W J MCGEE — OUTLINES OF HYDROLOGY 



wliicli would seem to engender the tindnlatory motion of the water itself 

 and the saltatory motion of its load. 



INTERNAL MOVEMENT OF RUNNING WATER 



When viewed broadly in the light of planetary and cosmic movements, 

 the motions of the saltatory particles exhibit instructive analogies, and 

 the analogies extend to the concomitant motions of the water particles : 

 The saltatory particle, whether small or large (neglecting the relatively 

 unimportant ease in which rotatory momentum predominates), visibly 

 moves in a downwardly curved path, and its movement is evidently the 

 variable resultant of factors which may be resolved into (1) the primary 

 impulse, or inertia, (3) the resistance of friction, impact, etcetera, and 

 (3) the direct gravitative pull with its inherent acceleration, and (4) the 

 consequent friction ; and, considered either with respect to general type of 

 curve or to components involved, the path apparently conforms to those 

 of projectiles, meteorites after entering the atmosphere, and comets on 

 approaching the sun; which paths (trajectories or orbits) approach the 

 parabolic form — that is, the resultants vary as the first and second powers 

 of their components save in so far as friction and other secondary factors 

 interfere. These approximately parabolic paths may be described as 

 paraboloid, despite the prior geometric use of the same term in a special 

 sense (etymologically irregular, except as connoting the collective curves 

 of the solid generated by rotation of the parabola). Manifestly if the 

 path of the single saltatory particle is paraboloid, the collective or mean 

 path (or sum of paths) of a series of particles must be similar, since each 

 impact, whether coUisional or frictional, merely enters into one or the 

 other factor of the equation and introduces no new order of motion. It 

 follows that all contiguous particles either just ready to enter or just 

 after coming to rest from the paraboloid trajectory must tend to arrange 

 themselves ceteris paribus in paraboloid forms, and the illustration of 

 this fundamental law of saltatory movement (and demonstration of the 

 analysis) appears in the prevailing paraboloid curves of land forms 

 shaped by riinning water. 



Now it also seems clear on scrutinizing the motion of saltatory particles 

 of variable sizes in running water that the movement of the water does 

 not interfere with the paraboloid paths, but, on the other hand, conforms 

 in such a way that the paths of all particles from the largest to the 

 smallest visible fall into a beautiful harmony. This concordance inevi- 

 tably suggests that the water particles themselves move in paraboloid 

 trajectories, each the resultant of inertia, resistance, and gravity, in which 

 case, too, it is manifest that the movements of the sum of particles must 



