204 



SCIENCE. 



[Vol. XVIII. No. 453 



ments opposes sudden change of direction of motion at the 

 edge of the oriflce, and the convergence continues for a dis- 

 tance of about half the diameter of the orifice beyond it. . . . 

 When the orifice is a sharp-edged orifice in a plain sur- 

 face, . . . the section of the jet is very nearly five eights of 

 the orifice. . . . Hence the actual discharge when contrac- 

 tion occurs is . . . 0.62." " The CO efficient of contraction 

 is directly determined by measuring the dimensions of the 

 jet. For this purpose fixed screws of fine pitch [Fig. 21] are 

 convenient. These are set to touch the jet, and the distance 

 between them can be measured at leisure." Without stop- 

 ping to inquire what reason there may be, either in theory 

 or from observation, for the assumption that the molecules, 

 or particles of water, form themselves into filaments, and 

 that the jet is formed from tliese filaments, it is obvious that 

 the assumption is not necessary to account for the phenome- 

 non, and that the diminution of the jet is the necessary result 

 of well-known mechanical laws operating on each molecule 

 separately. 



Each molecule put in motion by the outflow of the jet 

 moves from its position in the vessel towards the orifice: the 

 motion is constantly accelerated until it reaches the orifice, 

 and its velocity is determined by the pressure to which the 

 molecule is subjected and the resistance it encounters. The 

 molecules on the same horizontal plane as the orifice, and 



Fig. 21 (modified;. 



x)n lines which lead through it, move on these lines directly 

 outwards through the oriflce; but the molecules above and 

 below and on each side of the orifice move towards it at an 

 angle to the direction of the outflow, and a part of the kinet- 

 ic energy of the molecules moving directing in the line of 

 outflow is necessarily consumed in changing the direction 

 of the molecules from above, below, and from the sides, which 

 are moving at an angle to this direction. In other words, 

 it is the ordinary simple problem of moving bodies coming 

 into contact at an angle to their lines of motion, and the 

 direction of motion and kinetic energy are the resultant of 

 the forces operating at the impact. 



This can be illustrated by reproducing Fig. 21, omitting 

 the set-screws, and substituting for the filaments a few mole- 

 cules with lines showing the direction of their motion. The 

 molecules a, 6, and c move on the lines ax, bx, and ex, 

 while the molecules d, e, /, move on the lines dx, ex, and 

 fx, and the molecules g, h, i, move on the lines gx, hx, and 

 ix, and so with all the others. The amount of kinetic energy 

 consumed in changing the direction of the molecules moving 

 to the orifice at an angle to the direction of the outflow, de- 

 termines the diminution of area of the jet as compared with 

 the area of the orifice, and determines also the co-efiicient of 

 -discharge. 



When the point of maximum contraction is reached, the 



molecules, under another well-known law of mechanics, re- 

 bound from each other, and at about the distance from the 

 oriflce to the point of maximum contraction, the area of 

 the jet is enlarged so that it equals the area of the orifice, 

 and farther on becomes much larger. The amount of con- 

 traction of the jet is necessarily variable, depending as it does 

 on the direction of the molecules when they reach the orifice. 

 If the vessel is narrow, or if, in Fig. 21, an obstruction be 

 placed in the vessel in front of the orifice, so as to diminish 

 the relative number of molecules which can move on the 

 lines ax, hx, and ex, as compared with those which move at 

 an angle to the line of outflow, the area of the jet and co- 

 etfieient of discharge will be measurably diminished. 



If the orifice is bell-mouthed, or otherwise so constructed 

 that the kinetic energy required to change the direction of all 

 the molecules is exerted before any of them reach the orifice, 

 then there is no contraction of the jet. and the co-efficient of 

 discharge rises from about 0.62 to about 0.96 under the sarne 

 conditions in other respects. 



But it is in determining the depth at which the maximum 

 velocity is found in a fiowing stream that the molecular mo- 

 tion becomes of the greatest importance. We again have 

 recourse to the "Encyclopedia Britannica" for a description 

 of the phenomenon, and the existing theories in respect to 

 it: '■ In the next place, all the best observations show that 

 the maximum velocity is to be found, not at the free sur- 

 face of the stream, but some distance below it. In the ex- 

 periments on the Mississippi the vertical velocity curve in 

 calm weather was found to agree fairly well with a parabola, 

 the greatest velocity being at three-tenths of the depth of the 

 stream from the surface. With a wind blowing down- 

 stream the surface velocity is increased and the axis of the 

 parabola approaches the surface. On the contrary, with the 

 wind blowing up-stream the surface velocity is diminished, 

 and the axis of the parabola is lowered, sometimes to half 

 the depth of the stream. The American observers drew from 

 their observations the conclusion that there was an energetic 

 retarding action at the surface of a stream like that due to 

 the bottom and sides. If there were such a retarding action, 

 the position of the filament of maximum velocity below the 

 surface would be explained. It is not difficult to understand 

 that a wind acting on surface ripples should accelerate or 

 retard the surface motion of the stream, and the Mississippi 

 results may be accepted, so far as showing that the surface 

 velocity of a stream is variable when the mean velocity is 

 constant. Hence, observations on surface velocity by floats 

 and otherwise should only be made in very calm weather. 

 But it is very difficult to suppose that in still air there is a 

 resistance at the free surface of the stream at all analogous 

 to that at the sides and bottom. Further, in very careful 

 experiments, Boileau found the maximum velocity, though 

 raised a little above its velocity fcr calm weather, still at 

 considerable distance below the surface velocity, even when 

 the wind was blowing down-stream with a velocity greater 

 than that of the stream, and when the action of the air must 

 have been an accelerating and not a retarding action. Pro- 

 fessor James Thomson has given a much more probable ex- 

 planation of the diminution of the velocity at and near the 

 free surface. He points out that portions of water, with a 

 diminished velocity by retardation from the sides or bottom, 

 are thrown off in eddying masses and mingle with the rest 

 of the stream. These eddying masses modify the velocity in 

 all parts of the stream, but have their greatest influence at 

 the free surface. Reaching the free surface, they spread 

 out and remain there, mingling with the water at that level. 



