At every point the motion of the lamina will be the same as would have occurred in its absence, the pressure of the waves impinging from behind being just what is required to generate the waves in front.
- By the use of the complex variable and its conjugate functions, an attempt can be made to give a mathematical interpretation of problems such as the efflux of water in a jet or of smoke from a chimney, the discharge through a weir, the flow of water through the piers of a bridge, or past the side of a ship, the wind blowing on a sail or aeroplane, or against a wall, or impinging jets of gas or water; cases where a surface of discontinuity is observable, more or less distinct, which separates the running stream from the dead water or air.
(I) Over the jet surface 4'=m, q=Q, u=-e rr,lm= -berslc, ch SZ=cos n0= e>rsle+I, shS2 =i sin ins =tan ds 2n (3) e2 =tan nO, - c dB sin 2,10' For a jet impinging normally on an infinite plane, as in fig.
The motion of a jet impinging on an infinite barrier is obtained by putting j = a, j' = a'; duplicated on the other side of the barrier, the motion reversed will represent the direct collision of two jets of unequal breadth and equal velocity.
The impact will accordingly result in all the molecules being set into motion, and by the time that the masses have ceased impinging on one another the molecules of which they are composed will be performing oscillations about their positions of equilibrium.
Each impinging molecule exerts an impulsive pressure equal to mu on the boundary before the component of velocity of its centre of gravity normal to the boundary is reduced to zero.
This want of proportionality will have a periodicity, that of the impinging waves, and so will produce vibrations just as does the variation of pressure in the case last investigated.
This will become zero if V 1 is 2V 2, that is, if the linear velocity of the cupcentres is one-half that of the jet of water impinging upon them.
The old organism is more stable and responds in obvious ways to direct assaults from without; the young organism is at once less stable and more profoundly modified by environmental change, replying in terms less easy to predict from knowledge of the nature and amount of the impinging agency.