1899.] on the Motion of a Ptrfeet Liquid. 59 



does not permit me to describe, but which gives a slow and steady 

 motion that it would be impossible to improve upon in actual con- 

 ditions of practice, or even, 1 am inclined to think, by any experimental 

 method. Instead of using air to make this flow clear, we now allow 

 colour to stie.im behind the plate, and you will see (Fig 14, Plato II.) 

 that the water still refuses to flow round to the back, and spreads on 

 cither side. We have so slow a velocity as not to induce vortex 

 motion, but the inertia of the particles which strike the flat plato 

 causes them to be deflected to either side, exactly as tennis balls in 

 striking against a wall obliquely. The sheet of water is so thick, 

 that is to say, the parallel glass plates are so far apart, that they do 

 not enable the viscosity of the water to act as a sufficient drag to 

 prevent this taking place. 



To make the action of the water in front of the plate more visible, 

 a different coloured liquid is allowed to enter from orifices in a small 

 pipe placed across the slide in the thick sheet. You will now si e 

 that the general motion is steady enough to give a very clear idea of 

 the deflecting action of the plate, and streaks of colour set themselves 

 in such a way as to indicate the behaviour of the individual particles. 

 This effect is practically what is called " discontinuity," for, although 

 perfectly discontinuous motion can only take place when there is no 

 viscosity, the effect of the general flow upon the nearly quiescent 

 mass behind the plate is very slight. 



If we send the flow in impulses, we produce vortex motion at the 

 edge, due to viscosity, as shown in Fig. 15. This takes place in the 

 thick sheet directly the velocity is sufficiently increased, though only 

 at the edges of the plate, the motion being otherwise the same. 



Mathematicians, however, predicted with absolute certainty, that 

 with stream-line motion the water should flow round and meet at the 

 back, a state of things that, however slow we make the motion in the 

 present case, does not occur owing to the effect of inertia. They have 

 drawn with equal confidence the lines along which this should take 

 place. We could either effect this result with the experiment you 

 have just seen, by using a much more viscous liquid, such as treacle, 

 or, what comes to the same thing, bringing the two sheets of glass 

 nearly close together ; and the flow which you are now witnessing 

 (Fig. 16, Plate II.) shows the result of doing this. The colour bands 

 in front of the plate no longer mix at all with the general body of 

 flow, or are unsteady, as was the case in the last experiment, but flow 

 round the plate and flow so steadily, that, unless we jerk the flow of 

 the colour bands, it is impossible to tell in which direction they are 

 actually moving. 



A still more extraordinary case is that of a plate at an angle of 

 45 degrees, the central line no longer striking the plate at the centre, 

 but at a certain point whi^n, together with the actual curves of flow, 

 has been calculated and plotted by Professor Lamb. The calcula- 

 tions being made for an infinite fluid, we require the artificial border 

 to be prepared, corresponding to the different stream-lines, and when 



