1899.] on the Motion of a Perfect Liquid. 55 



the mathematical conception of a perfect liquid, although the mathema- 

 tician has in his mind the idea of something of the nature of a jelly 

 consisting of such small particles, rather than of the separate parti- 

 cles themselves. The solution of the problem of the grouping of the 

 little particles, upon which so much depends, and which may have at 

 first seemed so simple a matter, really represents, though as yet applied 

 to only a few simple cases, one of the most remarkable instances of 

 the power of higher mathematics, and one of the greatest achieve- 

 ments of mathematical genius. 



You will be as glad as I am that it is not my business to-night to 

 explain the mathematical processes by which the behaviour of a 

 perfect liquid has been to a certain extent investigated. You will 

 also understand why such models as we could actually make, or any 

 analogy with the things with which we are familiar, would not help 

 us very much in obtaining a mental picture of the behaviour of a 

 perfect liquid. If, for instance, we try to make use of the idea of 

 drilled soldiers, and move the lines with that object in view, we tee 

 that instead of the ordinary methods of drill, the middle rank soon 

 gains on the others, and enters again the parallel portion of the 

 channel in a very different relative position to the opposite lines, 

 although the stream-lines would all have the same actual velocity 

 when once again in the parallel poition. Since, then, we cannot use 

 models or any simple analogy with familiar things, or follow — at any 

 rate this evening — the mathematical methods of dealing with the 

 problem, what way of understanding the subject is left to us ? 



If we take two sheets of glass, and bring them nearly close 

 together, leaving only a space the thickness of a thin card or piece of 

 paper, and then by suitable means cause liquid to flow under pressure 

 between them, the very property of viscosity, which as before noted, 

 is the cause of the eddying motion in large bodies of water, in the 

 present case greatly limits the freedom of motion of the fluid between 

 the two sheets of glass, and thus prevents not only eddying or whirl- 

 ing motion, but also counteracts the effect of inertia. Every particle 

 is then compelled by the pressure behind and around it to move 

 onwards without whirling motion, following the path which corre- 

 sponds exactly with the stream-lines in a perfect liquid. 



If we now, by a suitable means, allow distinguishing bands of 

 coloured liquid to take part in the general flow, we are able to imitate 

 exactly the conditions represented in the diagrams (Figs. 4 and 5). 

 You are now looking at a projection on the screen (Fig. 8, Plate I.) 

 of liquid, which, in flowing through the gradually enlarging and con- 

 tracting channel, is obeying the conditions I have described. Such is 

 the steadiness of its motion, that it is scarcely possible to believe at 

 first that the figure does not consist of fixed bands of colour painted in 

 perfectly smooth curves. By varying the flow of the coloured liquid 

 however, you will realise at once tbat the painting is done by nature 

 and not by the hand of a human artist. 



Now you will notice that the bands widen out as they approach the 



