110 THE MOTION OF A PERFECT LIQUID. 



Now, when we know the pressure at every point of a liquid and also 

 the direction in which the particles are moving, together with their 

 velocity at ever}" point, we really know all about its motion, and you 

 will see how important the question of grouping is, and that, in fact, it 

 really constitutes the whole point of m^' lecture to-night. How, then, 

 shall we ascertain which of the two groupings (fig. 4 or 5) is correct, 

 or whether possibly some grouping totalh^ different from either does 

 not represent the real conditions of flow? 



Now, the mod(4 does not help us very far, because there seems to be 

 no means of making the grouping follow any regular law which might 

 agree with fluid motion. In whatever way we improve such a mod(d, 

 we can scarcely hope to imitate by men^ly mechanical means the motion 

 of an actual liquid, for reasons which I will now try to explain. 



In the first place, apart from the particles having no distinguishing 

 characteristics, either when the liquid is opaque or transparent, they 

 are so small and their number so great as to })e almost beyond our 

 powers of comprehension. Let me try, by means of a simple illustra- 

 tion, to give some idea of their munber as arrived at by perfectly well 

 recognized methods of physical computation. Lord Kelvin has used 

 the illustration that, supposing a drop of water Avere magnified to the 

 size of the <^artli, tlu^ ultimate particles would appear to us between the 

 size of cricket balls and footballs. I venture to put the same fact in 

 another way that may perhaps strike you more forcil)ly. This tumbler 

 contains half a pint of water. I now close the top. Suppose that, b}^ 

 means of a fine hole, I allow one and a half millions of millions 

 (1,500,00(),0()0,0( K )) of particles to floAV out per second— that is to say, an 

 exodus equal to about one thousand times the population of the world 

 in each second — the time required to empty the glass would be between 

 (for of course we can only give certain limits) seven million and forty- 

 seven million years. 



In the next place, we have the particles interfering with each other's 

 movements by what we call "viscosity." 



Of course, the general idea of what is meant l>y a "'viscous" fluid is 

 familiar to every bod}', as that (quality which treacle and tar possess 

 in a marked degree, ghcerin to a less extent, water to a less extent 

 than glycerin, and alcohol and spirits least of all. In lic^uids, the 

 property of viscosit}^ resembles a certain positive ''stickiness" of the 

 particles to themselves and to other bodies, and woidd l)e Avell repre- 

 sented in our model b}' coating over the various balls with some vis- 

 cous material, or by the clinging together which might take place by 

 the individuals of a crowd, as contrasted with the absence of this in 

 the case of no yiscosit}' as represented b}- the evolutions of a body of 

 soldiers. It ma}' be accounted for, to a certain extent, by supposing 

 the particles to possess an irregular shape, or to constantly move 

 across each other's path, causing groups of j^articles to be whirled 

 round together. 



