54 rrofessor H. S. Ilele-Show [Feb. 10, 



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

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

 recognised metbods of physical computation. Lord Kelvin has used 

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

 size of the earth, the 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 forcibly. 

 This tumbler contains half a pint of water. I now close the top. 

 Suppose that, by means of a fine hole, I allow one and a half billion 

 particles to flow 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 by a " viscous " fluid is 

 familiar to everybody, as that quality which treacle aud tar possess 

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

 than glycerine, and alcohol and spirits least of all. In liquids, the 

 property of viscosity resembles a certain positive "stickiness" of 

 the particles to themselves and to other bodies; and would he well 

 represented in our model by coating over the various balls with somo 

 viscous 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 viscosity as represented by the evolutions of a body 

 of soldiers. It may be accounted for, to a certain extent, by supposing 

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

 each other's paths, causing groups of particles to bo whirled round 

 together. 



Whatever the real nature of viscosity is, it results in producing 

 in water the eddying motion which would be perfectly impossible 

 if viscosity were absent, and which makes the problem of the motion 

 of an imperfect liquid so difficult and perplexing. 



Now, all scientific advance in discovering the laws of nature has 

 been male by first simplifying the problem and reducing it to certain 

 ideal conditions, and this is what mathematicians have done in study- 

 the motion of a liquid. 



We have already seen what almost countless millions of particles 

 must exist in a very small space, and it does require a much greater 

 stretch of the imagination to consider their number altogether without 

 limit. If we then assume that a liquid has no viscosity, and that it 

 is incompressible, and that the number of particles is infinite, we 

 arrive at a state of things which would be represented in the case of 

 the model or the diagram on the wall, when the little globes were 

 perfectly smooth, perfectly round and perfectly hard, all of them in 

 contact with each other, and with an unlimited number occupying the 

 smallest part of one of the coloured or clear bands. This agrees with 



