THE MOTION OF A PERFECT LIQUID. Ill 



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

 water the eddjang 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 made by first simplifying the problem and reducing it to certain 

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

 ing 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 recjuire a much greater 

 stretch of the imagination to consider their number altogether without 

 limit. If Ave then assume that a liquid has no viscosit}', 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 per- 

 fectly 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 colored or clear bands. This agrees with 

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

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

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

 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 onh' a few simple cases, one of the most remarkable instances of 

 the power of higher mathematics, and one of the greatest achievements 

 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 behavior of a perfect 

 liquid has been, to a certain extent, investigated. You will also under- 

 stand why such models as we could actually make, or any analogy with 

 the things with Avhich Ave are familiar, Avould not help us very much 

 in obtaining a mental picture of the behavior of a perfect liquid. If, 

 for instance, Ave trA^ to make use of the idea of drilled soldiers, and 

 moA c the lines with that object in vicAV, Ave see that instead of the 

 ordinary methods of drill, the middle rank soon gains on the others, 

 and enters again the parallel portion of the chanmd in a A'ery different 

 relative position to the opposite lines, although the stream lines Avould 

 all have the same actual velocity when once again in the parallel por- 

 tion. Since, then, we can not use models or any simple analogy Avith 

 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 Ave take tAvo sheets of glass, and bring them nearly close together, 

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



