1899.] 



on the Motion of a Perfect Liquid. 



51 



Perhaps you may think that if these wires were removed, and the 

 wooden balls allowed to find their own positions, they would group 

 themselves as with an actual liquid. This is not the case ; and, for 

 reasons that you will see presently, no model of. this kind would give 

 us the real conditions of actual flow. By means of a model, however, 

 we may be able to understand why it is so absolutely cs.-ential wo 

 should realise the correct nature of the grouping which occurs. 



First look at the two diagrams on the wall (Figs. 4 and 5), which 

 you will see represent channels of similar form to the experimental 

 one. The same number of particles 

 enter and leave in each under ap- 

 parently the same conditions, so that 

 the idea may naturally arise in your 

 minds, that if the particles ulti- 

 mately flow with the same speed 

 whatever their grouping in the larger 

 portion of the channel, it cannot 

 much matter in what particular 

 kind of formation they actually pass 

 through that wider portion. To 

 understand that is really very im- 

 portant. Let us consider a model 

 (Fig. 6) specially made for tlie 

 purpose. You will see that we have 

 two lines of particles which we may 

 consider stream-lines, those on the 

 left coloured white, and those on the 

 right coloured red. The first and 

 last are now exactly 18 inches apart, 

 there being eighteen balls of 1 inch 

 diameter in the row. If I move the 

 red ones upvvaid, I cause them to 

 enter a wider portion of the channel, 

 whei'e they will have to arrange 

 themselves so as to be three abreast 

 (Fig. 7). It is quite clear to you, 

 that as I do this their speed in the 

 wider portion of the channel is only 

 one-third of that in the narrow portion, as you will see from the 

 relative positions of the marked particles. Now, directly the first 

 particle entered the wider channel, it commenced to move at a re- 

 duced speed, with the result that the particles immediately behind 

 it must have run up against it, exactly in the same way that you have 

 often heard the trucks in a goods train run in succession upon the 

 ones in front, when the speed of the engine is reduced ; and you will 

 doubtless have noticed that it was not necessary for the engine actu- 

 ally to stop in order that this might take place. Moreover, the force 

 of the impact depended largely upon the suddenness with which tho 



e 2 



Fig. 3. 



