56 Professor H. S. Hele-Shaw [Fob. 10, 



wider portion of the channel, afterwards contracting to their original 

 width ; but 1 have already prepared you for the fact that they do not 

 do this uniformly, and, in spite of the fact that they were all equally 

 sj aced in the narrower portion of the pipe, they are very unequally 

 spaced in the wider portion — in this you will see the resemblance to 

 the model, Fig. 3, and the case given in Fig. 5. 



You will not, I trust, now fall into the very natural nr'stake of 

 thinking that the nature of the substance is more attenuated because 

 the band has become wider, but will realise that the particles are in 

 the wider portion just as close together as in the narrower. I have 

 already explained that as more particles are required to fill the greater 

 width, and can only be supplied from the same band behind, the band 

 at that part cannot possibly be moving as fast as the narrow bands at 

 the same cross-section, that is, on the line drawn across at right angles 

 to the central line of the stream. 



This I will now prove to you by a very simple but conclusive ex- 

 periment, for by opening and closing the tap regulating the colour 

 bands, we can start a fre>h supply exactly at the same instant in each 

 of the bands — in the same way as the starter attempts, though usually 

 not with the same success, to carry out his duties on the racecourse. 

 (Fig. 9, Plate I.) shows the different position of various colour band 

 fronts which were all started in line, and gives a good idea of the 

 relative changes of velocity. You will see that the straight formation 

 of the row is not maintained, even in the parallel portion of the 

 channel, the middle row gaining on the sides, which is not because 

 of any resistance on the sides, but because the influence of the enlarge- 

 ment is felt before that is actually reached. Then, you see, the middle 

 portion slows down considerably, and, for an instant, of course, the 

 portions which lag behind on the sides appear to be overtaking it ; 

 they in turn, however, have to occupy so much more space on the 

 sides, that they fall rapidly behind and the once straight row of par- 

 ticles becomes, in leaving, more and more curved. This curve is so 

 drawn out as to leave no doubt in your minds as to which band of 

 particles wins the race; and, although ultimately these particles are 

 again flowing along the narrow channel at the same velocity, whether 

 in the middle or at the sides, the particles which stated at the 

 middle, at the same time as the particles at the sides, have obtained 

 the lead in finally entering the channel again. This lead tliey 

 will continue to maintain, unless they should encounter an obstacle 

 in the middle of the channel, when, as I shall be able to show you 

 in a subsequent experiment, their positions may possibly be reversed. 



By now gradually closing in the slides, so as to reproduce conditions 

 of a narrow diaphragm or channel with ordinary flow, instead of the 

 turbulent or whirlpool motion which then resulted, the colour bands 

 at once respond to the altered conditions (Fig. 10), and, like a perfectly 

 drilled body of troops, perform the required evolutions immediately, 

 even though the defile through which they are compelled to pass in- 

 volves almost incredibly rapid change of speed. So great, indeed, is 



