1899] on the Motion of a Perfect Liquid. 57 



the confidence which we may place upon their behaviour, that the en- 

 largement from the original channel, Figs. 1 and 2, as you see, Las 

 been much exaggerated in order to make the conditions as severe as 

 possible, and intensify the effect. The greater pressure in the wider 

 portion may be illustrated by the fact, that while the plugs remain at 

 rest in the middle, where the narrow hands are, they are forced out, 

 when removed to the sides, by the greater pressure, which there acts on 

 the ends. This is where the bands were widest and the velocity slowest. 

 This is quite contrary to what might have been expected, seeing that the 

 liquid was forced so rapidly through the narrower channel, but it needs 

 many illustrations to bring home to us this apparent contradiction of 

 our ordinary experience. Fig. 11 shows the liquid now flowing out 

 through the new channel thus made, as well as through the original 

 place of exit. 



But at this stage you may reasonably enquire how it is that we are 

 able to state, with so much certainty, that the artificial conditions of 

 flow with a viscous liquid are really giving us the stream-line motion 

 of a perfect one ; and this brings me to the results which mathema- 

 ticians have obtained. 



The view now shown represents a body of circular cross-section, 

 past which a fluid of infinite extent is moving, and the lines are plotted 

 from mathematical investigation and represent the flow of particles. 

 This particular case gives us the means of most elaborate comparison ; 

 although we cannot employ a fluid of infinite extent, we can prepare 

 the border of the channel to correspond with any one of the particular 

 stream-lines, and measure the exact positions of the lines inside. 



By means of a second lantern, the real flov of a viscous liquid for 

 this case is shown upon the second screen, and you will see that it 

 agrees with the calculated flow round a similar obstacle of a perfect 

 liquid. The diagram shown on the wall is the actual figure employed 

 for comparison, and upon which the experimental case was projected. 

 By this means, it was proved that the two were in absolute agreement. 

 It' we start the impulses, as before, in a row, we at once see how the 

 middle particles lag behind the outer ones, as indicated by the width of 

 tho bands, showing that it is not necessarily the side stream-lines that 

 move more slowly. It may be more interesting to you to see, in addi- 

 tion to the foregoing case — in which for convenience, and as quite 

 sufficient for measurement only, a semi-cylinder was employed — tho 

 case of a complete cylinder, and this is now shown (Fig. 12, Plate I.). 

 In this case two different colours are used in alternate bands, and these 

 bands are sent in, not steadily but impulsively, in order to illustrate 

 what I have just pointed out. You will see how the greater width of 

 the colour bands before and behind the cylinder indicates an increase 

 of pressure in those regions. This in a ship-shaj)e form accounts for 

 the standing bow and stern waves, whereas the narrowing of the bands 

 at the sides indicates an increase of velocity and reduction of pressure, 

 and accounts for the depression of water level, with which you are 

 doubtless familiar at the corresponding part of a ship. 



