THE MOTION OF A PERFECT LIQUID. 109 



reduced 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 doubt- 

 less have noticed that it was not necessar}^ for the engine actuall}' to 

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

 mipact depended largely upon the suddenness with which the speed of 

 those in front was reduced. Appljdng this illustration to the model, 

 you will see that the impact of these particles in the wider portion 

 would necessarih^ involve a greater pressure in that part. Turning- 

 next to the white balls, I imitate, by means of the left-hand p®rtion, 

 the flow which will occur in a channel six times as large as the original 

 one, and you now see (fig. 7) that as the particles have placed them- 

 selves six abreast, and the first and last row are 3 inches apart instead 

 of 18 inches, the speed in the wider portion of the channel must have 

 been one-sixth of that in the narrow portion. Evidently, therefore, 

 the velocity of the particles has been reduced more rapidly than in the 

 previous case, and the pressure must consequently be correspondingly 

 greater. 



We may now take it as perfectly clear and evident that the pressure 

 is greater in the wider portion and less in the narrower portion of the 

 channel. Turning now to the two diagrams, we see that the pressure 

 is in each case greater in every row of particles as in the wider por- 

 tions of the channel, but that instead of being suddenly increased, as 

 in the model, it is gradually increased. The width of the colored 

 bands, that is, rows of particles, or width apart of stream lines, is a 

 measure of the increased pressure. Thus j^ou will now regard the 

 width of the bands, or, what is the same thing, the distance apart of 

 the stream lines, as a direct indication of pressure and the narrowness 

 or closeness of the stream lines as a direct indication of velocity. 



Next notice the great difi^erence between the two diagrams. In one 

 diagram (fig. 4) the change of width is uniform across the entire sec- 

 tion. In diagram (fig. 5), however, this is not the case. In the nar- 

 rowest portion of the channel in each diagram there are seven color 

 bands of little balls, each containing three abreast, but Ave find that in 

 one diagram (fig. 4) they are equally spaced in the wider part six 

 abreast throughout. In the other diagram (fig. 5) the outer row is 

 spaced eight abreast, the second row rather more than six, and the 

 inner rows rather more than four abreast, and the middle row less than 

 four abreast, making in all forty-two in a row, as in the previous 

 case. One diagram (fig. ,5), therefore, will represent an entirely dif- 

 ferent condition to the state represented by the other diagram (fig. 4), 

 the pressure in the wide part of the hitter varying from a maxinuun 

 at the outside to a minimum in the middle, while the corresponding 

 velocity is greatest in the middle and least at the outside or borders. 



