1899.] 



on the Motion of a Perfect Liquid. 



53 



section. In diagram (Fig. 5), however, this is not the case. In tho 

 narrowest portion of the channel in each diagram, there are seven 

 colour bands «f little balls each containing three abreast, but we 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 different condition to the state represented by the other 

 diagram (Fig. 4), the pressure in the wide part of the latter varying 

 from a maximum 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. 



Now, when we know the pressure at every point of a liquid, and 



Fig. 6. 



Fig. 7. 



also the direction in which the particles are moving, together with 

 their velocity at every point, we really know all about its motion, 

 and you will see how important the question of grouping is, and 

 that, in fact, it really constitutes the whole point of my lecture to- 

 night. How then shall we ascertain which of the two groupings 

 (Fig. 4 or 5) is correct, or whether possibly some grouping totally 

 different from either does not represent the real conditions of flow ? 



Now, the model does not help us very far, because there seems to 

 be no means of making the grouping follow any regular law which 

 might agree with fluid motion. In whatever way we improve such a 

 model, we can scarcely hope to imitate by merely mechanical means 

 the motion of an actual liquid, for reasons which I will now try to 

 explain. 



In the first place, apart from the particles having no distinguishing 

 characteristics, either when the liquid is opaque or transparent, they 

 are so small and their number is so great as to be almost beyond our 



