THE MOTION OF A PERFECT LIQUID/ 



Bv Prof. H. S. Hele-Shaw. 



If we look across the surface of a river, we can not fail to observe 

 the difference of the movement at various points. Near one bank the 

 velocity may be much less than near the other, and generally, though 

 not always, it is greater in the middle than near either bank. If we 

 could look beneath the surface and see what was going on there, we 

 should find that the velocity was not so great near the bottom as at the 

 top, and was scarcely the same at any two points of the depth. The 

 more we study the matter, the more complex the motion appears to 

 be; small floating bodies are not only carried down at different speeds 

 and across each other's paths, but are whirled round and round in 

 small whirlpools, sometimes even disappearing for a time beneath the 

 surface. By watching floating bodies we can sometimes realize these 

 complex movements, but they may take place without giving the 

 slightest evidence of their existence. 



You are now looking at water flowing through a channel of var34ng 

 cross section, but there is very little evidence of any disturbance taking 

 place. By admitting color, although its effect is at once visible on the 

 water, it does not help us much to understand the character of the flow. 

 If, however, flne bubbles of air are admitted, we at once perceive (fig. 1) 

 the tumultuous conditions under which the water is moving and that 

 there is a strong whirlpool action. This may be intensified by closing 

 in two sides (fig. 2), so as to imitate the action of a sluice gate, through 

 the narrow opening of which the water has all to pass, the presence of 

 air making the disturbed behavior of the water very evident. 



Now 3"ou will readily admit it is hopeless to begin to study the flow 

 of the water under such conditions, and we naturally ask, Are there not 

 oases in which the action is more simple? Such would be the case if 

 the water flowed very slowly in a perfectly smooth and parallel river 

 bed, when the particles would follow one another in lines called "stream 

 lines," and the flow would be like the march of a disciplined army 



^ A discourse delivered at the Royal Institution, London, on Friday, February 10, 

 1899, by Prof. H. S. Hele-Shaw. Printed in Nature September 7, 1899. 



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