IO UNIVERSITY OF MISSOURI STUDIES 



nearer the openings, move much more quickly than those 

 farther to the right. This is seen from the fact that the 

 left wall d of the white "bottle" has been separated entirely 

 from the opening A and is just getting ready to disappear 

 altogether through the opening B, whereas the right wall e 

 is merely beginning to sever its connection with A. We 

 have here a simple experimental proof for the statement of 

 the preceding paragraph that friction prevents the spreading 

 of the motion beyond narrow limits, causing it to occur as 

 near the two openings as possible. Although the experiment 

 in this form does not show it, the reader hardly doubts that 

 somewhat farther to the right, say six inches from the open- 

 ings, no motion whatsoever has occurred during the whole 

 time. The quickest motion, of course, is in this particular 

 case not found at the extreme left, at g, but about a fourth 

 of an inch to the right, since the friction at g is too great. 

 Without entering into a detailed study of the hydrodynamic 

 problem which confronts us here, in which friction against 

 the walls, internal friction in the fluid, and the momentum 

 of the fluid play their roles, let it be sufficient to say here 

 that the motion is practically limited to the portion of the 

 tube near the windows in accordance with the general law 

 of nature that whatever occurs, occurs with the least pos- 

 sible expenditure of energy. Some clay is pressed in at A. 

 The same quantity has to pass out at B. This can be made 

 possible by many kinds of displacement of the particles with- 

 in the box. But only one form of displacement becomes 

 actual, the one that requires the smallest amount of work to 

 be done by the piston at A. And this form of displacement 

 consists in the displacement being confined to the neighbor- 

 hood of the openings. 



