1883.] On the Motion of Water. 89 



Fig. 1. 



the other, as shown by the curve in fig. 2, eddies appeared in the 

 middle regularly and readily. 



Fig. 2. 



8. Methods of Investigation. — There appeared to be two w T ays of 

 proceeding, the one theoretical, the other practical. 



The theoretical method involved the integration of equations 

 for unsteady motion in a way that had not then been accomplished, 

 and which, considering the general intractability of the equations, was 

 not promising. 



The practical method was to test the relation between U, -, and c; 



P 



this, owing to the simple and definite form of the law, seemed to 

 offer, at all events in the first place, a far more promising field of 

 research. 



The law of motion in a straight smooth tube offered the simplest 

 possible circumstances and the most crucial test. 



The existing experimental knowledge of the resistance of water in 

 tubes, although very extensive, was in one important respect incom- 

 plete. The previous experiments might be divided into two classes — 

 (1) those made under circumstances in which the law of resistance 

 was as the square of the velocity, and (2) those made under circum- 

 stances in which the resistance varied as the velocity. There had 

 not apparently been any attempt made to determine the exact circum- 

 stances under which the change of law took place. 



Again, although it had been definitely pointed out that eddies 

 would explain the resistance as the square of the velocity, it did not 

 appear that any definite experimental evidence of the existence of 

 eddies in parallel tubes had been obtained, and much less was there 



