LAW OF THE WAVE. 63 



a point at which the channel became deeper, and here its velocity was suddenly 

 accelerated. The channel was also constructed as to become alternately narrower 

 and wider, but no sensible effect was produced by the change ; and when the wave 

 once more reached that part of the channel which was of the original depth, its 

 velocity returned to the original quantity. 



Another observation equally simple served to shew that a large or high wave 

 had a greater velocity than a small one. When a small wave preceded a large 

 one, the latter invariably overtook the other, and when the large wave was before 

 the less, their mutual distance invariably became gi-eater. 



In channels of rectangular section, the velocity was found by numerous expe- 

 riments not to differ sensibly from that which is acquired by a heavy body in fall- 

 ing freely by gravity through a space equal to half the depth of the fluid. 



In channels of variable depth in the transverse section, the velocity was found 

 to be diminished below that which was due to the maximum depth, and to be 

 equal to the mean of the velocities due to the differential depths. 



The experiments on the magnitude of the wave shewed, that the velocity of 

 larger, that is, of higher waves, appears to be greater than that of smaller ones, 

 nearly in the ratio which is obtained by supposing the depth of the channel to be 

 increased by a quantity equal to the height of the wave above the level of the sur- 

 face of the quiescent fluid. 



Experiments on the age and history of the wave, that is, upon the time which 

 has elapsed, and the distance which has been travelled, and the route which has 

 been described by it from the time and place of generation to the time and place 

 of observation, shew that, after having traversed spaces from 100 to 2500 feet long 

 in a sinuous channel, the wave remains unchanged in form and in velocity. 



As the full investigation of the laws of the Genesis and Propagation of Waves 

 forms a very extensive subject, in which I am at present engaged as a separate 

 investigation, I have not loaded this paper with such observations as belong more 

 properly to that subject. But I have given in this paper those examples which 

 have peculiar reference to those experiments on resistance which I haye now oc- 

 casion to discuss in connection with the wave of the channels in which they were 

 made. — (See Parts II. and III.) 



The experiments on resistance were made in a channel 5.5 feet deep in the 

 middle, but of irregularly diminishing depth towards the sides. The velocity of the 

 wave in these experiments is about 8 miles an hour, being from 11 to 12 feet per 

 second, varying with the height of each wave according to the law already given. 



Very small waves, whose height does not exceed 0.1 of the depth of the 

 quiescent fluid, are considerably retarded below the velocity due to the length, 

 and move slower than the larger waves in a less depth. 



The following extracts from the tables of a separate series of investigations 



