364 REPORT — 1844. 



The Standing Wave of Running Water. — Among oscillating waves of the 

 second order, I know none more common or more curious than the standing 

 wave of running water. I begin the account of my examination of waves 

 of the second order, because it is that species which appears to me to be the 

 most easy to be conceived, because it presents the closest analogy to the ordi- 

 nary known phsenomena of \^ ave motion, and because, although most fre- 

 quently exhibited to the eye of the common gazer, it has not, as far as I 

 know, ever been made the subject of accurate observation. 



If the surface of a running stream be examined as it runs with an equal 

 velocity along a smooth and even channel, its surface will present no remark- 

 able feature to the eye, although it iti known by accurate observation that 

 the surface of the water is higher above the level in the middle or deep part 

 than at the sides of the channel. On the bottom of the channel let there be 

 found a single large stone ; this interruption, although considerably below 

 the surface of the water, will give indication of its presence by a change of 

 form visible on the surface of the water. An elevation of surface will be 

 visible, not inmiediately above it, but in its vicinity. Simultaneous with the 

 appearance of this protuberance, there will appear a series of others lower 

 down the stream. These form a group of companion phsenomena, are waves 

 of the second order, oscillatory, and of the standing species, their place re- 

 maining fixed in the water, while the water particles themselves continue to 

 flow down with the stream. For examples see PI. LV. 



This species of wave is especially deserving of the notice both of the ma- 

 thematician and of the natural philosopher, for this cause especially, that the 

 apparent motions of the water are in this case identical with the actual paths 

 of individual particles ; each particle on the surface actually describes the 

 path apparent on the surface ; the outline of the surface of the water is the 

 true path of a particle during its progress down the stream. It does not ex- 

 hibit like other waves the form merely, a form very different from the true 

 motion of the water particles, nor does it exhibit the motion of a motion, nor 

 do the particles themselves remain behind while they transmit forward the 

 wave. The particles are themselves translated along the fluid in the paths 

 which form the apparent outline of the fluid. 



In this respect, therefore, this wave appears to me important as presenting 

 a case of transition from ordinary fluid motion to wave motion. 



I found by observation on a mountain stream that waves 3^ feet long rise 

 in water moving at the rate of 2>\ feet per second. 



Also, that waves 2 feet long rose in water moving at 2\ feet per second. 



These numbers coincide with those given in Table XXI. from which the 

 following approximate numbers are deduced. These numbers will enable an 

 observer to judge of the velocity of a stream by inspection of the waves on 

 the surface. 



The length of wave being 1 inch, the velocity of the stream per second is \ foot. 

 „ „ *3 inches, „ „ „ *1 foot. 



„ „ 1 foot, „ „ „ If feet. 



5, ,, 1^ ICCL, „ ,, 5, .. ICCb. 



,, ,, z leet, ,, ,, ,, ^2 J6et. 



35 ,j o'2 leet, ,, ,, jj o'^ leet. 



„ „ 6 feet, „ „ „ 4|feet.' 



„ „ 7 feet, „ „ 5, 5 feeti 



„ „ 10 feet, „ „ „ 6 feet. 



*30 feet, „ „ „ *10 feet. 



This Table is given for convenience of reference to observers, and it isl 



useful and easy to recollect the velocities corresponding to 3 inches, 3^ feet, 



