ON WAVES. 



339 



The Magnitude and Form of the Wave of the First Order. — This is one of 

 the subjects to which, since the date of the former Report, I have devoted a 

 good deal of attention. The exact determination of the dimensions and 

 form of the wave, although at first sight it may seem simple enough, is not 

 without peculiar difficulties. When it is observed that the two extremities 

 of the wave are vertices of curves of very small curvature tangent to the 

 plane of repose, it will be understood how difficult it is to detect the place of 

 contact with precision. A variety of methods have been tried : reflexion of 

 an image from the surface, tangent points applied to the surface so as to be 

 observed simultaneously at both ends of the wave, and the self-registration 

 of a float moved by the wave have all been tried with various success. On 

 the whole, however, the most perfect observations have been obtained by a 

 very simple autographic method, in which it was contrived that the Avave 

 should leave its own outline delineated on the surface without the interven- 

 tion of any mechanism*. The method was simply this : a dry smooth surface 

 was placed over the surface of the water in the channel, with such arrange- 

 ments that it could be moved along with the velocity of transmission of the 

 wave, and at the instant of observation it was pushed vertically down on the 

 wave, and raised out again without sensibly disturbing the water ; the sur- 

 face when brought out, brought with it a moist outline of the wave, which 

 was immediately traced by pencil, and afterwards transferred to paper. 1 

 have given a few of these autographic types of the wave in Plates L. and LI., 

 the engravings being precise copies of the lines as drawn by the wave itself. 



Another method of obtaining an autographic representation of waves of 

 the first order was this. Two waves were generated at opposite ends of the 

 same channel at given instants of time, so that by calculating their velocities 

 they should both reach a given spot at the same instant; here a prepared sur- 

 face was placed, and as one passed over the other it left a beautiful outline 

 of the excess in height of each point of one wave above the summit height 

 of the other. These forms are not identical with those of the same wave 

 moving along a plane surface, but as true registers of actual phaenomena they 

 are interesting. 



The results of all my observations on this subject are as follows : — 



That the wave of the first order has a definite ybrm and magnitude SiS 

 i^rAuch characteristic of it as the uniform velocity with which it moves, and 



* I find that I am not the first person who employed an apparatus of this sort. MM. 

 Webers employed a powdered surface to register the form of agitated mercury, the fluid 

 rubbing off the powder. 



z 2 



