THE EXPERIMENTS OF 1834. 85 



of a well defined form, moving with an uniform velocity along the surface of the 

 fluid ; the forms of the fluid vary, but maintain an obvious relation to one another; 

 they are of the same family of waves, or may be resolved into compounds of the 

 members of the same family. A few of those that have been carefully and fre- 

 quently observed, are given in Plate I. figs. 2, 3, 3 and 4. 



The three first examples appear to be simple examples of the trochoid, a 

 curve that appears to comprehend all the elementary forms of the wave. Other 

 forms which make their appearance, seem to be compounds of these, into which 

 they may be resolved by a very simple analysis, as is done in the succeeding 

 figures. When one portion of such a compound wave is higher than another, I 

 have invariably observed the higher portion move more rapidly than the rest, and 

 finally separate itself, leaving the rest behind, and assuming a definite element- 

 ary form. Figs. 5, 6, and 7, shew the outline and analysis of some compound 

 waves, which afterwards resolved themselves into simple ones of the forms given 

 in Figs. 2, 3, or 4. - . 



The first series of experiments on the wave, were directed to the determination 

 of the relation between its velocity and the form and dimensions of the channel. 

 A sheltered situation and calm day were selected, so that the form of the waves 

 might be sufficiently perfect to enable the observers to mark with precision the 

 place of the summit of the wave. At the termination and the commencement of 

 distances that had been accurately measured, graduated rods were placed in a ver- 

 tical position, and careful observers, furnished with assistants and accurate chro- 

 nometers, were stationed opposite to each of them. A wave was generated by 

 giving rapid motion to a vessel, and then depriving it of motion at a given distance 

 from station A ; and at the instant of the coincidence of the summit of the wave 

 with the rod at A, a signal was communicated by sound to station B, the time of 

 the transit being recorded at A, and the time of the sound at B. The wave now 

 passed on towards B, and at the instant of its arrival time was observed at B, 

 and the time of the signal of arrival communicated to A was also registered by 

 chronometer A. Thus, without calculating the velocity of sound or ^, the time of 

 describing the space, or s, was determined ; for 



s — ^ = difference of times at B. 



s + ^ = difference of times at A, 



" ^ • ^ , — '^ — = true time corrected for the velocity of sound. 



The following observations were made at the experimental station at Her- 

 miston, where also almost all the experiments on resistance were subsequently 

 carried on. 



