ON WAVES. 



Differences. 



337 



The conclusion which Mr. Airy deduces from this comparison is somewhat 

 surprising, " we think ourselves fully entitled to conclude from these experi- 

 ments that the theory (Mr. Airy's) is entirely supported"! This conclusion 

 being so completely the opposite of that to which we should be led on the 

 same grounds, it has appeared necessary to make a still more complete re- 

 examination and discussion of all the experiments in our possession, to see 

 whether from any or the whole of them there should appear to be any ground 

 for a conclusion so contrary to the appai'ent phsenomena. 



I have, therefore, directed the whole of the experiments to be re-discussed*. 

 They are graphically represented in the diagrams on Plates XL VIII. and 

 XLIX., which, and the description, the reader is requested to examine care- 

 fully. The result of the whole is, that there is an irresistible body of evidence 

 in favour of the conclusion that Mr. Airy's formulae do not present anything 

 like even a plausible representation of the velocity of the wave of the first 

 order, and that the formula I have adopted does as accurately represent them 

 as the inevitable imperfections of all observations will admit. It is deeply 

 to be deplored that the methods of investigation employed with so much 

 knowledge, and applied with so much tact and dexterity, should not have led 

 him to a better result. 



Table VIII. 



Re-discussion of the Observations by the Method of Curves. 



The observations of height and time were laid down on paper, as shown in 

 Plate XLIX. (see description), each star representing an individual obser- 

 vation of height or time. The curves being drawn through among the ob- 

 servations, were taken to represent the corrected observations, and the velocity 

 was then deduced from the corrected observation of time and height. The 

 table consists of results of this process. 



Column A gives the corrected depth in inches (A + ^) of my formula. 



Column B gives the corrected time in seconds employed in describing 

 40 feet. 



* For the accuracy and good faith with which these discussions were all conducted, I am 

 indebted to my valued assistant Mr. I. Cimie. 



184-t. z 



