ON WAVES. 336 



Mr. Airy has adopted, or that which I have always used, more truly repre- 

 sents the phaenomena. 



In the following table, E represents the velocity of the wave of the first 

 order as taken from my observations by Mr. Airy himself. I have placed 

 beside these results of experiments, the number given in column F, by the 

 formula which I use to represent them. In the next four columns are Mr. 

 Airy's numbers, calculated by himself, according to four different formulae, 

 which he appears here to have applied as a sort of tentative process for the 

 purpose of selecting the one which should prove on trial least defective. I 

 have next given five columns, which exhibit the results of comparing the phae- 

 nomena of experiment with the results of the formulae. The first of these 

 columns represents the defects of my formula, the others those of Mr. Airy's. 

 The results of the first table are as follows : — 



The errors of Mr. Airy's first column amount to 2635 



The errors of Mr. Airy's second column amount to 1994 



The errors of Mr. Airy's third column amount to 1674 



The errors of Mr. Airy's fourth column amount to 1680 



The errors of mine amount to 406 



The greatest error of Mr. Airy's first column is ... . 809 

 The greatest error of Mr. Airy's second column is. . 690 

 The greatest error of Mr. Airy's third column is . . 463 

 The greatest error of Mr. Airy's fourth column is. . 575 

 The greatest error of mine is 87 



The results of the second table are as follows : — 



The errors of Mr. Airy's first column amount to 6157 



The errors of Mr. Airy's second column amount to 3350 



The errors of Mr. Airy's third column amount to 3226 



The errors of Mr. Airy's fourth column amount to 2274 



The errors of mine amount to 447 



The greatest error of Mr. Airy's first column is. ... 911 



The greatest error of Mr. Airy's second column is. . 689 



The greatest error of Mr. Airy's third column is . . 473 



The greatest error of Mr. Airy's fourth column is . . 480 



The greatest error of mine is ]22 



Table VI. 

 Small Waves. 

 Column A is a mean height of wave crest. H a i 



„ B the selected examples from whicii A is taken. p taken 



„ C the depth of the fluid in repose. K *''"'." ^^ ^,''- 



„ D the height of the wave. fpennients by 



„ E the velocity of the wave observed. J ^' y* 



„ F the velocity of the wave as given by my formula. 

 „ G the velocity of the wave as given by Mr. Airy's first formula. 

 „ H the velocity of the wave as given by Mr. Airy's second formula. 

 „ K the velocity of the wave as given by Mr. Airy's third formula. 

 „ L the velocity of the wave as given by Mr. Airy's fourth formula. 

 ,, F' the difference between observation and my formula. 

 „ G' the difference between observation and Mr. Airy's first formula. 

 „ H' the difference between observation and Mr. Airy's second formula. 

 „ K' the difference between observation and Mr. Airy's third formula. 

 „ L' the difference between observation and Mr. Airy's fourth formula. 



