334 REPORT — 1844. 



Anotlier example : 



Theoretical value (when /< = 1 and 2e=0"3) c=l"54'7 

 Observed value 0=1*8, 



showing the error in defect = — -f^ of the whole theoretical velocity. 



Again, 



-Theoretical value (when A=7"04' and 2e=0'89)c=4"0 

 Observed value c=4'*6, 



showing the error in defect = — ^ of the whole theoretical velocitj'. 



I think it due to Mr. Kelland to say, that notwitiistanding all the anxiety 

 for success which naturally exists in the mind of one who has bestowed much 

 time and talent on perfecting, as he has done, an elegant theory ; he has not 

 yielded to the temptation of twisting his theory to exhibit some apparent ap- 

 proximation to the facts, nor distorted the facts to make them appear to serve 

 the theory, a proceeding not without precedent ; but he has candidly stated 

 the discrepancy, and says, " my solution can only be regarded as an approx- 

 imation, nor does it very accurately agree M'ith observation." This is a can- 

 dour which cannot be too highly valued, and can only be justly appreciated 

 by those who have, as I have, after \vorking at a favourite theory, it may be 

 for months and years, found it necessary to abandon it, and make the sacri- 

 fice for the sake of truth with readiness and candour. 



Mr. Airy has followed Mr. Kelland over the same ground, in an elaborate 

 paper on waves in the ' Encyclopedia Metropolitana,' published since the greater 

 part of this Report was ready for the press. This paper I have long expected 

 with much anxiety, in the hope that it would furnish a final solution of this 

 difficult problem, or at least tend to reduce the number and extent of the un- 

 happy discrepancies between the wave-prediction and the wave-phaenomena, 

 a hope justified by the reputation and position of the author, as well as by 

 the clear views and elegant processes which characterize some of his former 

 papers. 



Mr. Airy has obtained for the velocity of a wave, an expression of a form 

 closely resembling that which Mr. Kelland had previously obtained, viz. 



m £'«*+£-'"* 



CD.] 



From the resemblance of this form of expression to the form previously 

 given by Mr. Kelland, we are prepared for the conclusion that Mr. Airy has 

 advanced in this direction little beyond his predecessor. And we accordingly 

 find that a theory of the wave of the first order, accurately representing this 

 characteristic phaenomenon, is still wanting, a worthy object for the enterprise 

 of a future wave-mathenicitician. 



I have already stated that I have found, that by introducing the element of 

 the wave's height into Lagrange's formula, I get the expression 



v= \^g{h + k), 



and that I find it represent with great accuracy the characteristic velocity of 

 the wave of tlie first order. As however Mr. Airy appears to intimate to 

 his readers that his own formula is as close an approximation to my experi- 

 ments as the nature of these experiments will warrant, I have thought it ne- 

 cessary to make a complete re-examination of my experiments, and to make a 

 laborious comparison of the phsenoniena discussed after the best modern me- 

 thods employed in inductive philosophy ; the results of these discussions I have 

 presented in a series of graphic representations, which will enable the reader 

 at once to attain a sound conclusion on the ((uestion, whether the formula 



