114 



and 



PROFESSOR KELLAND ON THE THEORY OF WAVES. 



depth at first 

 depth at x ' 



f A z + h ax~ 



o 



that is, the elevation of the crest of the wave varies reciprocally, as the total 

 depth of the fluid. 



We shall not attempt to form a table exhibiting a comparison of this with 

 observation ; we are sure that a comparison cannot be hoped for at present, owing 

 to the want of a sufficient number of observations, or perhaps to the want of some 

 element in the tables referred to. So far as we can see, many waves differ 

 widely in the results to which they give rise, whilst the elements of the waves 

 themselves are identically the same. We may mention waves 112, 123. and 126 

 (Report, p. 494). The second and third commence similarly, and end similarly 

 as to position, whilst the one continues unchanged in depth, and the other varies 

 from .5 to .7, every thing else remaining the same. The discrepancy is more ob- 

 vious in waves 113 and 131. In the second table given by Mr RUSSELL (p. 494) 5 

 the original height of the wave is wanting. We have restored it roughly, on the 

 hypothesis that waves of the same depth will break at the same distance from 

 the extremity of the canal. By calculating t' from the expression 



t=-(l-Vl(lx)) there results the following table. 



In this table No. represents the number of the wave ; No', that of the wave in the pre- 

 ceding table, which breaks at the same point, and which is therefore presumed to 

 have the same height ; No", that of a wave giving the value of c a ; t is the ob- 

 served, f the computed value of the time. 



