PROFESSOR KELLAND ON THE THEORY OF WAVES. 



527 



It may be thought necessary to verify this result, although, from its sim- 

 plicity, I suspect it must have been known to Poisson and others. As, how- 

 ever, I have never seen it, or met with any reference to such an investigation, I 

 have added a few examples from Mr Russell's Report on Waves, in the last 

 volume of the Reports of the British Association. The wave which Mr Russell 

 has examined, is different from that which has been assumed as the basis of cal- 

 culation ; but the difference makes no alteration in this result, as will be seen 

 hereafter. 



From the analysis which Mr Russell has given of his experiments, I select 

 the following results ; being those for which the height of the fluid in the tri- 

 angular tube most nearly coincides with that in the corresponding experiment in 

 the quadrilateral one. 



Depth of Fluid 

 in inches. 



Velocity observed 



in rectangular 



channel. 



Velocity observed 



in triangular 



channel. 



Do. computed 



from those in the 



second column. 



Difference. 



4.15 



3.20 



2.19 



2.2 





4.23 



3.35 



2.42 



2.4 





4.32 



3.40 



2.43 



2.4 





4.38 



3.40 



2.46 



2.4 





5.69 



4.05 



2.66 



2.8 



.1 



6.26 



4.08 



2.88 



2.9 





6.38 



4.04 



2.85 



2.8 





6.52 



4.05 



3.02 



2.8 



.2 



7.21 



4.32 



3.02 



3.0 





7.36 



4.39 



3.02 



3.1 





The only discrepancies are those which I have placed in the table ; but it 

 may be remarked that, in all cases, the circumstances are very different in the 

 two experiments, depending partly on the height and partly on the length of the 

 wave. That the two cases fixed on should be at variance, is not to be wondered at, 

 when it is remarked that, in the rectangular channel, the velocity is the same for 

 both cases, whilst the depths differ by about an inch ; and it is by means of the 

 depth alone, that we have compared the results in a triangular channel with 

 those in a rectangular. 



On the whole, I conceive the coincidence between the different results as a 

 striking confirmation of the process which has been employed, approximative as 

 that process confessedly is. 



26. Let us now take the general case of any shape whatever to the vertical 

 section. 



