233 



in oscillating waves diminishes in a geometrical ratio as their di- 

 stance below the surface increases, which result agrees with Mr. 

 Scott Russell's observations ; but that it is interesting to examine 

 whether a series of oscillatory waves can exist in a channel of uniform 

 breadth and depth, upon the supposition that the horizontal excursion 

 of the particles is the same from the top to the bottom. From the 

 analytical investigation of the author, it appears that there can exist 

 in a channel of uniform breadth and depth a series of waves of the 

 same magnitude and moving with the same velocity. In the case 

 of rivers, the tide- wave appears to be of this description. If the 

 effect of friction on the bottom be neglected, the horizontal velocity 

 of the particles may be considered to be the same throughout the 

 whole depth — and the motion is oscillatory, if that due to the stream 

 be separated. But the length of the wave is very great in com- 

 parison with the depth, and the vertical motion is so slight, that it 

 may be neglected altogether. On this supposition, which simplifies 

 the investigation, the velocity for a wave of translation is 



and for an oscillating wave is (h + k) 



which differ but little from the results previously obtained, and are 

 rather in excess, as was to be expected, when no part of the force 

 has been expended in producing vertical motion. 



Referring to the solution of this problem, given by Mr. Airy in 

 the Encyclopaedia Metropolitana, and the equation there arrived at, 

 the author states that it is with great diffidence, and not until after 

 the most careful examination, that he ventures to question the 

 accuracy of this result. In a further investigation, he points out 

 the source of this inaccuracy ; and in conclusion observes, that it 

 must be confessed to be unsatisfactory to point out an error without 

 supplying the deficiency caused by it, but that the analytical diffi- 

 culties are such, that he cannot, consistently with the attention 

 required by other avocations, attempt, for the present at least, to 

 continue an investigation which is interesting as a matter of science 

 and useful in its application to hydraulic engineering. 



November 30, 1852. 



At the Anniversary Meeting, 



The EARL OF ROSSE, President, in the Chair. 



Dr. Booth, on the part of the Auditors of the Treasurer's Accounts, 

 announced that the total receipts, during the past year, including a 

 balance of £147 85. Qd. carried from the account of the preceding 

 year, amounted to £3528 55. Id. ; and that the total expenditure, 

 including an investment of 56115 Os. Od. in the Funds, was 

 ^3346 55. Od., leaving a balance in the hands of the Treasurer of 

 ^182 05. Id. 



