no. 15.] APPENDIX. 139 



APPENDIX. 



NOTE ON THE MATHEMATICAL TREATMENT OF THE WAVES AND THE 



WAVE-MAKING RESISTANCE. 



Keeping to suitably simplified cases, it is possible to calculate mathe- 

 matically the wave-making resistance at different velocities, in shallow water 

 as well as in "dead-water". The results of these calculations as far as worked 

 out, agree remarkably well with the experimental measurements; which is not 

 always the case with exact solutions of hydrodynamical problems. Such 

 agreement seems indeed to be rather usual in the case of wave- and other oscil- 

 latory motions, presumably because these motions are stable. Below, some 

 of the results will be given and compared with the experimental results, but 

 the method of calculation will be only indicated; a fuller account of the me- 

 thod and its application to some other problems, will be given on a subse- 

 quent occasion. 



In No. Ill of a series of papers: "On stationary waves in flowing water" 1 , 

 Lord Kelvin has solved a problem which in a way represents the case of a 

 vessel moving in a shallow and narrow channel. The channel is supposed 

 to be of rectangular section, and the vessel is replaced by a small ridge on 

 the bottom, right across the channel. The ridge is supposed to be very low, 

 and with smooth and even slopes. 



(Sir William Thomson) Phil. Mag. Ser. 5 Vol. 22-23 (1886-87). No. Ill is found in 

 Vol. 22 p. 517. A few errors which influence, although not essentially, the results of 

 this paper, may perhaps be noted. The factor 2 on the right hand side of (26) p. 523, 

 should be omitted, and the two last members in (30) p. 524, as well as the right hand 

 side of (31), (34), and (40), should in consequence be doubled. In (47) and (48) p. 528, 

 the denominators 1 +■ Djb should be replaced by 1 — Djb. 



