326 REPORT — 1841. 



lation in a channel of trian^ilar section. Some other subjects, demanding 

 additional experiments, had also occurred to Mr. Russell since last meeting, and 

 an apparatus capable of generating large waves in a large triangular channel 

 had been constructed. The point to be determined, regarding the velocity of 

 the great primary wave in the channel of triangular section, was this, — whether 

 the velocity were that which is due by gravity to a depth of one-fourth part 

 of the depth of the channel, or of one-third. The difficulty of this determi- 

 nation arises from several causes : first of all, the wave in the triangular sec- 

 tion had a less continuous form than in the I'ectangular channel ; and, se- 

 condly, the portion of fluid in the angle of the channel at the bottom does not 

 acquire the same motion of translation with the remainder of the fluid in the 

 wider parts of the channel. These causes tend to retard the motion, and to 

 render it matter of doubt whether the actual velocity approaches nearer to 

 that due to one-third or one-fourth of the depth. An example of the results 

 obtained by experiment is as follows : — 



The velocity due to one-third of the depth being ... 6-5 feet per sec. 

 The velocity due to one-fourth of the depth being... 5-7 feet per sec. 

 The velocity observed by experiment was 6'3 feet per sec. 



The general conclusion being, that the velocity of the great primary wave of 

 translation in a triangular channel is nearly that due to one-third of the depth, 

 making allowance for the resistance of the small portion in the angle of the 

 bottom, the result being nearer to the velocity due to one-third than to one- 

 fourth of the depth. The next point investigated was a curious phaenomenon 

 to which Mr. Russell had given the designation of the " great negative wave." 

 This phenomenon was in some respects the counterpart of the great wave of 

 translation. It has this curious property, that instead of being propagated 

 across other waves as the common oscillatory waves are, both in their posi- 

 tive and negative portions, this negative wave and the positive wave, when 

 meeting, had the effect of neutralizing each other so perfectly, as altogether 

 to leave the fluid in a state of rest, with the exception only of certain residual 

 oscillatory waves of the second order. With this wave a number of curious 

 phaenomena were associated, and it appeared to form an important element in 

 the resistance of fluids to the posterior portion of a ship, while the positive 

 wave was closely associated with the resistance to the anterior part. A series 

 of experiments had also been made on a point which had not previously been 

 examined, — the influence of the velocity of the wave on the resistance of a 

 fluid to bodies moving with velocities remote from the velocity of the wave ; 

 whether, when a body moves with a given velocity less than that of the wave, 

 it will be more or less resisted according as the velocity of the wave is more 

 remote or less remote from its own ; and whether, when a body moves with a 

 given velocity greater than that of the wave, it will experience more or less re- 

 sistance, according as the velocity of the wave is more or less remote from its 

 own. The general result is, that with velocities less than that of the wave, 

 the resistance increases in a certain manner as the velocity of the wave dimi- 

 nishes, and that in velocities greater than that of the wave, the resistance di- 

 minishes as the velocity of the wave diminishes. Slowness of motion of the 

 wave, while it is least favourable to low velocities, is most favourable to high 

 velocities ; hence rectangular canals are best for low velocities, and sloping 

 sides for high velocities. 



