LAWS OF THE MOTIONS OF WAVES EXCITED IN WATER. 527 
had ever been issued at that sta^e of 
their proceedings ; the probability, 
therefore, seemed to be, that the num- 
ber of members attending the Associa- 
tion would be larger than ever they were 
before, and the pecuniary benefit pro- 
portionably greater. 
TUESDAY, AUG. 23. 
Section A. -MATHEMATICS AND 
PHYSICAL SCIENCE. 
The president upon taking the chair 
this morning called upon Mr. Russel, of 
Edinburgh, for his * Notice of a Series 
of Experimental Researches regarding 
the Laws of the Motions of Waves 
excited in Water.’ 
This notice regarded one department 
of a series of investigations In Hydro- 
dynamics, in which the author has been 
engaged for three years. — (See Sec. G, 
Monday.) It was discovered in the course 
of these investigatins, that the pheno- 
mena of waves interfered with the phe- 
nomena of resistance, to such an extent, 
as to render an investigation of the laws 
of the propagation of waves essential to 
the farther prosecution of the inquiry into 
the laws of resistance. The importance 
also of these inquiries, in connexion 
with the investigations of Mr. Whe- 
well and of Mr. Lubbock, regarding the 
tide-wave, gave an importance to the 
inquiries which had induced Mr. Russel 
to prosecute the investigation in such a 
manner, as to render it subservient to 
the improvement of a department of sci- 
ence, of which the applications are so 
highly important. 
Much confusion has arisen from con- 
founding different species of waves fol- 
lowing different laws. Mr. Russell has 
observed four species ; — 3. Waves of 
the first species are seen in what is com- 
monly called ripple on the surface of a 
pool ; these may be called dentated, and 
are not propagated beyond the place of 
their generation ; 2. Waves of the second 
species, or oscillatory waves, are found 
when a stone is dropped into a quiescent 
fluid, and these succeed each other in 
concentric rings — these are the waves of 
Newton and Young, and correspond to 
the second species of Poisson ; they are 
propagated with a velocity proportioned 
to the magnitude of the displaced fluid ; 
3. The third species of waves are called 
breakers, surges, and tidal-bores; and 
4. The fourth species of waves, is the 
solitary wave, analogous to the great 
tidal wave of the ocean; it is propagated 
with nearly a uniform velocity. The two 
last species, tlie surge and the solitary 
were, are the subjects of this investiga- 
tion. It was observed, 1st, When a 
considerable and permanent addition is 
made to the volume of a limited portion 
of fluid contained in an open reservoir, 
such addition produces an elevation of 
the surface of the fluid, which is propa- 
gated in the form of a solitary wave, 
moving with a velocity nearly uniform. 
2nd, The velocity of the propagation 
of such waves, is equal to that vvhich 
would be acquired by a heavy body, in 
falling through a space equal to half the 
fluid. 3rd, The length of such a wave is 
nearly constant for a given depth. 4th. 
The height of the wave varies with its 
volume, and must be added to the depth 
of the fluid, in calculating the velocity 
according to art. 5th, When the height 
of a wave exceeds twice the depth, it 
form ceases to be a form of equilibrium, 
and it breaks. Gth, When the anterior 
part of a wave is found at a depth less 
than that of the posterior portion, and 
the height is greater than twice the 
depth, the wave curls forward, forming 
the common surge. 7tb, when the width 
of a channel diminishes in an arithmeti- 
cal ratio, the height of the wave increases 
in a geometrical one, until it exceeds 
twice the depth, when it breaks. 
The Members expressed their satis- 
faction at the ingenious devices by 
which Mr. Russell had contrived to 
effect his observations — as where he 
noted the arrival of the wave at a 
given position, by placing a white rod 
across the top of the canal along 
which the wave was propagated, and 
watching its image in the approaching 
wave: while the inclined part of the 
wave was passing under it, the reflected 
image of the white rod was transferred, 
of course, to a considerable angular dis- 
tance, ; but as soon as the top came 
under the rod, a very small portion of it 
being horizontal, the reflected image 
assumed a position exactly beneath the 
rod. By this most ingenious contri- 
vance, he was enabled to determine both 
the velocity of the wave, and, to some 
extent, its length, and ultimately its 
form. The clear manner in which his 
experimental results explained the 
change of form of the greater wave, by 
the incompatable velocities of two waves 
of a lower height, at first generated, un- 
