(417.) 
Naval ar- 
chitecture. 
(418.) 
Resisted 
motion of 
projectiles, 
(419.) 
Experi- 
ments on 
waves in 
water. 
(420.) 
Observa- 
tions of 
MM. We- 
"ber on the 
form of 
waves. 
888 
dulum mentioned in Art. (246), and the agreement 
appears satisfactory, With reference to Coulomb’s 
experiments on oscillating disks there remains some 
doubt whether the theory applies satisfactorily to 
viscid fluids such as oil, 
On the very difficult and still empirical subject of 
naval architecture as regards forms of least resist- 
ance, I shall not here speak; but one very interesting 
case of the resistance of fluids in canals will be noticed 
in the course of this section—Arts. (422), &c. 
The theory of military projectiles has perhaps re- 
ceived no improvement so considerable during the 
last 100 years as by the previous experiments of 
Robins, and the invention of the Ballistic Pendulum 
referred to in the preceding Dissertation; though the 
experiments of Borda in France, and of Hutton in 
this country, have of course increased the technical 
precision of artillery, Poisson has considered, in a 
mathematical way, some of the simpler cases of pro- 
jectiles moving with a moderate velocity. 
II. Experiments on Waves—MM. Weser—Mr 
Russetz.— Whilst the theory of the dilated and com- 
pressed waves which constitute sonorous vibrations 
in elastic fluids was being successfully investigated 
by Lagrange and Laplace, the case of waves in water, 
due to a disturbance of hydrostatic pressure only, 
was attacked by the same mathematicians with far 
less success. It is generally allowed that the more 
recent and abstruse researches of Poisson and M. 
Cauchy, though very valuable as improvements in 
pure mathematics, have been also singularly barren 
of valuable results admitting of the very desirable 
confirmation of direct experiment. The greatest of 
all hydrodynamical problems, that of the Tides, is, as 
has been seen in the second section of the chapter on 
Physical Astronomy, Art. (69) &c., so excessively 
complex as to be the last, instead of the first, which 
analysis might have been expected to resolve. 
When, on the other hand, we see the light which has 
been thrown even upon it by experiments on a com- 
paratively small scale, we learn to value them in 
proportion to their rarity. 
The brothers Ennst HeryrtcH WEBER and WILHELM 
Weser, known for many ingenious experiments in 
physics, and particularly in magnetism, are the authors 
of a useful book on waves.! They made experiments 
on the velocity of waves in glass troughs, by means of 
which they determined in several cases the velocity 
of the wave with different depths of fluid; they also 
ascertained mechanically the form of the wave, which 
they found to be that of the curve of sines. But the 
most important of the Webers’ experiments is pro- 
bably the determination of the motion of individual 
_ particles of the water, which they ascertained by 
watching from the exterior of the glass trough the 
MATHEMATICAL AND PHYSICAL SCIENCE. 
[Diss. VI. 
curve described by minute floating particles as the 
wave passed over them. The usual form of the trajec- Trajectory 
tory is an ellipse having the greater axis horizontal, the }: 
whole ellipse being described when the wave includes 
a ridge followed by a depression of the surface; but 
if there be only an elevated wave propagated, then a 
semi-ellipse is deseribed in the direction in which 
the wave moves, and the particle returns to rest in a 
new position; if the wave be a hollow one the con- 
verse takes place. The limits of oscillation diminish 
with the depth of the fluid, particularly the vertical 
limits; consequently at some depth the motion of 
the particles is nearly in a short straight line. The 
rapidity of the degradation of the individual motions 
depends on the relation between the length of a wave 
compared to the depth of the fluid: where the wave 
is very short compared to the depth of fluid, the el- 
lipses near the surface become circles, and the mo- 
tion rapidly disappears beneath; when the length of 
the wave is great compared to the depth of fluid, 
the motion of the particles is nearly the same from 
top to bottom. The conclusions of theory are on the 
whole confirmed by these experiments. 
The experiments of Mr Joun Scorr RussEx1, so Sear 
far as we shall notice them, refer to two closely con- 
nected subjects :—the transmission of waves, and oxperi- 
the resistance of water to vessels propelled through ments on 
They are principally to be ¥®V°- 
it as affected by waves. 
found in the Edinburgh Transactions, vol. xiv., and 
the British Association Report for 1837. The velo- 
city of waves in troughs of different depths and sec- 
tions was ascertained by allowing the wave to be re- 
flected at either end of the trough, which does not in 
any way affect the time of its propagation, and gives 
great facility for accurate observation, as the distance 
travelled over may thus become large, at the same 
time that all casual and interfering waves are gra- 
dually eliminated, The instant of the passage of 
the wave was ascertained by reflecting the light of a 
candle vertically upwards from its horizontal sum- 
mit. The length of the trough was 20 feet, but 
since the wave was made to traverse it as often as 
60 times, a distance of 1200 feet was really ob- 
served. The waves were single or “solitary” 
waves, either “positive” produced by a gush of 
water from behind a sluice, or “ negative” by with- 
drawing water suddenly. Mathematicians seem not 
agreed as to whether or not the “ solitary”? waves of 
Mr Russell are to be treated as a species apart.’ 
Unquestionably it has long been known that a par- 
tial wave either positive or negative may be propa- 
gated without any farther disturbance of the fluid. 
Theory also shows that the velocity of a wave long in 
proportion to the depth of the water is nearly as the 
square root of the depth; but it does not clearly ap- 
1 Wellenlehre auf experimente gegriindet, oder tiber die Wellen tropfbarer Fli. 
wellen. Leipzig, 1825. 
igkeiten mit dung auf die Schall und Licht- 
® Compare Mr Airy in the article “ Tides and Waves,”’ Encycl. Metropolitana; Prof. Stokes in British Assoc. Report for 1846, 
and Mr Earnshaw in Cambridge Zrans., vol, viii. 
