438 
the intensity of their action (all other things re~ 
maining the same) must be proportional to their 
areas respectively. Sometimes the Rays glide 
sideways, in which motion the pectoral and 
caudal fins exchange their office, the former 
striking horizontally, and the latter vertically, 
the result of which may be obtained by the 
composition of forces, when their directions 
and intensities are given. The Rays, being 
destitute of an air-bladder, require a much 
greater force in the vertical direction upwards 
to sustain themselves in swimming ; hence the 
necessity for the power and mobility of the 
ral fins which we find conferred on them. 
e great lateral development of the surface of 
the Rays compared with their depth, and the 
great depth of the Pleuronectides compared 
with their breadth, entitle the former, rather 
than the latter, as Mr. Yarrell justly observes, 
to the appellation of flat fish. 
The first movement of a fish from a state of 
rest is usually produced by the flexion of its 
tail, as to a, fig. 232; during this action 
the centre of gravity (c) recedes slightly from 
its previous position ; the tail being flexed into 
the position a, is forcibly extended by the 
muscles on the opposite side, in the direction 
of the line a i, perpendicular to its plane. 
The force of its action upon the water in a i 
is translated to the body of the fish in ¢ a, 
causing the centre of gravity c to move obliquely 
forwards in the direction of ¢ A, parallel to i a. 
The tail having reached the mesial line c d, its 
power of urging the centre of gravity forwards 
not only ceases, but during its flexion in eo, 
it acts backwards in the direction of o e ; having 
reached the point 0, it is again forcibly ex- 
tended in the line o e, causing an impulse on 
the centre of gravity in c 6, parallel to oe; if 
the two forces c A and c 6 acted simulta- 
neously, we should obtain the resultant cf, but 
as they do not, the point c will not move ex- 
actly in the right line cf, but in a curved line, 
which lies evenly be- 
tween d c f and a 
line drawn parallel 
to it through k. The 
fish being in motion, 
the tail describes the 
arc of an ellipse,* 
whereas if it were 
stationary, it would 
describe the arc of a 
circle. If we sup- 
pose the force re- 
sulting from the flex- 
ion of the tail to be so 
great as to neutralise 
the velocity which the 
centre of gravity had 
acquired during its 
extension, the result 
would be a state of 
rest whenever the tail 
reached the points a 
and o, and a greater 
force than this would 
Fig. 232. 
* Borelli, loco cit. prop. 24, p. 259. 
MOTION. 
cause it to recede; which, i r Jol 
Lubbock,* is the case, although it pever 
been detected in the movements of the li 
animal. The minute investigation of this: 
ject, however, embraces a very complex 
lysis. There are several circumstances w 
militate against the hypothesis of Sir 
Lubbock ; first, the muscles which move th 
tail are capable of varying its surface during 
flexion and extension, and of contracting ii 
during the former and expanding it during the 
latter action, by which the resistance is propor= 
tionably varied. Secondly, the muscles of th 
tail incline its plane to the direction of its mo- 
tion during flexion, and present its plane 
pendicularly to that direction during extens 
which causes the effective resistances in the 
strokes to be to each other as 1 : s*, where 
is the sine of the inclination of the tail to th 
horizon. Thirdly, according to Dr. Roget, the 
water having been set in motion during the 
tension of the tail, in the same direction, a 
comparatively but little resistance in flexion 
on the contrary, when the motion of the tail 
is reversed, the water meeting it in an op 
direction produces a resistance proport 
the sum of the squares of the two 
These are so many causes which contrib: 
diminish the force of the tail during its flexio 
without producing a retrograde motion in the 
fish. e same demonstration serves whe 
the plane of the tail is directed horizontally, 
in the Cetacea and Flat Fishes, but # 
pulse given must be estimated in a vertical 
stead of a horizontal plane. The velo 
some fishes is very considerable, and 
maintained for lengthened periods. ord 
to Lacepede, that of the Salmon is eight r 
or 26°24 feet in a second; others are said 
to travel upwards of sixteen miles in an hb 
the Shark, for instance, will often Ly 
and gambol around a ship in full sail ae oss t 
Atlantic. In those fishes which have the gre 
est velocity the tail is forked, the area is 
inverse ratio of the distance from the centre | 
gravity; in these the centre of force is ¢ 
half the distance from the centre of motio 
When the tail presents a triangular surfa 
of which the apex is the centre of motion, 
centre of force is three-fourths the distances 
its base from the axis of oscillation. With 
form of tail the muscles act at a mechan 
disadvantage, and consequently the ani 
moves very slowly. ~ 
If we consider the density of the m 
in which these animals move, the 
which it opposes to their bodies, and # 
periods during which they will continue 
progression, we may form some idea of 
great energy with which their muscular sys 
is endowed. ie 
Aquatic Birds.—In the Aquatic 
thorax and abdominal regions present a fo 
* See Dr. Roget’s Bridgewater Treatise, 1 " 
369. 
~~) 
~ 
accom) 
= 
‘eS 
2 +t See Chabricr, Mém. de l’Acad. des 
tom. xi. In this paper formule are given: or 
ing the velocity of the centre of the tail 
quantity of action expended in swimming. — 
a4 
bid 
a 
