438 



MOTION. 



the intensity of their action (all oilier 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 

 pectoral fins which we find conferred on them. 

 The 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, Jig. 232 ; during this action 

 the centre of gravity (c) recedes slightly from 

 its previous position ; the tail being flexed into 

 the position , 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 i , 

 causing the centre of gravity c to move obliquely 

 forwards in the direction of c h, parallel to i a. 

 The tail having reached the mesial line c d t its 

 power of urging the centre of gravity forwards 

 not only ceases, but during its flexion in e 0, 

 it acts backwards in the direction of o e ; having 

 reached the point o, it is again forcibly ex- 

 tended in the line o f, causing an impulse on 

 the centre of gravity in c b, parallel to o e ; if 

 the two forces c li and c b acted simulta- 

 neously, we should obtain the resultant cj] 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- 



Fig. 232. 



tween d c f and a 

 line drawn parallel 

 to it through h. 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 



Borclli, loco cit. prop. '24, p. 259. 



cause it to recede; which, according to Sir John 

 Lubbock,* is the case, although it has never yet 

 been detected in the movements of the living 

 animal. The minute investigation of this sub- 

 ject, however, embraces a very complex ana- 

 lysis.f There are several circumstances which 

 militate against the hypothesis of Sir John 

 Lubbock ; first, the muscles which move the 

 tail are capable of varying its surface during 

 flexion and extension, and of contracting it 

 during the former and expanding it during the 

 latter action, by which the resistance is propor- 

 tionably varied. Secondly, the muscles of the 

 tail incline its plane to the direction of its mo- 

 tion during flexion, and present its plane per- 

 pendicularly to that direction during extension, 

 which causes the effective resistances in the two 

 strokes to be to each other as 1 : .s 3 , where s 

 is the sine of the inclination of the tail to the 

 horizon. Thirdly, according to Dr. Roget, the 

 water having been set in motion during the ex- 

 tension of the tail, in the same direction, offers 

 comparatively but little resistance in flexion ; 

 on the contrary, when the motion of the tail 

 is reversed, the water meeting it in an opposite 

 direction produces a resistance proportional to 

 the sum of the squares of the two velocities. 

 These are so many causes which contribute to 

 diminish the force of the tail during its flexion,, 

 without producing a retrograde motion in the 

 fish. The same demonstration serves when 

 the plane of the tail is directed horizontally, as 

 in the Cetacea and Flat Fishes, but the im- 

 pulse given must be estimated in a vertical in- 

 stead of a horizontal plane. The velocity of 

 some fishes is very considerable, and often 

 maintained for lengthened periods. According 

 to Lacepede, that of the Salmon is eight metres, 

 or 26'24 feet in a second ; others are said also 

 to travel upwards of sixteen miles in an hour ; 

 the Shark, for instance, will often accompany 

 and gambol around a ship in full sail across the 

 Atlantic. In those fishes which have the great- 

 est velocity the tail is forked, the area is in the 

 inverse ratio of the distance from the centre of 

 gravity ; in these the centre of force is one 

 half the distance from the centre of motion. 

 When the tail presents a triangular surface, 

 of which the apex is the centre of motion, the 

 centre of force is three-fourths the distance of 

 its base from the axis of oscillation. With this 

 form of tail the muscles act at a mechanical 

 disadvantage, and consequently the animal 

 moves very slowly. 



If we consider the density of the medium 

 in which these animals move, the resistance 

 which it opposes to their bodies, and the long 

 periods during which they will continue in 

 progression, we may form some idea of the 

 great energy with which their muscular system 

 is endowed. 



Aquatic Birds. In the Aquatic Birds, the 

 thorax and abdominal regions present a form 



* See Dr. Roget's Btidgewater Treatise, vol. i. 

 p. 369. 



f See Chabrier, Mem. do 1'Acad. des Sc. 

 torn. xi. In thU paper formulae are given for find- 

 ilia; the velocity of the centre of the tail and the 

 quantity of action expended in swimming. 



