LOCOMOTION OF FISHES. 



253 



159 



Diagram of locomotive act, 

 Fish, cxxxi. 



flexion in e o, acts backward, in the direction of o e ; having 

 reached the point o, it is again forcibly bent in the line o e, 

 causing an impulse on the centre of gravity in c b, parallel to o e ; 

 if the two forces c h and c b acted simul- 

 taneously, we should obtain the resultant 

 c f\ but, as they do not, the point c will 

 not move exactly in the line cf, but in a 

 curved line, evenly between 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 station- 

 ary, it would describe the arc of a circle. 

 The power of varying the position and ex- 

 panse of the tail-fin during the side-strokes 

 complicates the problem ; its plane may be 

 perpendicular to the stroke's direction, and 

 its expansion greatest at the beginning of 

 the stroke, as in a i ; and it may be oblique 

 to the direction of the rest of the stroke, 

 as in e o, with contraction of the surface. It 

 must, further, be considered that the water 

 having been set in motion by flexion in one direction, produces, 

 when meeting the tail moving in the opposite direction, a resis- 

 tance proportional to the sum of the squares of the two velocities. 

 The shape of the caudal fin varies much in fishes, according 

 to the kind and degree of motion required : in the imprisoned 

 embryo, or newly-hatched fry, in the long and slender undulating 

 eel, in the sluggish Lepidosiren, the vertebras continue to the end 

 of the body in a straight line, distinct, and decreasing to a point ; 

 and the tail is bordered above and below by a vertical fold of 

 skin; terminating either in a point, as in fig. 100, or obtusely. 

 Such fold or fin is symmetrical, but not f homocercal.' l The 

 vertical folds deepen ; at first, in some Plagiostomes, e. g., 

 equably, forming a terminal lobe ; then excessively, in the lower 

 or haemal fold, with the developement therein of rays, and with an 

 upward or neural inclination of the supporting vertebra. Shorter 

 rays are developed in the shallower neural fold, which terminates 

 at the pointed end of the vertebral series. The anterior rays of 

 the hasmal fold, which are the longest, form a second point. The 

 tail-fin is thus bifurcate, but unsymmetrical ; and this stage of 



1 By this latter term M. Agassiz signifies a subsequent grade of modification and 

 developement, and a grave fallacy lurks in its misapplication to the common embryonal 

 condition of the tail-fia in Fishes, as by the Author of cxcvm. 



