LOCOMOTION OF FISHES. 



253 



nf h>ri>inotive act, 



^li. C-\XXJ. 



flexion in e o, acts backward, in tlic direction of o e ; havinf; 

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

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

 if the tAvo forces c h and c h 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 c f, but in a 

 curved line, evenly between d ey"and a line 

 drawn parallel to it tln-ough /(. The fish 

 being in motion, the tail descril)es 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 ])roblem ; its plane may be 

 perpendicidar to the stroke's direction, and 

 its expansion greatest at the begiiniing 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 nuich 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 vertelDra; 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 f(.)ld of 

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

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

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

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

 or ha3mal fold, with the developement therein of rays, and with an 

 upward or neural inclination of the supporting vertebras. Shorter 

 rays are developed in the shalhjwer neural fold, which terminates 

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

 the ha?.mal fold, which are the longest, form a second point. The 

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



' By tliis latter terra M. Agassiz signifies a subscrnient grade of moilificatiDn and 

 developement, and a grave fallaey lurks in its misapplieation totheeonimon embryonal 

 condition of the tail-fin in Fishes, as by the Author of cxcvin. 



