368 THE MECHANICAL FUNCTIONS. 



of the fish having expended their principal force 

 in the extension of the tail from ii to m, that is, in 

 bringing it to a straight line with the body, exert a 

 weaker force in bending it from m to l, and conse- 

 quently the reaction of the water is in the same 

 proportion more feeble. When, again, the tail has 

 arrived at the position l, a similar energetic action 

 of the muscles on the right side of the fish, creates 

 a powerful resistance in the water, which now acts 

 in the direction k l, and consequently gives an 

 impulse to the whole fish in the same direction a ; 

 and this reaction of the water is the stronger, inas- 

 much as it was previously moving, together with 

 the tail, in the opposite direction k l. Thus do the 

 alternate movements of the tail to the right and to 

 the left give to the fish alternate impulses in the 

 directions cb and ca; and these impulses being 

 repeated in quick succession, the body moves for- 



opposed by the more resisting mass of water previously set in motion 

 by the first lateral stroke of the tail. 



In the popular view given in the text, I have also purposely 

 omitted to notice some mechanical circumstances, which, in a more 

 accurate mathematical analysis of the problem, would claim atten- 

 tion as having a sensible influence on the results. It is to be con- 

 sidered, in the first place, that a motion of rotation round the centre 

 of gravity \yill be given to the fish by every impulse, the direction 

 of which does not pass through that centre The muscular action by 

 which the tail is first bent from m to R, gives, by the reaction of the fluid, 

 an impulse in the contrary direction, and hence a rotatory force is 

 created, which turns the snout round c, towards b ; and the contrary 

 effect is produced by the opposite motion of the tail from r to l, 

 whereby the snout is turned back towards a. It is next to be 

 observed, that the first action of the tail when changing its position 

 is more energetic than during the remainder of the stroke, when its 

 velocity gradually diminishes till it is brought to rest, preparatory 

 to its reversing its motion. As the angle which the tail makes with 



