FISHERY BULLETIN; VOL. 72, NO. 4 



Tr 



standard metabolism 



internal cost of food utilization. 



The growth efficiency and subsequent relations 

 derived from Ty. are important in estimating fish 

 yields in relation to standing food resources and 

 other factors important to fisheries management. 

 It is this larger view which gives relevance to the 

 rather involved procedure of simply calculating 

 one part of the value of T-,, namely Tp. 



THEORY 



The derivation of the excursion energy esti- 

 mate is based on Gray and Hancock's (1955) de- 

 velopment for spermatozoa. Instead of a cylinder 

 with an inert head attached, the anchovy larva is 

 regarded here as a ribbon or plate of specified 

 width attached to an inert head (Figure 1). The 

 assumption that the body is a ribbon is justified 

 only if the ratio of the width to thickness (Wit) is 

 » 1. In the larvae examined in this study this 

 ratio averaged 2.5. While this ratio is not » 1 I 

 have assumed that it is to simplify the problem. 

 However, the error introduced is, I believe, min- 

 imal. 



From Figure 1 the following relation is noted 

 and will be used in the following derivations: 



With the body approximated as an inextensible 

 ribbon we find the use of the normal drag 

 coefficient, Ca^ , and the tangential drag 

 coefficient, C^, convenient in addition to an ap- 

 propriate sagittal contour function h{s ) where s 

 denotes distance along the spine of the fish (see 

 Figure 4). 



The expression for the velocities Vy and Vj is 

 first expressed in terms of the function which rep- 

 resents the propagated wave along the body 

 y{x,t), and V^^ . By noting, 



dy dy 



Vy = — and tan 9 =^- 



dt dx 



we can rewrite Equations (1) and (2) as. 



V^ dy dy 



T- ■= — Vr —, — and 



cos Q dt dx 



Vj _ dy dy 

 COS0 ~ ~dt ~dx 



Given cos Q 



1 



[1 + tan2 0]i2 



1 + 



m 



1/2 



we 



-' -^- 1 -.!][€): 



-1/2 



(!') 



y V = ^v cos e - y, sin e 



Vr^ = Vy sin e + V, COS B 



where V^ = normal velocity of an element 

 of body 

 Vf = tangential component 

 Vy = ^-component 

 V^ = x-component. 



(1) 



(2) 



Figure 1. — Diagram illustrating the relationship of the velocity 

 components of an element of body when moving transversely in 

 the X-direction. 



i. 



^^ \dt dx ^' 



] [ ^m 



-1/2 



(2') 



Now we may proceed to write the contributions to 

 the total work of excursion made by the head, 

 body viscous reactive terms, and accelerative 

 body virtual mass. 



The element of work performed in moving the 

 inert head is given by, 



dV 

 dW^ =1/2 p Cf^A ^3 dt + (m + M) ^ V, dt 



886 



