HUNTER and ZWEIFEL: SWIMMING SPEED AND TAIL BEAT FREQUENCY 



support-plane intervals for «^ in all species in- 

 cluded unity (Table 3). Clearly if a common 

 slope-length coefficient exists among these spe- 

 cies, it must be close to 1. We conclude the 

 assumption of unity for the slope-length co- 

 -efficient is an acceptable practice and that it 

 appears to introduce no significant bias in the 

 species studied. 



We now turn to the problem of estimation 

 of the length-dependent coefficient for the in- 

 tercept of the speed-tail beat relationship, that 

 is, a.,. We noted previously that the biological 

 significance of the existence of an intercept dif- 

 ferent from zero in the speed-frequency rela- 

 tionship may be that fish have a minimum speed 

 below which they cannot swim by movements 

 of the caudal fin. If we assume that the inter- 

 cept is a function of the minimum swimming 

 speed of a fish we can make an independent esti- 

 mate of the intercept coefficient using an equa- 

 tion derived by Magnuson (1970) for estimation 



of the minimum swimming speed (Vo) of E. 

 affinis. A somewhat simplified form of his equa- 

 tion is: 



Vo = 



1 — 





g * Ma 



(C«A/0 * — 

 2 



where D,. is 1.025 (the density of sea water), 

 Df is the density of the fish, g is 980 cm/sec 

 (the acceleration of gravity), Ma is mass of 

 fish in air, Cu is the coefficient of lift for the 

 pectorals (assumed to equal 1), Aft is the total 

 lifting area of the extended pectoral fins in 

 square centimeters, and p is the density of sea 

 water, 1.025 g/cc. If we let Ma = 0.004407 

 7^321215 (i^jjg length-weight relationship for T. 

 symmetrictis, N = 264, unpublished data, Na- 



Tarle 3. — Estimates of length coefficients for slope and intercept for five 



species of fish. 



1 Simultaneous confidence intervals for all poronneters (Conway, Glass, and Wilcox, 1970). 

 a Data from Boinbridge (1958). 



259 



