experimental data are not possible. However, indirect comparisons are possible. The first step in a 

 comparison is to determine the experimental values of co 0m , Q, a, and e. Then to 0c is set equal to co 0m and s 

 calculated utilizing equations IV- 1 and IV- 18 and figure 1 . If surface tension has a negligible effect on co 0m , s 

 can be assumed to be equal to 10" dyne/cm, based on the data given in Appendix A. Q rad and Q th are then 

 calculated from equations IV-4 and IV-6 and Q VIS is determined from the equation: 



1 1.1 1 



(IV-19) 



Q 



+ 



+ 



Qrad Qvis Qth 



Finally, £, is calculated from equation IV-5. The results of this procedure are given in Table II, where L is the 

 fish length, D, a, co 0m , and Q are experimental data, and s and E, are calculated by equating the model to the 

 data. 



The new model can be indirectly compared to the experimental data by examining the values of s and J; 

 given in Table II. The values shown in Table II are within the limits chosen in Appendix A to give reasonable 

 ranges for s and <;. This is a necessary condition for the model to be valid, but it is by no means a sufficient 

 condition. In order that the model can be used with some degree of confidence to predict resonant 

 scattering from swimbladder-bearing fish, the variations in s and <; shown in Table II must also be explained. 



The five sets of data can be separated into two groups, based upon the magnitude of tension in the 

 swimbladder wall. Swimbladder tension had little or no effect on the measurements made by Coate, Batzler and 

 Pickwell, and Sundnes and Sand, where s < 10 s dyne/cm. Swimbladder tension appears to have had a significant 

 effect on the measurements by McCartney and stubbs and Sand and Hawkins, where 

 2 x 10 s dyne/cm < s < 4 x 10 6 dyne/cm. 



Table II — Experimental Data and Results of Comparisons to the New Model 



29 



