The total range of data is 



4 poise < E, < 1 ,800 poise. 



Thus, for this study, limits of 



1 poise < S; < 10 4 poise 

 will be used, with a more likely range being 

 50 poise < £, < 2 x 10 3 poise. 



The swimbladder wall of a fish is a membrane which is capable of supporting tension. In the present 

 model, the swimbladder wall has zero thickness, so that the tension in the membrane is effectively a surface 

 tension. Measurements of the internal swimbladder pressure can be used to calculate surface tension 

 since 



AP = (2s/a), (A" 6 ) 



where AP is the difference between the internal swimbladder pressure and the ambient pressure [50]. 

 Several researchers have measured internal swimbladder pressures, but since it is probable that a fish can 

 control the tension in the swimbladder wall, only measurements on live, unanesthetized, fish are 

 considered. Excess internal pressures from 2 x 10 4 to 6 x 10 5 dynes/cm 2 have been measured in fishes 

 which were 2 to 20 cm long [A17]. These results correspond to surface tensions of 6 x 10 3 to 7 x 10 4 

 dyne/cm for fish with swimbladder radii of about 0.1 to 1 .0 cm. The majority of these fish were less than 10 

 cm long with swimbladder radii less than 0.5 cm. 



Surface tension is probably a function of fish size, so that measurements on larger fish are needed for 

 the present study. No measurements of excess pressure of larger, unanesthetized fish are available. 

 However, another means can be used to estimate the upper limits of surface tension in larger fishes. As 

 discussed in the text, Sand and Hawkins have attributed high experimental resonant frequencies to 

 swimbladder tension [33]. If this is true, then an upper limit of surface tension can be calculated by 

 assuming that the fish is a free bubble with surface tension and utilizing equation 1-12, neglecting viscosity, 

 and equation I-25 to account for spheriodal swimbladder shapes. Although this method does not 

 necessarily give accurate estimates of surface tension, it does produce values which can be used as upper 

 limits. These limits are useful because it is the possible range of surface tension that is required. Surface 

 tensions calculated from resonance measurements range from about 10 6 to 10 8 dyne/cm for swimbladder 

 radii from 1 to 2.5 cm [33,37]. 



The surface tension of an air bubble in water is 74 dyne/cm [50]. Hence, the range of surface tension for 

 small swimbladders (a» 0.1 cm) is chosen to be 



10 2 dyne/cm S s 2 10 6 dyne/cm. 



For larger swimbladders (a«5 cm) the range is chosen to be 



10 2 dyne/cm - s ^ 10 s dyne/cm. 



39 



