There are essentially two sources of the variations in the calculated values of E, between the two groups 

 and within the group where s> 2 x 10 5 dyne/cm. One source is the experimental data and the other is the 

 model. The most likely, and probably greatest, source of error in the experimental data is the uncertainty in 

 swimbladder volume. Since the calculated values of E, are proportional to a 2 , an error in a can cause a large 

 error in E,. However, as mentioned earlier, the experimental data were examined assuming various 

 swimbladder volume-depth relationships. None of these relationships produced consistent results or values 

 as low as those obtained for the first group, although in some cases the variability was reduced. For example, 

 if a constant a=0.69 cm is assumed for the cod examined by Sand and Hawkins, ^varies from 1 ,500 to 900 

 poise as the depth increases from 25 to 50 m. This variation is smaller than that for the swimbladder-depth 

 relationship which was utilized, but the values are still much higher than those of the first group and are by no 

 means consistent. It is possible, though, that the cod-like fish, which have a well-developed muscle system, 

 have an intrinsically higher tissue viscosity than fish such as goldfish or anchovies. 

 At the beginning of this chapter, it was assumed that 

 E, < 2 x 10 3 poise 

 and the equations were simplified accordingly. It might be suspected that this could be a source of error in the 

 cases where E, > 2 x 10 3 poise. However, the error caused by simplifying equations III-26 and III-34 to 

 equations IV-1 and IV-2 is less than ten percent for values as high as E, = 6 x 10 3 poise. Thus, the simplified 

 equations are not a significant source of error. 



The other primary source of error is the model itself. Since it does not seem to be possible to attribute all 

 the variations in E, to the errors in the data, it appears that the remaining variations are due to inadequacies 

 in the model. 



An examination of all the data in Table II indicates that ^generally increases with s. There is no indication 

 that this is so for the group of data for which s < 10 s dyne/cm. However, there is definite correlation between s 

 and E, when the two groups of data are compared. Also, despite the wide variations of E, within the group of 

 data for which s > 2 x 10 5 dyne/cm, there is a rough indication that E, increases with s for this group of data. 

 Thus, it appears that increasing tension in the swimbladder wall has little or no effect on E, for s < 1 5 dyne/cm, 

 but that it does cause E, to increase for s > 2 x 1 s dyne/cm. The apparent increase in viscosity with increasing 

 tension in the swimbladder wall for s > 2 x lOsdyne/cm would not be expected to occur in a Newtonian 

 fluid. This indicates that modelling a fish as a Newtonian fluid may not be appropriate for s > 2 x 10 5 

 dyne/cm and that some type of non-Newtonian model, such as a dilatant or viscoelastic fluid, may be more 

 appropriate. However, the present model is appropriate for s < 10 5 dyne/cm. 



31 



