Andreeva and Chindonova (1964) simplified equation (2) io 

 (H + 30) ^/2 



f. = 1.5 



(Vbi) i/3 





where f^ is in kHz, H is the depth in meters, and W^\ is the volume of the 

 swimbladder in mm^. From Haslett's consideration of fish dimensions (Haslett, 

 1962), fish volume is related to fish length (L) by the expression 



Vfi3h = 0.01 l3. (4) 



Following Marshall's assumption (1951) that the volume of the swimbladder in 

 a marine fish is about 5 percent of the volume of the fish, the swimbladder 

 volume can be expressed as 



Vbi = 5 X 10 ""^ l3, (5) 



By combining equations (3) and (5) an expression is given for fish length as 



'r 



where L is in cm. 



Although Capen's measurements of swimbladders in dissected fish (Capen, 

 1967) as well as our own, indicate that in bathypelagic fish, the expression 

 Vbi - 0.05 Vfjg^ is not entirely accurate, the direct measurements of swimbladder 

 volume by Kanwisher and Ebeling (1957) agree well with this relationship. Since 

 the term (H + 30) v 2 takes fish tissue effects into account as mentioned above, 

 equation (6) can be modified to 



L .1M1M}/1 (7) 



'r 



This equation neglects tissue effects for these deep layers, and was used to estimate 

 the range of fish lengths for the two layers (Table V) reported by Gold and Van 

 Schuyler (op.cit.). 



As previously discussed, the 1000 m to 800 m sample from tow 1-D in 

 November 1965 yielded the relatively high fish concentration of 29.6 fish/1000 m 

 (Table III), primarily due to the large number of Cyclothone braueri and 

 C. microdon . However, none of the specimens of swimbladder bearing fish 

 collected even approaches 11 .0 cm in length, the theoretical size for 5-6 kHz 



27 



