Zeldis et ai: An estimate of biomass of Hoplostethus atlanticus 
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Another situation in which the assumptions clearly did 
not hold was at the 13 stations where z nl > w v For these 
stations, z x was set equal to w v and P nl was taken to be 
vertically below P vV 
Calculating the net path during hauling 
From assumptions 1 and 3, the position of the vessel and 
length of the warp at any time during hauling was calcu- 
lated by using 
In solving Equation A13, the solution using the positive 
square root was ignored because it led to large values of 
p(t) and large vertical oscillations in the net path. 
Flow of water through the net 
Because, by assumption 4 above, the net mouth was al- 
ways perpendicular to the warp, the flow of water through 
the net at time t (in m3/s) is given by 
Fit) = 2V_ nw *U wp , (A14) 
P v (t) 
(*2 -*>£■! +<*-*■>£. 2 
«2-fl) 
where V nw is the velocity of the net relative to the water, 
given approximately by 
and 
wit) = P v (t)~ P n it) = 
(t 2 - t)w 1 
%-k) 
(A7) 
V 
P n it+8t)-P n it) 
~5t 
C(z n it)), 
(A15) 
To calculate the position of the net during hauling, we 
made one further assumption: that the velocity of the net 
is the sum of the water velocity and a vector in the direc- 
tion of the warp. With this assumption, an iterative pro- 
cedure was used to calculate P it) at times t { +*t, t x +2*t, 
etc, for a small time interval *t. The basis of this proce- 
dure is the ability to calculate P n it+*t) once P n it) is known. 
This is done as follows. 
The velocity assumption may written approximately as 
H is a unit vector in the direction of the warp, given by 
jj _ £,(*)-£„(*) 
~ uip \P v (t)-P n (t)\’ (A16) 
and factor 2 is the net mouth area in m 2 . 
Calculation of correction factors 
P n (t + 8t) -P.it) ... P v (t)-P n (t) . . .... 
pU) j~ +C[z n (t)), (A8) 
St 
\P .it) -P.it) 
where pit) is an unknown scalar which varies with t. Re- 
placing t by t+*t in Equation A7, we get 
| (A9) 
and substituting for P it+*t) from Equation A8, Equation 
A9 may be rewritten as 
where 
and 
|p(f )A + JBl = — 2 * 6t)Wl , 
A = — (<a / tl)5t {P v (t)-P n (t)) 
w 1 (t 2 - 1 ) v 
(A10) 
(All) 
B = P v (t +8t)-P n (t)-8tC{z n (t)]. (A12) 
Expanding Equation A10, we get the quadratic equation 
A • Ap(t) 2 +2 A • Bp(t) + B • B 
( t 2 -t-8t)w l 
(t 2 -tA 
which may be solved for pit) in the usual manner. 
(A13) 
The correction factor associated with a horizontal layer of 
water is given by 
CF = 
Thickness of layer 
Volume of water filtered by net within layer 
(A17) 
Thus, for the layer of water that the net passed through 
between times t and t+*t, the correction factor is given 
approximately by 
z n (t) - z n (t +8t) 
F(t)8t 
which is treated as the correction factor associated with 
depth z n it). Thus, for each plankton tow, correction fac- 
tors for depths z n (tf) (=z nl ), 2„(f 1 +*f), z n (t l +2*t), etc. were 
calculated. 
Finally, the correction factor for a given egg stage at a 
given plankton tow was calculated, by interpolation, as 
the correction factor at the mid-point of the depth layer 
associated with that egg stage. 
Appendix 2: Calculation of centroids 
This appendix describes the procedure for calculating the 
centroid (= center of gravity) of each age group (plotted in 
