184 
BULLETIN OF THE BUREAU OF FISHERIES 
Since the amount of pulp liquor in the bay bears the constant ratio of 
a 
( 4 ) 
d + b 
to the value of pulp liquor plus new water, therefore the proportion of pulp liquor (p) 
to the total volume of the bay may be expresses as 
Note— The writer wishes to acknowledge the assistance of Prof. Harold Hotelling of Stanford University in mathmatical 
problems considered above. 
The assumptions made in the derivation of this formula are the source of a small 
error, but do not rob the results of their significance. In this case it is assumed that 
the liquor mixed instantaneously and completely with the water and that the inflow 
of both liquor and water is a continuous process rather than a discontinuous one. 
Over a long period of time the error due to these two assumptions is negligible although 
for a period of one or two days the error may be significant. Any error due to lack 
of mixing of the pulp liquor with the water would tend to increase the amount of 
liquor in the bay. 
By the use of equation 5, the increase in concentration of liquor in Oakland Bay 
has been calculated, assuming that 70,000 gallons of liquor per day were discharged 
at the mill. (Table 10.) At first the concentration rises rapidly but at a constantly 
decreasing rate as equilibrium is approached. As the time factor increases the value 
of expression (5) approaches the value (4) which expresses the equilibrium concen- 
tration, being in this case 1 part of liquor to 931 parts of sea water. 
The effect of sulphite liquor in various dilutions upon oysters is not within the 
scope of field observations. From data herein given it is concluded that any sulphite 
waste liquor dumped into Oakland Bay at the Rainier Pulp & Paper Co. plant of 
necessity must reach the oyster beds. From the physical character of the liquor and 
from observations, it is apparent that when concentrated liquor is discharged at the 
mill the accumulation over the oyster beds is greatest near the bottom. Due to the 
variety of currents the water above the bottom is not comparable to that in which 
the oysters live, and examinations of water taken at arbitrary locations about the 
bay can not indicate the conditions with which the oysters must contend. Chemical 
analysis of the water is not a complete index to the concentration of sulphite waste 
liquor because the chemical nature of the substances contained therein is unknown. 
The “oxygen balance” test for the detection of sulphite liquor can not be considered 
in this problem because no work has ever shown either that the toxicity of sulphite 
liquor to oysters is in any way proportional to its oxygen demand or that such liquor 
may not exist unchanged in a toxic state in the presence of dissolved oxygen. 
From these facts the following conclusions are drawn : 
(1) Conditions in Oakland Bay are unique in the history of oyster culture in 
Puget Sound. The adult oysters have experienced an abnormally high death-rate 
for some time, the living oysters spawn little if any, and no set has been obtained in 
three years. 
( 5 ) 
CONCLUSIONS 
