FISHERY BULLETIN: VOL. 75, NO. 2 



protein + O&G = 0.969 TR K . 



(7) 



This equation corrects the TR K so that it equals 

 the sum of the protein and O&G, and is convenient 

 to use in this form in the simultaneous equation. 

 The constant, 0.969, is the result of increasing the 

 analytical value for ash by 15.2% and represents, 

 in part, the difference in weight of ash between 

 drying at 500°C and 103°C. 



Simultaneous Equation 



In the preceding discussion we have shown the 

 two parts of the simultaneous equation: the first 

 showing the sum of the COD from protein and 

 from O&G to be equal to an adjusted total COD, 

 and the second showing the sum of the weights of 

 protein and O&G to be equal to the total residue 

 minus the ash content and corrected for the differ- 

 ence in weight caused by drying at 500°C or 103°C. 

 Equations (6) and (7) are combined in the follow- 

 ing so that a simple calculation can serve as a 

 substitute for the difficult direct analyses for pro- 

 tein and O&G: 



(8) 



X + Y = 0.969 TR K 

 1.338X + 2.678Y = 1.083 COD TR 



where: X = protein in milligrams/liter 

 Y = O&G in milligrams/liter. 



This equation should have general application to 

 fishery waste effluents provided: 1) TR K and 

 COD TR are known or can be derived, and 2) the 

 constant used to increase the value for COD TR has 

 general application. If our assumption is correct 

 that the COD is low because of the incomplete and 

 competitive oxidation of protein and O&G, the 

 constant would apply to any fishery waste having 

 a similar relative amount of protein and O&G, i.e., 

 about 5:1, respectively. 



The mean TR and ash data from Table 1 are 

 used to illustrate the use of this equation: From 

 Table 1, TR -- ash = 1,431 mg/liter and when 

 substituted into Equation (1) gives a value of 

 1,990 mg/liter for COD TR . These values, when sub- 

 stituted into the equation and solved forX and Y, 

 give, 



X + Y = 0.969(1,431) 

 1.338X + 2.678y = 1.083(1,990) 



where: X — 1,163 mg protein/liter 

 y = 224 mg O&G/liter. 



The calculated values are 29 mg higher for protein 

 and 12 mg lower for oil than the mean analytical 

 values of Table 1 (1,134 and 236, respectively). 

 The differences between data obtained by the 

 direct analysis for protein and O&G and the two 

 methods of calculation are compared in Table 4. 

 A negative or positive sign indicates whether the 

 calculated value is less or more than the analyti- 

 cal value. 



The analytical values of sample numbers 1,2,3, 

 and 12 for protein and 2 for O&G are obviously in 

 error and although these values were included in 

 the mean values in Table 1, they were omitted 

 from the regression lines and equations of Figure 

 2. The comparative data indicate that the calcu- 

 lated values are in reasonable agreement with 

 analytical values. Since a regression line deter- 

 mined by the method of least squares is by defini- 

 tion the best fit of empirical data containing 

 normal errors in precision and accuracy, and since 

 protein and O&G are less accurate analyses than 

 TR K or COD, it follows that a value for O&G cal- 

 culated from the simultaneous equation or from 

 the equation of the regression line should be more 

 correct than an individually determined value. 

 The data of Equations (4) and (5) in Table 4 are 

 merely a measure of the fit of each value to the 

 regression line. The data of Equation (8), however, 

 are independent of protein and O&G but depen- 

 dent upon COD and TR data. 



If the simultaneous equation is used to calculate 

 O&G, TR K and COD TR are required for the equa- 

 tion and can be obtained through analysis and 

 calculation, respectively. Alternatively, O&G or 



TABLE 4. — Comparison by difference of protein and O&G data 

 obtained by analysis or by calculation. 



258 



