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From APHA, AWWA, and WEF (1992). Standard Methods for the Examination of Water and Wastewater. 15th ed. American Public Health Association, Washington.

From APHA, AWWA, and WEF (1992). Standard Methods for the Examination of Water and Wastewater. 15th ed. American Public Health Association, Washington.

if the analysis had been done on more than three dilutions, only the three highest dilutions can be adopted for use in the table. To have an idea of what is meant by highest dilution, the 0.01 is said to be the highest dilution in a serial dilution of 1, 0.1, and 0.01. Also, the result of the experiment must not show a zero reading.

The reason why a zero reading is unacceptable can be gleaned from the following justification. Serial dilutions are prepared relatively far apart in concentrations. For example, consider the dilution used in Table 2.4, which is 10 mL, 1 mL, and 0.1 mL. Now, suppose the reading is 2, 1, 0 which means 2 positive readings in the 10-mL dilution, 1 positive reading in the 1-mL dilution, and 0 positive reading in the 0.1 mL dilution. Because 0.1 mL is far away from 1 mL, it is possible that the 0 reading would correspond not only to 0.1 mL but also to a dilution between 0.1 mL and 1 mL, such as a dilution of 0.6 mL. Thus, the reading of 0 is uncertain and therefore should not be used. For readings to be valid, they should not contain any zeroes.

Note that if the highest dilution has a reading, then the next higher dilution should have a reading at least equal to the highest dilution. The most accurate would be that it should have a reading greater than the highest dilution. Thus, before the table is used, it should be ascertained that this fact is reflected in the results of the experiment. If this is not the case, the table should not be used and the results of the experiment discarded. Note, however, that if the result of the experiment is erroneous, Table 2.4 cannot be used in the first place, since there will be no entry for this erroneous result in the table.

2.3.5 Interpolation or Extrapolation of the MPN Table

If the reading of a valid experiment cannot be found in the table, the corresponding MPN may be interpolated or extrapolated. For example consider the reading 2, 2, 1 for a certain serial dilution. Referring to Table 2.4, this reading cannot be found; it is, however, between readings 2, 1, 1 and 3, 1, 1. Thus, its corresponding MPN can be interpolated.

The MPN is proportional to the reading. Using this idea to calculate the MPN, assume that there are three dilutions, as are used in Table 2.4. Let MPNx be the MPN to be interpolated and the corresponding readings be Rx1, Rx2, Rx3. The weighted mean reading Rxave corresponding to MPNx is then

Rxl( Dx)+ Rx2( D2 ) + Rx3 ( D3 ) Rxave = -Dj + D2 + D3--(2.40)

where D1, D2, and D3 are the three dilutions used in the experiment.

Let MPNj and MPN2 be the MPN of the first and second known MPNs as found in the table, respectively. The corresponding readings of MPN1 are R11, R12, and R13 and those of MPN2 are R21, R22, and R23. The corresponding mean readings are, respectively, R1ave and R2ave as shown in the equations below:

From Eqs. (2.40), (2.41), and (2.42), we form the following table:

mpnj

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