The relative stability numbers, given in Table 72, are computed from the expression, S = 100(1 − 0.794t) in which S is the stability number and t is the time in days that the sample has been incubated at 20° C. The bio-chemical oxygen demand is more directly an index of the consumption of available oxygen by the biological and chemical changes which take place in the decomposition of sewage or polluted water. As such it is a more valuable, though less easily performed test than the test of relative stability.

The methods for the determination of the relative stability and the bio-chemical oxygen demand are given to show more clearly what these tests represent. The procedure in the relative stability test is to add 0.4 c.c. of a standard solution of methylene blue to 150 c.c. of the sample. The mixture is then allowed to stand in a completely filled and tightly stoppered bottle at 20° C. for 20 days or until the blue fades out due to the exhaustion of the available oxygen. There are three methods in use for the determination of the bio-chemical oxygen demand;[[127]] the relative stability method, the excess nitrate method, and the excess oxygen method. In the relative stability method the sample to be treated should have a relative stability of at least 50. If it is lower than this the sample should be diluted with water containing oxygen until the relative stability has been raised to or above this point. The oxygen demand in parts per million is then expressed as

O′ = (1 − P)O
RP,[[128]]

in which O′ is the oxygen demand, O is the initial oxygen in parts per million (p.p.m.) in the diluting water or sewage, P is the proportion of sewage in the mixture expressed as a ratio, and R is the relative stability of the mixture expressed as a decimal. For the effluents from sewage treatment plants, polluted waters, and similar liquids, the total available oxygen expressed as the sum of the dissolved oxygen, nitrites, and nitrates, divided by the relative stability expressed as a decimal will give the bio-chemical oxygen demand. The excess nitrate method requires the determination of the total oxygen available as dissolved oxygen, nitrites, and nitrates and the addition of a sufficient amount of oxygen in the form of sodium nitrate to prevent the exhaustion of oxygen during a 10–day period of incubation. At the end of the period the total available oxygen is again determined. The difference between the original and the final oxygen content represents the bio-chemical oxygen demand. The excess oxygen test requires the determination of the total available oxygen as before, and the addition of a sufficient amount of oxygen, in the form of dissolved oxygen in the diluting water, to prevent exhaustion of the oxygen in a 10–day period of incubation. The difference between the original and final oxygen content represents the bio-chemical oxygen demand. Theriault concludes as a result of his tests, that the relative stability and excess nitrate methods are open to objections but that the excess oxygen method yields very accurate and consistent results with as little or less labor than is required by other methods.

Dissolved oxygen represents what its name implies, the amount of oxygen (O2) which is dissolved in the liquid. Normal sewage contains no dissolved oxygen unless it is unusually fresh. It is well, if possible, to treat a sewage before the original dissolved oxygen has been exhausted. Normal pure surface water contains all of the oxygen which it is capable of dissolving, as shown in Table 73. The presence of a smaller amount of oxygen than is shown in this table indicates the presence of organic matter in the process of oxidation, which may be in such quantities as ultimately to reduce the oxygen content to zero. Normal pure ground waters may be deficient in dissolved oxygen because of the absence of available oxygen for solution. The presence of certain oxygen-producing organisms in polluted or otherwise potable surface waters may cause a supersaturation with oxygen however.

The dissolved-oxygen test for polluted water is probably the most significant of all tests. If dissolved oxygen is found in a polluted water it means that putrefactive odors will not occur, since putrefaction cannot begin in the presence of oxygen. It is possible for different strata in a body of water to have different quantities of dissolved oxygen, and putrefaction may be proceeding in the lower strata before the oxygen is exhausted from the upper strata. The oxygen content of a river water will indicate the ability of the river to receive sewage without resulting in a nuisance.

TABLE 73
Solubility of Oxygen in Water
Under an atmospheric pressure of 760 mm. of mercury, the atmosphere containing 20.9 per cent of oxygen.
Temperature, degrees COxygen in parts per million
014.62
114.23
213.84
313.48
413.13
512.8
612.48
712.17
811.87
911.59
1011.33
1111.08
1210.83
1310.6
1410.37
1510.15
169.95
179.74
189.54
199.35
209.17
218.99
228.83
238.68
248.53
258.38
268.22
278.07
287.92
297.77
307.63

211. Sewage Bacteria.—A slight knowledge of the nature of bacteria is necessary in order that the biological changes which occur in the treatment of sewage may be understood. Bacteria are living organisms which are so small that it is difficult or impossible to study them either with the eye alone or with the aid of powerful microscopes. They are studied by means of cultures, stains, and certain characteristic phenomena such as the production of a gas, the production of a red colony on litmus lactose agar, etc. Bacteria occur in three forms: spherical, called coccus; cylindrical, called bacillus; and spiral, called spirillum. In size they vary from the largest at about 1
10,000 of an inch to sizes so small as to be invisible under the most powerful microscope. An ordinary size is 1
25,000 of an inch. The cylindrical or rod bacteria are about four times as long as they are wide. Some bacteria possess the power of motion due to the presence of flagella or hairs which can be moved and cause the cell to progress at a rate as high as 18 cm. per hour, but usually the rate is very much less than this. The composition of the bacterial cell has never been definitely determined.

Bacteria are unicellular plants. They possess no digestive organs and apparently obtain their food by absorption from the surrounding media. Reproduction is by the division of the cell into two approximately equal portions. This reproduction may occur as frequently as once every half hour and if unchecked would quickly mount to unimaginable numbers. The natural cause limiting the growth of bacteria is the generation by the bacterium of certain substances such as the amino acids, which are injurious to cell life. The exhaustion of the food supply is not considered as an important cause of inhibition of multiplication. The products of growth of one species of bacteria may be helpful or harmful to other forms. Where the products are helpful the effect is known as symbiosis, and where harmful the effect is known as antibiosis. In sewage the presence of both aërobic and anaërobic bacteria is usually mutually helpful and the condition is an example of symbiosis. The aërobes, sometimes called obligatory aërobes, are bacteria which demand available oxygen for their growth. The anaërobes, or obligatory anaërobes, can grow only in the absence of oxygen. There are other forms that are known as facultative anaërobes (or aërobes) whose growth is independent of the presence or absence of oxygen.

Spores are formed by some bacteria when they are subjected to an unfavorable environment such as high temperatures, the absence of food, the absence of moisture, etc. Spores are cells in which growth and animation are suspended but the life of the cell is carried on through the unsuitable period, somewhat similar to the condition in a plant seed.