the number of cells in the water mixture (the seeding liquid) has the same proportion to the number of cells after seeding as the whole amount of liquid after seeding has to the amount of the seeding liquid. The quantity of liquid in the flask after seeding has taken place is thus p + x. From the given equation x = a,p a - a1 Example: It is found that the seeding liquid contains 75 cells per unit of volume and the flask to be infected contains 70 c.c. of wort, and it is further desired to have 5 volume after inoculation, accordingly x = cells per unit of 5 × 70 75- 5 = 5 cc. The result may to be withdrawn from the seeding liquid. be checked by another counting after seeding. If the result is incorrect either more liquid or more cells must be added. But in exact work this contingency does not arise. Suppose it is wished to sow a, cells of a yeast species A and b, cells of a species B in a flask containing p cc of culture liquid, from two seeding liquids containing a and b cells per unit of volume respectively, the number of cubic centimetres, x and y, to be sown from A and B respectively is found from the following two equations : the quantity of liquid after infection being p+x+y; from this we find Combinations of the above three cases may of course occur, but from the explanations given here it will not be difficult to solve them. It would lead us too far to go into more detail. 8.-The Biological Analysis of Yeast. Preliminary Investigation.-The biological analysis of yeast specimen is guided, to a large extent, by its origin and the eventual use to which the yeast is to be put. In general it is no small labour to determine all the elements of a specimen of yeast. This is begun by several preliminary experiments in order to obtain a basis for the real analysis. With this in view a microscopical examination of an average specimen of the yeast is made. The shape and size of the cells are observed; further, whether many dead cells are present, as that affects the use of the yeast in practice. It can also be found whether there are any mould spores and bacteria present. The detection of the latter is simplified by adding dilute soda solution to the preparation, by means of which dead particles of organic-chemical origin are in general dissolved; this is the case especially with resinous and albuminous bodies. It is often difficult to determine by microscopical examination whether the bacteria found are living or dead, especially if they belong to the non-motile species. Some information as to the constituents of the yeast specimen can also be obtained by putting a little of it in wort at 25° C.; the phenomena of fermentation are then observed on one hand (top or bottom fermentation), and on the other the time taken to form a film on the surface of the liquid. Lastly, a small sample is placed directly on a gypsum block at 25° C., and information is obtained in the course of a few days as to the conditions of spore formation. Separation of the Various Forms in the Sample.The actual separation of the different species in a particular sample is effected by means of a plate culture of a small average sample in wort gelatine. Yeast and mould fungi, but only a few bacteria, are thus brought to development. If it is then desired to recognise the bacteria also present, a gelatine or agar-agar preparation of either yeast water or peptone meat extract should be used in making the plate cultures. Plate cultures on wort gelatine are set away at 25° C. When the colonies have grown to a sufficient size they are examined microscopically and macroscopically. Those which exhibit differences are inoculated in wort and studied more closely. The yeast sediment formed in the process is examined under the microscope; cultures for the eventual film formations are set apart; experiments are made in which it is observed whether the fermentation is bottom or top fermentation; the amount of alcohol formed is determined, etc. A spore analysis is also carried out (see below). The comprehension of these analyses, of course, rests substantially on the insight which has been acquired into the biology of the organisms concerned, and on the use of the scientific results brought out by research. The analysis has been perfected chiefly for brewery purposes. In nearly all cases of analysis of a brewery yeast it will be a question of determining to what extent (1) wild yeasts, (2) bacteria, and (3) various species of culture yeasts, are present in the sample in hand. The problem will seldom be that of determining the species. Hansen's Spore Method for the Analysis of Brewery Bottom Yeast for Wild Yeast.-In testing for wild yeast, Hansen's spore method is generally employed. An average sample of the yeast is cultivated in wort at 25° C. for about twenty-four hours; gypsum block cultures of the yeast sediment produced in this manner are prepared in the usual way at 25° and 15° C.; after forty and seventy-two hours respectively the blocks are examined; if spores are found, wild yeast is present. Holm and Poulsen have shown that by this method part of wild yeast can be discovered in a mixture with culture yeast. Later, G. Syrée proved, with the aid of the same method, the presence of the wild yeast species Saccharomyces Pastorianus III. in a mixture with culture yeast in which it amounted to only part of the latter; the two species had been cultivated for four days at 25° C. In another case the original mixture was Sacch. Pastorianus III. and 900 Frohberg yeast; after they had been cultivated together for eight days, the presence of Sacch. Pastorianus III. was demonstrated in this case also by Hansen's spore method. 899 The wild yeast can be most easily obtained by infecting a wort flask with the yeast sample and placing this away at 25° C. or at room temperature. At the close of the first fermentation a specimen of the surface beer is taken out; Hansen's investigations have shown that at this period the greatest quantity of wild yeast is found in the position mentioned. A new wort flask is then infected with the surface beer, and gypsum block cultures are prepared from the new culture in the manner already described. Application of the Spore Method to Top Yeasts.While Hansen produced his method specially for investigating brewery bottom yeast, and the experiments described above on the sensitiveness of the method were performed with such yeasts, Alfred Jörgensen has shown that this method also gives good results with brewery top yeast. He showed further that it is necessary to perform the analysis at 12° C. on account of certain top yeast species. The method has also been used later in the other branches of the alcoholic fermentation industries. The Tartaric Acid Method. Often, however, the admixture of wild yeast is so small that the above method fails to find it. The tartaric acid method, also described by Hansen, is then applied. An average sample of the yeast is placed in a 10 per cent. aqueous solution of cane sugar to which 4 per cent. of tartaric acid has been added, and this culture is set away at the room temperature. This cultivation is repeated four times after every twenty-four hours, or the culture is put away at 25° C. and recultivated twice at twenty-four hour intervals. A wort flask is inoculated from the last culture; then ordinary gypsum block cultures are prepared at 25° and 15° C. with the yeast thus produced, and these cultures investigated. In this manner quite small traces of wild yeast can be detected. In all cases a microscopical investigation is, of course, also carried out. In the examination of cultures on gypsum blocks regard is paid to the appearance of the spores, the spores of culture yeasts generally containing a less refractive plasma with vacuoles, thus having an empty appearance, whilst the wild yeasts exhibit a strongly refractive plasma. The above mentioned analysis of yeast by means of spore cultures on gypsum blocks can be simplified if the culture yeast in hand forms spores with extreme difficulty or not at all, as then the simple detection of the spores on the gypsum blocks at 25° C. is sufficient confirmation that the sample contains wild yeast or a foreign culture yeast. Sporeless forms of the saccharomycetes can be prepared by the Hansen method, described in Section III.; the analysis is therefore simplified if a culture yeast of this kind is employed in practice. Since the asporogenous varieties of the saccharomycetes also form no films, this provides an additional means of detecting the presence of sporogenous, that is to say, foreign species; a wort culture being set aside to determine if film formation takes place. Analysis for Bacteria. In testing yeast for living bacteria an average sample is placed in yeast water and preserved at 25° to 30° C. When acetic acid bacteria are being sought, the beer can be kept at 32° to 33° C. if the |