With reference to the incredible rapidity with which the bacteria multiply under conditions favourable to the growth and development, Cohn writes as follows:--“Let us assume that a microbe divides into two within an hour, then again into eight in the third hour, and so on. The number of microbes thus produced in twenty-four hours would exceed sixteen and a half millions; in two days they would increase to forty-seven trillions; and in a week the number expressing them would be made up of fifty-one figures. At the end of twenty-four hours the microbes descended from a single individual would occupy 1/40th of a hollow cube, with edges 1/25th of an inch long, but at the end of the following day would fill a space of twenty-seven cubic inches, and in less than five days their volume would equal that of the entire ocean.” Again, Cohn estimated that a single bacillus weighs about 0·000,000,000,024,243,672 of a grain; forty thousand millions, 1 grain; 289 billions, 1 pound. After twenty-four hours the descendants from a single bacillus would weigh 1/2666th of a grain; after two days, over a pound; after three days, sixteen and a half million pounds, or 7,366 tons. It is quite unneccessary to state that these figures are purely theoretical, and could only be realised if there were no impediment to such rapid increase. Fortunately, however, various checks, such as lack of food and unfavourable physical conditions, intervene to prevent unmanageable multiplication of these bodies. These figures show, however, what a tremendous vital activity micro-organisms do possess, and it will be seen later at what great speed they increase in water, milk, broth, and other suitable media. The following bacilli, among others, have numerous flagella distributed over the whole of the organism: the bacillus of blue milk (_Bacillus cyanogenus_)[52]; the bacillus of malignant œdema; the hay bacillus (_Bacillus subtilis_); _Proteus vulgaris_, &c. The following have only one or two flagella at the poles: the _Bacillus pyocyaneus_, the _Spirillum finkleri_, the _Spirillum choleræ Asiaticæ_, &c. The _Spirillum undala_, _Spirillum rubrum_, _Spirillum concentricum_, and _Sarcinæ_, pocket-cocci, have several flagella. _Micrococcus agilis_ have also several flagella; these possibly arise from one point. As I have already pointed out, the _classification_ of the bacteria is one of great difficulty, since new kinds are being constantly discovered, and at present any attempt made in this direction can only be considered as quite of a provisional nature. The difficulties which stand in the way may be surmised from the fact that _Sarcinæ_, pocket-cocci, were originally believed to be a single species, described by me, under the name of _Sarcina ventriculi_, in the fourth edition of my book, “as remarkable bodies invading the human and animal stomach, and seriously interfering with its functions.” [Illustration: Fig. 268.--Sarcinæ.]