Researches Into the Theory of Probability

From the Introduction. Among newer investigations into the theory of probability I know none more important than those of Peakson in his admirable series of "Contributions to the Mathematical Theory of Evolution." The numerous school of biologists that has grown up during the last ten years, which has applied his methods to fundamental problems in botany and zoology, has richly demonstrated the importance of these methods for biology and shown the possibility of basing the science of life on exact mathematical methods. The branch of mathematics that is here in the first place needed is the theory of probability. For this reason Pearson was obliged, in attacking the problem of evolution from a mathematical point of view, to solve some importimt problems in this theory, that had not to that time been sufficiently dealt with. He has solved a great part of these problems. Others remained un- solved or only partially solved. The object of the present investigation is to treat some of these problems, which are of great importance not only to biology, but to all sciences based on observations of nature. I should be glad if the results obtained will contribute to further develop the line of research laid out by Peakson and his school. Taking an arbitrary individual in the living nature - a man, an animal, a plant - it will generally be found impossible to find out another individual in all respects identical to the one first chosen. If the difference is great, we say that the two objects belong to different orders, classes, species, subspecies a. s. o., but it is impossible to carry the classification so far, that the differences between the individuals of the same sub-class would disappear. Nevertheless there is something that rightly may be named classes, species a. s. o. of individuals, though the strict definition of these terms is difficult and scarcely can be made without employing mathematical methods. Let us consider a number of individuals all belonging to the same species, by which term we mean for the moment the narrowest group in the classification of the objects iu question. We take into consideration a certain character of these individuals, and assume that this character may be measured as to its magnitude or intensity, so that the measurements are expressed through numbers. Generally the character may vary continuously, and its true value in each individual can then only be measured approximately as the height of a man. In some cases the magnitude determinations of a character are expressed exactly iu numbers, as the numbers of petals in a flower. In either case we generally find that the character varies from one individual to another....