will still more impress upon the biologist, the significance and great importance in all his work of what may be called the «probable error concept». Whatever the material of scientific investigation, whether animate or inanimate, it is a fact of universal experience that just as soon as observation cr experiment concerns itself with any « quantitative » aspect of a phenomenon it is impossible ever to get « precisely » the same result twice. The more refined and delicate the instrument, and the finer the units in which the measurement is made, the more evident does it become that the « absolute » determination of any magnitude whatsoever is humanly impossible. The problem of all quantitative science, therefore, is to determine with a maximum of accuracy the probability that any particular unknowable magnitude lies within any assigned limits. One can never say, and be scientifically accurate, that a particular stick is precisely 11.5 cm. long, but if it be worth one's while, it is possible to determine the mathematical probability that the true length of the stick lies between say 11.498 and 11.502 cms. In the writer's opinion it must be regarded as the point of greatest value of statistical theory for science in general that it furnishes the method of determining such probabilities.
That the probable error concept is of high importance for biology is so evident as not to need lengthy discussion. When one considers what a large part of the results of experimental investigations of all kinds of physiological topics (to take but one instance) are quantitative in character, and based on the observation of relatively few individual cases, the significance of probable error determinations in that field is clear. Similarly in the experimental study of inheritance along mendelian lines the results are in almost every case quantitative and statistical in character. A statement of such results without probable errors is incomplete.
In the third place biometry gives us a method of measuring the relationship between phenomena, in the multitude of cases where this relationship is not of a « cause and effect» sort. In observed biological phenomena there very often exists a correlation rather than a strictly causal relation between events or characters. The reason for this doubtless lies in the fact that in biology we are dealing in most instances with complex phenomena, in which the actual condition
