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From the Preface. This monograph is the outgrowth of an experimental investigation begun in the psychological laboratory of the University of Pennsylvania in 1897 and continued at irregular intervals during the two following years. In 1900 it was presented substantially in its present form to the Faculty of the Department of Philosophy in the University of Pennsylvania and accepted as a thesis in partial fulfillment of the requirements for the degree of Doctor of Philosophy. From the Author's Preface. The theory of probability and the theory of errors now constitute a formidable body of knowledge of great mathematical interest and of great practical importance. Though developed largely through applications to the more precise sciences of astronomy, geodesy, and physics, their range of applicability extends to all of the sciences; and they are plainly destined to play an increasingly important role in the development and in the applications of the sciences of the future. Hence their study is not only a commendable element in a liberal education, but some knowledge of them is essential to a correct understanding of daily events. No special novelty of presentation is claimed for this work; but the reader may find it advantageous to know that a definite plan has been followed. This plan consists in presenting each principle, first, by means of a simple, concrete example; passing, secondly, to a general statement by means of a formula; and, thirdly, illustrating applications of the formula by concrete examples. Great pains have been taken also to secure clear and correct statements of fundamental facts. If these latter are duly understood, the student needs little additional aid; if they are not duly understood, no amount of aid will forward him. The passage from the elementary concrete to the advanced abstract may appear to be abrupt to the reader in some cases. It is hoped, however, that any large gaps may be easily bridged and that any serious difficulties may be easily overcome by means of the references given to the literature of the subject. In any event the student will find that in this, as in all of the more arduous sciences, his greatest pleasure and his highest discipline will come from bridging such gaps and from surmounting such difficulties. From the Author's Preface. The theory of probability and the theory of errors now constitute a formidable body of knowledge of great mathematical interest and of great practical importance. Though developed largely through applications to the more precise sciences of astronomy, geodesy, and physics, their range of applicability extends to all of the sciences; and they are plainly destined to play an increasingly important role in the development and in the applications of the sciences of the future. Hence their study is not only a commendable element in a liberal education, but some knowledge of them is essential to a correct understanding of daily events. No special novelty of presentation is claimed for this work; but the reader may find it advantageous to know that a definite plan has been followed. This plan consists in presenting each principle, first, by means of a simple, concrete example; passing, secondly, to a general statement by means of a formula; and, thirdly, illustrating applications of the formula by concrete examples. Great pains have been taken also to secure clear and correct statements of fundamental facts. If these latter are duly understood, the student needs little additional aid; if they are not duly understood, no amount of aid will forward him. The passage from the elementary concrete to the advanced abstract may appear to be abrupt to the reader in some cases. It is hoped, however, that any large gaps may be easily bridged and that any serious difficulties may be easily overcome by means of the references given to the literature of the subject....

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