Excerpt from The Principles of Measurement and of Calculation in Their Application to the Determination of Diophantine Quantities It will be noticed that in the above descriptions we have employed such expressions as obviously, reasonable, and' 'appropriate which are not defined and which are. Essentially incapable of exact definition. In fact, except perhaps in purely statistical problems, no mathematical method of treating the observational data can entirely replace the scientific good judgment of the investigator. At most it can only suggest an orderly procedure and point out the logical inferences involved. As an example of a measurement which 1s itself a simple operational element, let us consider the measurement of the distance between two parallel fine lines on a plane Surface. We will suppose that one of the lines is brought into coincidence with a graduation mark of a standard meter divided into millimeters and that the position of the second line is estimated, to the nearest tenth millimeter or better with the aid of a cross hair, no vernier being used. It will be generally agreed that a trained observer using the above apparatus and technic could not make an error of as much as mm. This agreement would still prevail for mm and probably for 0. 2 mm. In other words, the value mm would be generally approved as a reasonable and conservative choice for the' 'maximum error of the method. In fact, a smaller value, say mm, would doubtless meet the approval of many investigators accustomed to making observations of this character, but this smaller value is obviously approaching the dang er limit, and an investigator who proposed using it would probably be expected to justify his choice. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.