Discussion of the Precision of Measurements; With Examples Taken Mainly from Physics and Electrical Engineering (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ...problems on this subject are to be carried out to only two places of figures and need be correct only to 1 part in 10, and that the results are often (e.g., equal effects) to be regarded only as approximate guides. It will then be seen that simplifications of the original functions will be allowable to save labor, and that they may be of a much more extreme character than would be allowable in the actual computation of the results of the measurement. Moreover, different simplifications may be introduced when different components are being discussed. The one criterion for the admissibility of any proposed simplification, when the solution is being made with respect to any component mk, is that the value of Smk or the effect of Ak, as the case may be, must not be changed by more than i part in 10 by the simplification. Inspection, or a preliminary differentiation, will usually show easily whether the proposed change fulfils this condition. The two chief methods of simplification are the use of approximate expressions in place of the exact form for /(), and the omission of certain terms while differentiating. The tables of approximation formulae given in some text-books on physical manipulation will suggest available approximations. Many other ways of simplification will be suggested by experience and ingenuity in particular cases. In somewhat complicated functions one or more components, mk, etc., may occur in several parts of the expression, as in the complete formulae for the tangent galvanometer, in the expressions for the efficiency of a dynamo by any of the stray power methods, etc. If such a case is being treated by the general method, the differentiation may sometimes be simplified either by omitting to differentiate with respect to mk those terms in w...