Computation Rules and Logarithms: With Tables of Other Useful Functions

An excerpt from the beginning of the PREFACE: IT would probably be within safe limits to assert that one-half of the time expended in computations is wasted through the use of an excessive number of places of figures, and through failure to employ logarithms. This waste might be almost wholly avoided by following a few simple computation rules and practising slightly with logarithm tables. The loss from the use of superfluous figures will be appreciated when it is considered that in direct or logarithmic multiplication and division with four, five, and six places of figures the work is respectively in the ratio of 1:2:3, or perhaps more nearly 2:3:4. Thus contrary to the fallacious excuse so commonly given that it is just about as easy to use six. or seven place tables as smaller ones, the work is doubled or trebled by the use of six places instead of four. Even the employment of six. or seven place tables, and dropping superfluous places when four or five are desired, causes much loss of time. The proper employment of logarithms for work of four or more places effects a saving of one quarter and upward of the time required for direct multiplication or division, with a lessening of fatigue and a gain of accuracy. The following pages contain simple rules to enable one to answer for himself the question, how many places of figures ought I to use in this computation? - also, an explanation of the use of the notation by powers of ten; certain instructions, more or less novel in form, as to the use of the logarithm and other tables; and a collection of useful tables. This collection is designed to contain all the mathematical tables ordinarily required, and nothing more, in practical work in all branches of the engineering professions, and by students of physics, chemistry, and engineering, for work of any grade not exceeding about one twentieth of one per cent in accuracy. For many persons the present volume should, therefore, provide all the logarithmic and trigonometric tables needed for the entire range of their practice. For work of greater precision than the above limit, the more bulky Vega, or some similar reliable seven place table would be required. It is exceedingly rare that more than six or seven places are necessary, while for most work five are sufficient, although a striking chapter of absurd illustrations might be gleaned from various text books and tables where ten. and even twenty place logarithms are given, often for quantities uncertain in their fourth or fifth place. Persons doing much work with squares, cubes, square roots, cube roots, or reciprocals of more than four places would naturally make use of the Barlow Tables. The rules for significant figures (pages xi to xv) are intended to be terse, direct, and simple, so that they may be easily acquired and retained. The strong type emphasizes the leading portions. The ordinary and finer types give details and explanations. For the sake of affording still greater prominence to the main working portions, some explanatory matter which will be unnecessary to many persons has been transferred from its more logical position of precedence to the latter part of the text. These rules in various forms have been in successful use by large classes of students, in connection with the author's "Physical Laboratory Notes" (printed, but not published, by the Massachusetts Institute of Technology), and his "Precision of Measurements." The recognition of the need of such rules amongst engineers and others whose practical work demands rapid and reliable computations was the cause of their general introduction into this laboratory instruction. It is therefore hoped that they may render effective service to others besides the students for whom they have been more directly designed. In the arrangement of the tables, the effort has been exerted to make them correct, legible, systematic, and convenient in use. ...