MATHEMATICAL INSTRUMENTS VOL. I. DRAWING AND MEASURING INSTRUMENTS INCLUDING INSTRUMENTS EMPLOYED IN GEOMETRICAL DRAWING, AND IN THE MEASUREMENT OF MAPS AND PLANS PREFACE TO VOL. I. UPON the publication of the original edition of this treatise the author was very greatly and very agreeably surprised by the large number of complimentary letters that he received from persons engaged in a variety of pursuits, many of whom were entirely unknown to him. The praises, thus liberally bestowed on his humble work, were supplemented by its introduction, as a text-book, into numerous educational establishments, and its selection by the Admiralty to form part of a midshipman's kit. It was manifest, then, that his little book had supplied a want that was strongly felt; and the writer, fully aware of its deficiencies, has long been anxious for the opportunity to improve upon his first essay, which has been afforded him by the liberality of the present proprietors of the WEALE SERIES. The subjects of Optical Instruments, and of Surveying and Astronomical Instruments, having been removed, to be treated of more fully in separate volumes, sufficient space has been obtained in this volume for a considerable development of that portion of the work, entitled Part I., allotted to the description of Drawing Instruments; while in Part II., now devoted to the consideration of Instruments for Measuring, and for the mechanical performance of arithmetical computations, the principle of the slide-rule has been, it is hoped, clearly explained, the comparative merits of different modes of construction have been discussed, and plain and simple rules for the numeration of the results obtained have been given. The want of a method of so using the slide-rule, that it should of itself indicate the numeration of the results ob Th tained, and thus become its own interpreter, has been serious a drawback on its value as a mechanical calculat that the small extent to which it has hitherto come i general use is not to be wondered at. Not only has no su method been heretofore published, but the accomplishment so desirable an object has been deemed impracticable. the eminent writer of the article on the slide-rule Knight's "English Encyclopædia" remarks:-"Attemp are made in works professing to explain the slide-rule to gi rules for the denomination of the character of the figures the answer, but without any success. It is all very well f a few chosen examples, but an attempt to do without t book soon shows the insufficiency of rules. If on a larg scale 653 should be the figures of an answer, common sen applied to the problem must say whether it is 0653, 65 6.53, 65.3, 653, 6530, 65300, &c., which is meant." The principal obstacle to the discovery of the very simp rules for numeration on the A and B lines, laid down in th text (p. 102), appears to have arisen from the unnecessar repetition of the line of numbers, from 1 to 10, upon bot these lines. At all events, the Author was led to the discovery of thes rules by the examination of the rule designed by Mr. S. Coul son, supplied to him by the manufacturers, Messrs. Dring and Fage, on which the line of numbers, from 1 to 10, i laid down on the A line once only in the entire length o the rule, while it is laid down on the B line twice, on the slide, formed in two pieces, numbered on from one to the other. This rule, being used so that the results sought shall be found on the B line, or slide, the correct denomination of its figures is determined by the section of the slide upon which it appears. To apply, then, the same method of numeration to the ordinary form of the rule, in which the line of numbers, from 1 to 10, is laid down twice on the A line, it is manifestly necessary only to disregard one-half of this line, and work with a single section of it. It is evident, however, that, as regards the A lines, the ordinary rules are made twice as long as they need be, only to be encumbered with an useless repetition of the numbers laid down on them. *Professor de Morgan. |