storeroom, machinery and materials" so abundant in quantity and variety of stores, that it will answer every reasonable requirement. In excuse for the extreme simplicity of some of the problems presented, the author owns that this feature of the book was incorporated in it through its having come to his knowledge, through a member of the board of U. S. government examiners, some years since, that some score of high class marine engineers had come very near losing their positions on account of their ignorance of many of the simplest items of information. relating to their duties. It was in consequence of an order received from headquarters at Washington for the re-examination of all the engineers in a certain department, in the Eastern division of the marine service; the order was peremptory, and the examinations to the number of 60 or 70 were held forthwith. And it was a disagreeable fact that while few, or none, were really displaced, the positions of all these really competent engineers were in danger of being forfeited, because they had forgotten the little things they had acquired in earlier days. Hence the truly wise student of this hand-book, even if of established reputation, will not despise the elementary rules and examples presented. Nor must the humble beginner despair of the most difficult. Both extremes will be found in the completed volume. PLAN OF THE WORK. The leading idea intended to be illustrated in the following successive "parts" or chapters is this: that in an informal and not too "dry" a method, engineers or those aspiring to be such shall be taught to figure the problems relating to the steam engine and boiler; the steam pump; shafting and pulleys; and all other calculations required in the varied duties of steamengineering in its most intelligent and useful practice. The first four or five parts of the work will be occupied exclusively with what may be called the general principles of mathematics—principles which are used in all times and places and in an infinite variety of machines, and their application to the use of man. Next, these elements will be illustrated by the practice of to-day in steam engineering in its various departments. Rules for calculating horse power of engines and boilers will be given in the plainest manner and fully illustrated by diagrams; rules for figuring the safety-valve pressure of boilers, strength of materials, size and capacity of pumps, etc., etc., with help rules, notes and remarks based upon the most approved practical experience. The work will close with valuable and copious tables of roots and powers of numbers, and diameters and circumferences of circles, and all the data commonly found in the most advanced works written for mechanics; hence, the first part of the work, perhaps three-quarters of it, will be for instruction and the other part for reference. It must not be forgotten that the elements only of arithmetic, geometry, algebra, mensuration, etc., are to be introduced in the work, but it is upon these elements that the whole structure of mathematics rests, and form the groundwork where the most advanced and the most lowly beginner can meet with mutual respect. It is planned that the ultimate result of this publication will be the compiling of a standard and valuable volume, containing all the mathematics relating to steam engineering necessary for an intelligent engineer in his daily practice; hence the author, ere the work proceeds too far, will be pleased to receive the helpful suggestions of his kindly reader as to the most desirable contents for such a comprehensive work. For the space it occupies the explanation of the use of formulas or forms will be found to be most useful to the practical man, as it teaches him the school language of expressing calculations. This custom is the same as that followed by the physician in writing aqua pura instead of "pure water"; and the gardener giving Latin names to his plants instead of plain English terms. The use of formulæ is so universal that many publications, otherwise of great value to the engineer, are to him as a sealed book; but with the explanations to be found in this work a great part of the difficulty will be obviated. At the issue of Part 1 the whole work is in manuscript, but it will be printed in 10 monthly parts. This is to accommodate the student, to whom a single PART will be the moderate allowance for a month's study, and also to allow such changes as may seem necessary to perfect the plan of the work before it is advanced to book form. The index of the whole book will be issued with the last number, in convenient shape, and at that time a more formal preface will be written, in which due acknowledgement will be made for assistance from persons and authors whose advice and experience has been drawn upon. One other item may be added, but not enlarged upon: that is the desire to give for a moderate cost, information of large value to the purchaser. An engineer who can figure and do it correctly is of more value than one who cannot, and this esteem is (between the reader and the author) expressed by larger compensation and longer service in one position. ARITHMETICAL SIGNS. The principal characters or marks used in arithmetical computations to denote some of the operations, are as follows: = = - Equal to. The sign of equality; as 100 cts. $1-signifies that one hundred cents are equal to one dollar. - Minus or Less. The sign of subtraction; as 8-2-6, that is, 8, less 2, is equal to 6. + Plus or More. The sign of addition; as 6+8=14; that is, 6 added to 8, is equal to 14. × Multiplied by. The sign of multiplication; as 7×7=49; that is, 7 multiplied by 7 is equal to 49. Divided by. The sign of division; as 16÷4 4; that is, 16 divided by 4 is equal to 4. There are still other characters and marks which will be added as needed as the work progresses, but these are the principal ones. ARITHMETICAL FORMULAS. An arithmetical formula is a general rule of arithmetic expressed by signs. The following 10 formulas include the elementary operations of arithmetic and follow from the succeeding illustrations. 1. The SUM-all the parts added. = 2. The DIFFERENCE-the Minuend-the Subtrahend. = the Difference. 3. 4. 5. the Multiplier. the Multiplier. the Multiplicand. the Dividend the Divisor. = 10. The DIVISOR the Dividend the Quotient. Formulas or formulæ, express the plural of formula-a Latin word which means, simply, a form; hence a formula is a form of stating a problem. ARITHMETIC. Arithmetic is the science or orderly arrangement of numbers and their application to the purposes of life. The processes of arithmetic are merely expedients for making easier the discovery of results, which every mechanic of ordinary ingenuity would find a means for discovering himself, if really called upon to set about the task, for it is possible for a man to be a good working engineer, and at the same time be quite ignorant of reading, writing or figuring; but experience shows that in order to advance in the confidence of others, it is very necessary to know something of the elements, or first things, of mathematics related directly or indirectly to steam. Arithmetic is the science of numbers, and numbers treat of magnitude or quantity. Whatever is capable of increase or diminution is a magnitude or quantity; a sum of money, a weight, or a surface, is a quantity, being capable of increase or diminution. But as we cannot measure or determine any quantity, except by considering some other quantity of the same. kind as known, and pointing out their mutual relation, the measurement of quantity or magnitude is reduced to this: Fix at pleasure upon any known kind of magnitude of the same species as that which has to be determined, and consider it as the measure or unit. If, for example, we wish to determine the magnitude of a sum of money we must take some piece of known value, as a dollar, which is the unit of money, and show how many such pieces are contained in the given sum. |