retical training, and to whom such a book as this would be but of small service were they not first enabled to gather a few elementary principles, by which means they may learn to use and understand these Formulæ. whose works have been In justice to those authors whose wo consulted, it must be added that most of the Rules and Formulæ here given are not original, although perhaps appearing in a new shape with a view to making them simpler. who are There are many into whose hands this work will fall well able to criticise it, both as to the usefulness of the matter it contains." From such accuracy critics the Author invites any corrections or fresh material which may be useful for future editions. and the 182-186 186-209 . 210-219 . 220-221 222-266 267-268 BOARD OF TRADE REGULATIONS FOR MARINE BOILERS, ETC. 467–478 MACKROW'S POCKET BOOK OF FORMULE, RULES, AND TABLES FOR NAVAL ARCHITECTS AND SHIP-BUILDERS. SIGNS AND SYMBOLS. THE following are some of the signs and symbols commonly used in algebraical expressions: This is the sign of equality. It denotes that the quantities so connected are equal to one another; thus, 3 feet = 1 yard. This is the sign of addition, and signifies plus or more; thus, 4+ 3 = 7. This is the sign of subtraction, and signifies minus or less; thus, 4-3=1. This is the sign of multiplication, and signifies multiplied by or into; thus, 4 x 3 = 12. This is the sign of division, and signifies divided by; thus, 4÷2=2. [These signs are called brackets, and denote that the quantities between them are to be treated as one quantity; thus, 5{3(4+2)-6(3—2)}=5(18–6) = 60. " This sign is called the bar or vinculum, and is sometimes used instead of the brackets; thus, 3(4+2)—6(3—2) × 5 = 60. Letters are often used to shorten or simplify a formula. Thus, supposing we wish to express length x breadth x depth, we might put the initial letters only, thus, × b× d, or, as is usual when algebraical symbols are employed, leave out the sign x between the factors and write the formula l.b.d. When it is wished to express division in a simple form the divisor is written under the dividend; thus, (x + y) ÷ z = B x + 2 |