This book is not a course in mathematics, but a handy book for the practical engineer and electrician. As the book is chiefly intended for the operating engineer and electrician, it treats only of such subjects as the authors have found from their own experience will be of value to such men. A great many of the best operating engineers and electricians, while knowing their trade well, have never had the advantage of a college education, and the ordinary books on mathematics are written above their heads as well as being too voluminous. To those who have had a mathematical training, this book will also be of especial value on account of the practical way in which all subjects are treated. Most books published on technical subjects contain many useless pages, either of theory or of subjects which are of no especial value in the general reader. It has been the aim of the authors of this, book to make it of value to all such men by making it elementary, written in simple, clear language; and treating only of such subjects as are of especial value to all practical workmen. The authors have assumed that the reader knows but little of mathematics; and, while the subjects selected cover a wide scope, being such as are usually found scattered through two or three different volumes, no subject has been treated which requires knowledge of any preceding subject or any previous knowledge of mathematics. Any one who fully understands all the subjects here treated will find that, however elementary this book may be considered, he will have all the mathematics that is required to make him a first-class operating engineer or electrical worker. Chicago, May, 1912. THE AUTHORS. LIST OF TABLES. TABLE. 1. Weight of Cubic Foot of Steam at Different Pressures PAGE. 41 2. Heating Value of Coal... 45 3. Total Heat of Steam at Different Pressures. sures 51 4. Boiling Point of Water for Different Pres sures 52 5. Percentage of Moisture in Steam for Different Pressures and Degree of Superheat in Calorimeter 6. Factors of Evaporation... 53 57 7. Heating Value of Different Kinds of Fuel... 61 8. Five Place Logarithms. 9. Square Roots, Cube Roots, Squares and Cubes 10. Sines, Cosines and Tangents.. 11. Sines, Cosines and Power Factors. 12. Electric Wiring Table..... ...86, 87 96 119 120 124 13. Velocity of Air at Different Pressures...... 125 PRACTICAL MATHEMATICS FOR THE ENGINEER AND ELECTRICIAN The engineer and the electrician must be prepared to compute accurately the cost of supplies and the cost of power, to furnish estimates of cost of proposed installations including material and labor, and to work out the problems that arise in every power plant. In this series of articles on practical mathematics we shall give all the methods needed for making such estimates and calculations. We shall begin with Common Fractions. A fraction is a part or a certain number of parts, of a unit, as 1⁄2 cent, 34 foot, % inch, etc. Take the fraction % inch. An inch is divided into eight parts. The number below the line tells how many parts the unit is divided into. This number is called the denominator. It denominates or names the parts. Each part is one-eighth of an inch. The number above the line tells how many parts are taken. It is called the numerator, for it numbers or numerates the parts. If we say that a screw is % inch long, we suppose an inch to be divided into 8 parts and the screw is as long as 7 of these parts. The name of each part is one-eighth, and the number of parts is 7. The denominator is 8. The numerator is 7. Multiplying Fractions. To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number. For example: if we have three pieces of piping each 3/4 of a foot in length, then when the three pieces are placed end to end, the three together will be 3 times 34 or 4 feet in length. Now, since there are 4 fourths in one foot, and 8 fourths is two feet, then 4 will be 1 fourth more than 2 feet, that is 24 feet. Again, if we buy 50 feet of pipe that costs 3/4 cent a foot, the 50 feet will cost 50 times 34, that is 15% cents. Now, since in 1 cent there are 4 fourths, we find how many times 150 fourths contains 4 fourths. 4 goes into 150, 37 times and 2 remaining, that is there are 37 and 2 fourths cents. Since 4 fourths make a cent, 2 fourths make one-half cent. We have 372 1. Find the cost of 70 feet of pipe, at 3/4 cents a foot. Answer, 521⁄2 cents. 2. Find the cost of 120 feet of pipe, at 7% cents a foot. Answer, 105 cents, or $1.05. If we have a number that consists of a whole number and a fraction, to multiply the number we multiply the whole number and the fraction separately, and add the results. Thus to multiply 254 by 3-3 times 25 equals 75, and 3 times 4 equals 34. Adding we have 75 and 3 fourths. Hence, 254 X 3 = 7534, or 254 3 7534 To multiply 271⁄2 by 3, 3 times 27 equals 81, and 3 times 1⁄2 equals. But equals 12. Adding 81 and 11⁄2 we have 822. Hence, 272 X 3 822, or written in another way, = 274/2 3 822 |