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This sustainable residence features an exterior made of maintenance-free Cor-ten steel, Trex, copper and stucco. Designed by Ehrlich Architects, located near the Pacific Ocean, in Venice, CA.& last but not least, my favorite for its seamless indoor/outdoor transition and its location in Dolores Heights, San Francisco. A 1970’s Hill Street home remodeled and designed by John Maniscalco Architecture. BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND THE GIFT OF HENRY W. Circuit — The Horizontal Auxiliary Circle — The XV 111 TABLE OF CONTENTS Construction of the Phase Angle — The Vertical Auxiliary Circle — The Eccentric Circle — Multiple Auxiliary Circles — Reactance and Resistance in Series with a Constant Voltage Circuit — Parallel Circuits with Constant Applied Voltage — Relabeling the Lines of a Circle Diagram — The Deter- mination of the Equivalent Resistance and Equivalent Reactance — Parallel Circuits whose Constant Elements are Unlike — The Circle Diagram for a Constant Current Circuit — Circuits having Constant Resistance and Constant Induct- ance with Variable Frequency — Multiple Circuit Circle Diagrams 601 APPENDIX Greek Alphabet — Instructions for Preparing and Reporting Daily Work 631 TABLES FOR REFERENCE TABLE PAGE IV. The unit of measure, as its name implies, has a magnitude of one. The annexing of zeros after a number multiplies by powers of ten. We then have the following summary, assuming the original number to be 95623 : 95623 = 95623X1 956230 = 95623X10 9562300 = 95623 X 100 = 956230 X 10 95623000 = 95623 X 1000 = 9562300 X 10 It is observed that the multiple value of each figure depends on its position in a given number. 9 FUNDAMENTAL OPERATIONS 3 inclusive require one figure. To write a number one-tenth of this value remove one zero on the right and move each figure one place to the right. 3 has a capacity of 80 amp.- hrs., how long could the above current be maintained?

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SAGE 1891 ar V17967^°™*" ""'"^'^'^V Library oljn, ,an^ 1924 031 234 226 The original of tliis book is in tlie Cornell University Library. Armature — Torque — Flux Density in Armature 182 CHAPTER X Winding Calculations The Dimensions of Insulated Wire — Square Winding — Stagger or Imbedded Winding — Number of Tiu'ns — Diameter of Wire in Terms of Resistance and Winding Volumes — Volumes of Winding Space 197 CHAPTER XI Formulas op Mensuration Units of Area and Volume — Area of a Parallelogram, Triangle, Trapezoid, Regular Polygon, Circle, Annulus or Circular Ring, El Upse — Squaring the Circle — Rectification of a Circular Arc — Approximate Perimeter of an Ellipse — The Sector and Segment of a Circle — Area of Segment of Ellipse, Parabola — Approximate Length of a Parabola Segment of an Hyperbola — Ai-ea of an Irregular Figure, by Planimeter, Squared Paper, Weighing, Mean Ordinate Rule, Mid Ordinate Rule, Trapezoidal Rule, Simpson's One-third and Three- eighths Rule, Durand's Rule, Weddle's Rule — The Cycloid —The Helix— The Spiral— The Conical Spu-al — Unit of Volume — Cube — Rectangular Prism — Triangular Prism — Oblique Prism — Quadrangular, Pentagonal, Hexagonal, Right and Oblique Prisms — Total Surface of a Prismatic Figure — The Volume of a Pyramid — Volume of a Cone — Plane Sections — Frustum of a Pyram-'d or Cone — Volume of a Prismoid — Ungula of a So Hd — Cyhndric Surface, Surface of a Cone — Figures of Revolution — ^Guldinus' Theorems, Solid Rectangular and Circular Rings — Comparison of Cy Hn- der. To write a number ten times as great move the figure one place to the left and fill in its former position with a zero. If this process be continued the number will be divided by ten in each stage. There are no known copyright restrictions in the United States on the use of the text. Cone and Sphere — Segment of Sphere, Spherical Zone, Oblate and Prolate Spheroids — Volume of Segment of Sphe- roid, Paraboloid, Hyperboloid — -Regular Solids — Volumes of Irregular Solids — Binomial Theorem — Approximations and Errors — Applications of Pythagorean Theorem 202 xii TABLE OF CONTENTS CHAPTER XII The Quadratic Equation PAGE Degree . 559 CHAPTER XXXI Series Parallel Circuits 570 CHAPTER XXXII Alternating Current Problems A- and F-Connections — Transmission Lines 573 CHAPTER XXXIII The Algebra of a Transpobmeb The Transformer — Equivalent Resistance and Reactance — Losses and Efficiency — Design of Core — Connections — ^Auto- transformer 590 CHAPTER XXXIV The Circle Diagram Variable Elements in an A. Although we may continue to move the figures to the right we shall have exhausted all the zeros in three stages, i.e., we have reached the number 95623. Express in coulombs and also in ampere-hours (amp.-hrs.). THE MATHEMATICS OP APPLIED ELI^CTRICITY A PRACTICAL MATHEMATICS BY EENEST H. High School of Commerce, New York City "THE KEY TO EVERY MAN IS HIS THOUGHT". of an Equation — Solving a Quadratic Equation by Factoring — Solving a. of Self-induction — Unit of Inductance — Inductive Reactance — Inductance Formulas — Mutual Induc- tance — Practical Values of Inductances — Capacity — Capacity of Condensers — Table of Dielectric Constants — Practical Values of Capacities — Formulas for Calculating Capacities — Parallel Connection of Condensers — Series Connection of Condensers — Condensers Connected in Series Parallel-Ar- rangement — The Energy Equation of an A. Circuit — Reactance 504 CHAPTER XXVI Elementaey Operations of Vector Analysis Vectors — Vector Representation — Equal Vectors — The Addition of Vectors — Concurrent Forces — The Vectorial Representa- tion of Currents and E. Fs 524 CHAPTER XXVII Vector Algebra Symbohc Representation of a Vector — Vector Notation — The Magnitude and Inchnation of a Vector 536 CHAPTER XXVIII The Graphic Solution of A. Problem.s Circuits having Resistance and Inductance — Power Factor — Circuits having Resistance and Capacity — Circuits having TABLE OF CONTENTS :PAGE Inductance, Capacity and Resistance — General Expressions for an A. Circuit 539 CHAPTER XXIX Semes Circuits The symbols for R, X, Z — Standard Frequencies — Problems Solved Graphically and Numerically — Resonance — Problems Solved by Adding Impedances 546 CHAPTER XXX Parallel Circuits Graphic and Numeric Treatment of Problems Relating to Parallel Circuits — Equivalent Impedance — Circle Diagram. To write a number one-tenth of 95623, move the figures one place to the right and insert a decimal point between 2 and 3.

FIRST EDITION, CORRECTED SECOND THOUSAND NEW YORK JOHN WILEY & SONS, Inc. Quadratic Equation by Completing the Square — The Graphic Construction of the Roots of a Quad- ratic Equation — The Removal of the Radical from an Equa- tion — Indicated Operations and Inverse Operations — Homo- geneous Equations — Parenthetical Quantities 247 CHAPTER XIII The Elements of the Stkength of Materials Stress per Unit Area — The Strength of any Material — A Beam — Lever Arm, Moment — Bending Moment — A Canti- lever — Center of Gravity, Centroid — Moment of Inertia, Radius of G3Tation — Biquadratic Inches — Neutral Axis, Resisting Moment — I-beam, T-beam, Channel — Comparative Strength of Beams of Equal Length and Equal Cross-section — Stiffness, Deflection — Polar Moment of Inertia — Combined Bending and Twisting — Pulley Diameter, Armature Bearings — Riveted Joints and Their Efficiency 259 PART II THE GRAPHS OF FORMULAS AND THE FORMULATION OF GRAPHS CHAPTER XIV The Use of Squared Paper Graphic Methods, Data, Cross-section Paper — Plotting Tabulated Data — Transformation of the Axes — Plotting of a Third Variable — Plotting of Formulas — The Graphic Representa- tion of Ohm's Law 279 TABLE OF CONTENTS :.;iil CHAPTER XV Linear Graphs PAGE Preparation of Tables and Plates — Slope — • Dependent and Independent Variables — Characterization of Linear Graphs — Degree of an Equation — The Proof that a Linear Graph Represents a Simple Equation — Intercepts — Writing the Equation of a Given Straight Line — Graphic Representation of Simultaneous Equations 300 CHAPTER XVI Non-Linear Algebraic Equations A Non-Linear Equation, Algebraic Equations — Parabolic Curves — Family of Standard Parabolas — Famihes of Curves — Odd-Odd, Odd-Even, Even-Odd Parabolas — The Composi- tion of Curves by Addition and Subtraction — Hyperbolic Curves — Powers, Roots, Reciprocals — Other Non-Linear Equations, Power Series — Conic Sections, Conic Test — The Meaning of the zy Term — The Solution of Non-Linear Simultaneous Equations 316 CHAPTER XVII Eccentricity op Conics Analytic Definition of a Conic — Eccentricity — Construction of Conics with Straightedge and Compass — Properties of Parabolas and Hyperbolas 342 CHAPTER XVIII The Formulation op Graphs Writing the Equation of a Curve — Linear Forms of Non- Liuear Equations — Logarithmic Cross-section Paper — ^The Plotting of Curves on Logarithmic Paper — Special Forms of Cross-section Paper for Linear Plotting of Non-Linear Equa- tions — ^Exponential Equations — The Exponential Family of Curves — Exponential Table 348 XIV TABLE OF CONTENTS CHAPTER XIX The Use of Polar Paper PAGE Polar Coordinates — Polar Paper — Plotting on Polar Paper — Polar Equations — Polar Equation of Conies, Circle — The Logarithmic Spiral — Roulettes, Cycloid, Epicycloid, Hypocy- cloid — Evolutes and Involutes — The Trisection of an Angle, Conchoid — The Multisection of an Angle, Chordel 367 CHAPTER XX Solving Formulas by Charts Graphic Solution by Charts — Linear Coordinates — Chart Solution of Quadratic and Cubic Equations — The Change of Chart Scales — The Reduction of a Cubic — The Charting of Linear Forms, Reciprocal Forms and Composite Forms — Chart of Charts 383 CHAPTER XXI Measurement of Angles Angle Designation — Radian of Arc, Radian of Angle — Verification of Trigonometric Equations — Functions of Algebraic Sums of Angles — Functions of Half Angles — Tangent Functions — Exponential and Trigonometric Series — Hyperbolic Functions 393 CHAPTER XXII Harmonic Motion Simple Harmonic Motion — The Sine Curve, a Record of Simple 'Harmonic Motion — Plotting the Fundamental Sine Curve — Angular Velocity, Period, Frequency — Comparison of Sine Curves of Different Frequency — The Amplitude of a Sine Curve — Angle of Phase — The Resultant of Two Simple Harmonic Motions — The Product of Two Sine Curves, Power Curves — The Curve of Damped or Decaying Oscillation — The Graphic Solution of Inverse Functions 401 TABLE OF CONTENTS xv CHAPTER XXIIl Rates, Derivatives and Integrals PAGE Speed — Velocity — Slope — Scale of Velocity — Initial Average and Final Velocity — Linear and Angular Velocity — The Derivative — The Graphic Determination of the Derivative of a Curve — Primitives and Derivatives — Differentiation of Formulas — The Proof of the Law of the Derivative of a Power — ^The Operation of Obtaining a Derivative — Integration of a Power, Exponential and Logarithmic Forms — An Abridged Table of Integrals — Graphic Integration — The Graphic Inte- gration of a Linear Form — Graphic Double Integration — The Scales of Integral Curves — The Integi-ation Formula for the Area of a Curve — The Area of the Sine Loop — Mean Effec- tive Value of an Harmonic E. F., or Current — The Moment of Inertia Formula for a Structural Section — The Static Mo- ment Formula for any Figure — Graphic Determination of Static Moments, Moments of Inertia, and Centers of Grav- ity of Sections — Nomenclature and Interpretation of Dif- ferential and Integral Expressions ■. PROBLEMS CHAPTER XXV Inductance and Capacity PAGE Counter E. To write a number one- tenth of the last result, move the figures one place to the right and shift the decimal point one place to the left, and so on. What is the increase for any group of ten numbers following a set of ten numbers? London: CHAPMAN & HALL, Limited 1914 Copyright, 1912 BY ERNEST H. SCIENTIFIC PRESS ROBERT DRUMMOND AND COMPANY BROOKLYN, N Y. PREFACE This text was developed primarily for the mathematics instruction of second year students in applied electricity courses at Pratt Institute. — A Resistor, Resistance — Drop of Potential — Power — Conductance — Temperature Coefficient — British Thermal Unit, Pound and Small Calorie — Efficiency of Transformation and Transmission — Net Work in an Elec- tric Circuit, Kirchhoff's First Law — Kirchhoff 's Second Law — Back Pressure ' 151 CHAPTER VIII Efficiency of Generators and Motors Efficiency — Electrical Efficiency — Commercial or Not Efficiency — Gross Efficiency 179 CHAPTER IX The Algebra of the Magnetic Circuit Comparison of Magnetic and Electric Circuit Relations — Mag- netizing Force — Flux Density — Reluctance — Permeance — The Field within a Coil, a Solenoid — Ampere-turns — Reluctance of a Compound Circuit — Total Ampere-turns — Leakage Permeance — The Flux in a Generator — The Energy TABLE OF CONTENTS xi PAGE Loss due to Hysteresis — The Energy Loss due to Eddy Cur- rents—The Average E. 430 CHAPTER XXIV Experimental Curves The Effect of the Variation of Load and Terminal Voltage on the Operation of a Shunt Motor — Characteristic Curves of a Compound Generator — Characteristic Curves of a Series Generator — The Changes in the Current, Voltage and Density of the Electrolyte of a Storage Battery during Discharge — The Efl&ciency Test of a Shunt Motor — Comparison of the Starting Torque of Shunt and Series Motors — The Perform- ance of a Rotary Converter — Electrical Measuring Instru- ments — Siemens Dynamometer, Thomson Ammeter, Queen Ammeter, Whitney D, C. 483 xvi TABLE OF CONTENTS PART III VECTORS AND VECTOR DIAGRAMS. This is illustrated below: 95623000 9562300 =t V of 95623000 956230 =t V of 9562300 95623 = iw of 956230 9562.3 = t V of 95623 956.23=t V of 9562.3 Fractions whose denominators are powers of ten are 3 9 7 6 united into a decimal. Each numerator takes its 10 102 103 10* position in the decimal answer corresponding to the power of 10 in its denominator. The addition of numbers should be checked by adding the columns from the top downward as well as from the bottom upward. PREFACE TO FIRST EDITION, CORRECTED The hearty reception which has been given to this book by the technical public has demonstrated not only that it supplies a practical self help to knowledge for the uninitiated, but also an unexpected want as a reference book of mathe- matics for teachers and graduates of colleges, schools of technology, and technical and trade high schools. It is intended to follow a year of drill in the essential elements of algebra, plane geometry and plane trigonometry and also in the elementary prin- ciples of mechanics, heat and electricity. CHAPTER I Fundamental Operations PAGE Numbers, Magnitude, Measurement — The Decimal System — Addition, the Use of Letters as Symbols of Abbrevia- tion — Subtraction, Parentheses — Multiplication, Factors — Properties of Simple Geometric Constructions — Axioms and Their Applications — Summary of Theorems on Lines and Angles — Demonstration — Triangles, Quadrilaterals and Polygons — Areas of Figures — Variation, Ratio, Proportion — Theorems on Proport'ons — Projection — Trigonometric Func- tions — The Use of Trigonometric Tables — Functions of Angles of Any Quadrant — The Right Triangle — Square Root Operations upon Fractions — Laws of Numbers — The Oblique Triangle — Logarithms — The Slide Rule — Trigonometric and Logarithmic Tables 1 CHAPTER II The Teansfobmation op Foemulas The Formula — The Notation — The Data — The Transforma- tion — The Solution — The Interpretation — The Analysis of a Formula — Transformation of Formulas 124 CHAPTER III Inteepretation op Foemulas 131 ix X Txk BLE OF CONTENTS CHAPTER IV The Formulation of Problems PAGE The Ampere-hour 133 CHAPTER V Variation Problems Applied to the Electric Circuit Variation of Resistance with Length and Area — Mnemonics of Ptesistance — Square and Circular Mil 136 CHAPTER VI The Algebra op a Simple Electric Circuit 145 CHAPTER VII The Applications of Ohm's Law Current, E. The number 956.23 means 9 times 100 and 5 times 10 and 6 units and 2 tenths and 3 hundredths. Where the numbers contain many figures, the sums of each column should be written below the columns, and finally the total sum should be written at the bottom as shown in the following example.

The book is now free from errors and is substantially unchanged except for the insertion of the Law of Conversion Factors on page 178. The introductory chapter has been written to meet the requirements of other young men who are occupied in various electrical industries and who find their progress retarded in electrical matters owing to their deficiency in the knowl- edge of elementary practical mathematics. In other 2 3 words 956.23 means 900 and 50 and 6 and — and — — , or 4 PRACTICAL MATHEMATICS 2 3 to 900 add 50 add 6 add — add — . The marks *, f, °, ', to the right of the figures indicate that those similarly marked were grouped in the summing. Interpret this formula as hours follows : Law for ampere-hours consumed in an electric circuit : multiply the average strength of current (in ? Owing to the size of the book in its present single volume form it has been considered inadvisable to respond to the demand that some of the chapters be en- larged. Goodwin, Jr., chief electrician of the Weston Electrical Instrument Co., for the changes which have been made in the Table of Mil-foot Resistances and a few minor corrections. The text will prove a very helpful aid as a short practical course in Trade,, Industrial and Technical High Schools, and in Apprentice- ship courses. TABLE OF CONTENTS PART I THE TRANSFORMATION AND INTERPRETATION OF FORMULAS. The symbol for add 10 100 is ( ) read plus, so the above may be written, OOO SO G .2 . The sum of the figures in the units column is 66, which is the same as 60 and 6. The author wishes to acknowledge his indebtedness to Mr. The purpose of practical mathematics is to bring to the student's attention the underlying basic structure of the relations of the elements of electrical phenomena so that he may formulate them, interpret them physically and work with accuracy and facility in making numeric and graphic computation. 03, or, rearranging in a vertical column, we have 900 50 6 .2 .03 956.23 Therefore 956.23 is a condensed form which saves space and the writing of zeros. X^e addition of numbers is a process of condensation or uniting of figures in the same column, file or row. Rearrange the digits in double rows so that their sums will gives nines, eights, sevens, sixes, fives, fours, threes, twos, ones. Therefore we write 6 in the units column and 6 under the tens column. CHAPTER IV THE FORMULATION OF PROBLEMS The Ampere-hour. When correlated with a practical, industrial or theoretic course in electricity, practical mathe- matics gives the student a better appreciation of his .major subject and assures him an intellectual penetration into secrets of nature and the utilization of her powers. It is read nine fifty-six point twenty-three, or nine five six point two three. An excess over nine in any column is counted into the next column to the left. (1) (2) (3) (4) (5) (6) (7) (8) 12 37 48 52 73 94 50 66 37 64 78 32 90 33 62 98 45 76 21 45 67 78 32 54 68 43 64 38 23 79 22 65 77 11 13 6 60 5 4 23 29 46 7 8 23 54 59 31 column j 38 sums 1 23 sum 268 The process is identically the same when the numbers are arranged horizontally, 12 37 -1-45 68 -|- 77 -h29 =268. It will be observed that some of these combinations are repetitions. The sum of the figures in the tens column is 18, which means that we have 18 times 10, or 180, or 100 and 80. The coulomb is a very small quan- tity of electricity. What is the equivalent of one amp.-hour (a) for a current flowing for 4 hours; (&) J ampere requires what equivalent time; (c) show that 3600 coulombs is the equivalent of an amp.- hour. Instruc- tion from the mimeographed form of this text has been conducted for a number of years and has demonstrated its YJ PREFACE usefulness as a powerful and interesting presentation which has promoted the student's judgment, fidelity, poise, com- mon sense and tact in his applied work and in subsequent success in foremanship, superintendence and in other exec- utive and administrative positions. Brown, for valuable assistance in preparing plates and diagrams. In the latter case the figures are united in the order of their numeric position. FUNDAMENTAL OPERATIONS 5 It is of primary importance for the computer to be able to recognize instantly the sum of two integers. Write the integers in any mixed order, then state or write immediately the complementary number. Therefore we write 8 under the tens column and 1 under the hundreds column. 4 for V and interpret as follows : Law for the volume of a gas generated by a known current in a given time : . For commercial purposes a larger unit, the ampere-hour, is used.

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The author aims to present the text according to the modern principles of education which makes the text not only teachable but also self-instructive. It gives me great pleasure to commend the engravers, printers and publishers for their careful and conscientious labors in producing this book. In the following arrangement of two reversed rows of integers the student should recognize that each column sums 10. Proceeding in like manner with the other columns, we obtain 80 for the sum of the hundreds column, which means 80 times 100, or 8000. One ampere-hour is the quantity of electricity that would pass any point in a circuit in one hour when the strength of current is one amp. Although the work is graded and arranged in logical sequence it is so written that it may be presented in any order irrespective of chapter divisions. Therefore we write 8 under the thousands column and zero or nothing under the hundreds column. There is considerable material of a more advanced character which may be omitted on first assignment and used later for review or in further preparation for more advanced study. The sum of the thousands column is 45, which means 45 times 1000, or 45,000, or 40,0. Setting down the 6 PEAOTICAL MATHEMATICS figures under the columns enables us to check the work more rapidly.

One aim has been to use simple diction, good English, and carefully phrased statements which shall assist the student in becoming familiar with technical terms and guide him in expressing his observations in his own language. Therefore we write 4 under the ten-thousands column and 5 under the thousands column. Therefore we write 9 under the ten-thousands column. 3 1° 4 1* 6* excess over 9 =6 1 5 7 8t 3 7* 8 5 4t 6 3* 9 2 7 3 2 7t 8 1 8t 8 1 3t 9 9 4 4- 5 4* 5* 9 9* 3 3- 6 6- 9 6* 4- 6 1 3° 3 1- 8 1 6° 6 2- excess over 9=3 6 6 6 56 excess over 9 the sums 1 8 of each 8 8 column 4 5 9 sum 14 3 2 4 6 excess over 9=2 11 excess over 9=2 hundred-thousands ten-thousands thousands 1 ll M The sum total is a short way of stating that we have altogether 100,000, 40,000, 3,000, 200, 40, and 6. Abstract mathematic theory has been avoided as non- essential since the author realizes that any so-called utili- tarian or practical book cannot fail to provide the so-called cultural aspects of education. The Graphs of Formulas and the Formulation of Graphs. Vectors and Vector Diagrams, Alternating Current Problems. Williston, Principal of Wentworth Institute, who inspired the creation of the text. am indebted to many of my former students, more particularly to Messrs. In words we have one hundred-thousands plus four ten-thousands plus three thousands plus two hundreds plus four tens plus six units. 3 for W and interpret as follows : Law for the weight of any metal that will be deposited in a voltameter by a given current in a given time : .   The text contains a limited but an adequate amount of information concerning electrical phenomena so as to minimize the necessary references to supplementary electrical texts. I have collected problems during a number of years from many sources, making it impossible to give specific acknowledgment. Marsh, Head of the Department of Mathe- matics, to Mr, S. Edmands, Director of the Schooi PEEFACE vii of Science and Technology, Pratt Institute, and to Mr. Therefore 100000 40000 -1-3000 -1-200 -|-40 & = 143246.  

Problems and examples are both designated under the abbreviation of exercise — Ex. I am indebted to my colleagues for many suggestions and express my thanks and appreciation to Mr. An additional check is obtained by casting out the nines. For convenience the text is divided into three parts, viz. Write the excess over 9 from the sum of the digits in each row and also from the sums of excesses.

The unit of measure must possess the same quality, characteristic, i.e., denomi- nation of the object measured. In the decimal notation, all numbers are based on a system of ten, making it possible to write a number with comparatively few figures. A number followed by 000 is multiplied by 1000, and so on. Magnitude is a number which states how many and not what kind of units the object contains. The observation from the above list of examples is that magnitudes express the results of measurements or comparisons. How long a time will be required to deposit 5 grams of silver on a copper-plated teaspoon with a current of 2 amps.?

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(9) Describe at least ten other scales not used in the above examples. (8) Measuring and weighing a brick, cement building block. The negative plate of a copper voltameter has increased its weight 1.9 grams in 35 seconds. (6) Weighing a quart of water, sand, cement, loose earth, packed earth, 100' No. (7) Measuring the length, breadth, and thickness and also by weighing a copper bus-bar, bars of steel, wrought and cast iron. (5) Measuring the sides and perimeters of regular and irregular sections of materials provided by the instructor. (4) Measuring the parts of a motor, generator, engine, shafting. In an electroplating bath how many grams of zinc will be deposited by a current of 5 amps, in 60 min? (3) Measuring a table, desk, box, quart can, ash can, oil can. The magnitude of a quantity is the number of units which it contains. (2) Measuring the length, breadth and thickness of a door. The following data are recorded in a gas voltameter test: Level of burette before test 2.7

Any division or part of a scale may be used as a unit of measure and thereby extend the range of measurement. If the weight were expressed in ounces, its magnitude would be eighty. In as manv ways as possible express the magnitude by 2 PRACTICAL MATHEMATICS (1) i Measuring the length, breadth and height of your room. A scale is a measuring stick, instrument, or device upon which there is a series of graduated lines numbered in sequence. In the following measurements use the most convenient devices at hand, such as a yardstick, foot-rule, tape- measure, store scale.