UNIVERSITY OF CALIFORNIA AT LOS ANGELES GIFT OF MRS. JOHN C.SHEDB LABORATORY EXERCISES TO ACCOMPANY CARHART AND CHUTE'S FIRST PRINCIPLES OF PHYSICS BY ROBERT W. FULLER AND RAYMOND B. BROWNLEE STUYVESANT HIGH SCHOOL, NEW YORK CITY ALLYN AND BACON Boston Itfeto gork C COPYRIGHT, 1912 AND 1913, BY ROBERT W. FULLER AND RAYMOND B. BROWNLEE F151 PREFACE IN the preparation of a Physics laboratory manual, it is nec- essary to take into account the diversity of courses and equip- ment in different schools. The individuality of the teacher and the limitations of equipment have been recognized in the selection and treatment of topics, in these Exercises, and a wide choice of experiments has been provided, only a few of which require highly specialized apparatus. Where such apparatus is decidedly superior to that commonly used, specific directions for its preparation have been given in footnotes. Experiments which have proved their value in generally accepted courses have been retained with such simplifications as seem desir- able to secure directness. Other experiments which repre- sent the more modern trend in Physics teaching are introduced in considerable number to enrich the course. Many students lose the value of the laboratory period be- cause it is spent in following directions in a purely mechanical way, while they wonder why the particular problem on which they are engaged should be done at all. In order to settle this question in the student's mind, the authors have been in the habit of furnishing their students with an introductory paragraph for each experiment. This introduction connects the experiment with the pupil's experience and furnishes defi- nitions of such terms as are necessary to the understanding of the directions. This introductory paragraph also permits the laboratory experiment on a particular topic to be given either before or after the subject is discussed in class, as the instructor may desire. Following the plan of the best laboratory manuals, definite provision has been made for recording observations and calcu- lated results either in tabulations or in simple diagrams. This plan permits the student's record to be made in a minimum time and leaves a larger proportion of the period available for actual laboratory work and the consideration of results than is possible when a running record is made. It also reduces the iv PREFACE time necessary for the instructor to judge the accuracy of the student's results, as well as his grasp of the principles involved. The Conclusion always calls for a definite answer to the question which is raised in the Object of the experiment. Other important facts or principles which may be deduced in connection with the experimental work are subjects for ques- tions in the Discussion. These may be answered orally as the instructor passes from student to student, or, in large classes particularly, the answers may be written in the note-book. In any case, these questions direct attention to the salient points of the experiment and should be taken up in the quiz on the laboratory work. The authors wish to express their grateful appreciation of the assistance which they have received in the preparation of this book. Among their associates in the Stuyvesant High School they are particularly indebted to the principal, Dr. E. K. von Nardroff for valuable suggestions and for the stimulus which his interest in the experiments has afforded; to their colleagues in the Physical Science Department, particularly Mr. J. G. Baier and Mr. H. W. Mott, for many helpful criti- cisms and suggestions; and to Dr. H. E. Fritz, for valuable assistance in the preparation of the drawings. Many of the drawings have been made by the following students : Charles E. O'Rourke and Harold Jay, of the Stuyvesant High School, and John G. Smith, of the Geneseo Normal School. In connec- tion with particular experiments, acknowledgment is made to the teachers who rendered assistance in these experiments. Thanks are tendered also to Professors Carhart and Chute for permission to use several cuts (Figs. 3, 35, 68, and 112) from the " First Principles of Physics " ; to Professor W. H. Timbie for the use of the Eesistance Table (p. 315) from his "Ele- ments of Electricity"; and to the L. E. Knott Apparatus Company for the use of several cuts. The authors will gladly receive criticisms and suggestions from teachers who may use the Exercises in their classes. R. W. F. R. B. B. FEBRUARY, 1913. CONTENTS PAGB Suggestions to the Instructor 1 Directions to Students 9 Mechanics KXPERIMEKT 1. Metric Units of Measurement ..... 18 2. Properties of Materials . . . . . .21 3. Measurement of Bodies ...... 24 4. Volume Measurement of an Irregular Body . . 30 5. Density .32 6. Elasticity Hooke's Law . . . . .34 7. Tenacity of Wire 37 8. Relation between Pressure and Depth ... 40 9. Archimedes' Principle 43 10. Law of Flotation 45 10. (Alternative) Law of Flotation .... 46 11. Specific Gravity of Solids 48 12. Specific Gravity of a Liquid (Bottle Method) . . 50 13. Specific Gravity of a Liquid (Hydrometer Method) . 52 14. Specific Gravity of a Liquid (Hare's Method) . . 55 14. (Alternative) Specific Gravity of Liquids (Balancing Columns) ........ 58 15. Density of Air 62 15. (Alternative) Density of Air 65 16. Boyle's Law 68 17. Measurement of Gas Pressure . 71 yi CONTENTS EXPERIMENT PAO 18. Water Pumps 74 19. Principle of Moments 77 20. Lever Arm of a Force . ' . . . . .80 2 1 . Composition of Several Parallel Forces . . . 82 22. Four Forces at Right Angles ... . . .85 23. Parallelogram of Forces . .. .... .87 24. Resolution of Forces ..... . ... 90 25. Force at the Center of Gravity of a Body . . . 93 26. Pendulum ........ 96 27. Inclined Plane . 99 28. Pulleys 102 29. Wheel and Axle 107 30. Mechanical Efficiency of Machines . . . .110 31. Coefficient of Friction . . . . . .113 Sound 32. Vibrations of a Tuning Fork 116 33. Velocity of Sound in Air 120 34. Sympathetic Vibrations 122 35. Wave Length of a Sound 125 36. Laws of Vibrating Strings 129 Light 37. Measurement of Candle Power Jolly or Bunsen Photometer 133 37. (Alternative) Measurement of Candle Power Rum- ford Photometer 136 38. Law of Reflection of Light . . . . .-139 39. Images in a Plane Mirror 142 CONTENTS Vii EXPERIMENT PAO* 40. Reflection in a Concave Mirror . . . .144 41. Reflection in a Convex Mirror . . . . .148 42. Refraction through a Glass Plate . . . ' . 1 49 43. Refraction through a Prism 151 44. Index of Refraction 153 45. Total Reflection '*.'. . . . . . 155 46A. Study of a Converging Lens . . . . .159 46 B. Focal Length of a Converging Lens . . .164 47. Conjugate Foci of a Converging Lens . . .166 48. Magnifying Power of a Lens ' ." . . .169 49A. Astronomical Telescope ''. . . . .172 49B. Compound Microscope 176 50. Dispersion of Light by a Prism . . . .179 Heat 51. Fixed Points of a Thermometer . . . .181 52. Phenomena of Boiling . . . . . .185 53. Coefficient of Linear Expansion . . . .190 54. Coefficient of Cubical Expansion . . . .193 55. Increase in Volume of a Gas at Constant Pressure . 197 56. Increase in Pressure of a Gas at Constant Volume . 201 57. Law of Heat Exchange 205 58. Specific Heat of a Metal 209 59. Cooling through Change of State . . . .213 60. Melting Points and Boiling Points . . . .216 61. Heat Changes during Solution and Evaporation . . 220 62. Heat of Fusion of Ice 223 63. Heat of Vaporization 226 64. Dew Point 230 viii CONTENTS Magnetism and Electricity EXPERIMENT PAGE 65. Magnetic Induction 232 66. Magnetic Lines of Force 235 67. Development of an Electrostatic Series . . . 238 68. Simple Cell 241 69. Two-fluid Cell 244 70. Electroplating . ' 247 71. Electrotyping . . . . . . . .250 72. Storage Cell 252 73. Laws of Resistance 255 74. Effect of Temperature on Resistance . . . 258 75. Internal Resistance of a Cell . . . . 26 1 76. Grouping of Cells 263 77. Resistance and Current in a Divided Circuit . . 266 78. Resistance by Substitution 269 79. Heating Effect of an Electric Current . . . 272 80. Study of an Incandescent Lamp .... 276 8 1 . Lines of Force around a Conductor .... 278 82. Electromagnet . . . . . . .281 83. Electric Bell . 284 84. Telegraph Instruments 286 85. Operation of an Electric Motor .... 288 86. Power and Efficiency of a Motor .... 290 87. Relation between Fall of Potential and Resistance . 296 88. Resistance by the Wheatstone Bridge . . . 298 89. Induced Currents , 302 90. Study of a Dynamo . 304 CONTENTS . ix Appendix PAGE I. Important Numbers and Equivalents . . . 309 II. Properties of Materials 310 III. Density of Water 312 IV. Index of Refraction 312 V. Electromotive Farce of Cells . . . .312 VI. Table of Natural Sines and Tangents . . .313 VII. Size and Resistance of Annealed Copper Wire . 314 VIII. Specific Resistance and Temperature Coefficient . 315 INTRODUCTORY SUGGESTIONS TO THE INSTRUCTOR Selection of Experiments Scope of the Experiments. The experiments in this book provide a wide range of laboratory work for an elementary course in Physics. The exercises have been selected on the basis of their educational value to the student. Their aim is to impart to him certain fundamental principles, to acquaint him with some physical phenomena qualitative in character, and to show the operation and the use of practical devices or instruments that are applications of physical principles. The authors have not hesitated to omit from their list certain well-known experiments which have persisted in many elementary courses, rather by inertia than because of any special interest or value to the beginner. On the other hand, it is impossible to include in a small book all the experiments of merit suitable to a first course in Physics. Yet, from those given, it will be possible for any instructor to make a selection of the experiments which the great majority of Physics teachers include in their courses, so as to afford a well-balanced laboratory training, both interesting and instruc- tive to the student. Recommended Lists. Only the institutions most favored as to laboratory time will be able to complete in one scholastic year all the experiments outlined in this book. Any choice of experiments must depend upon the apparatus available and upon the laboratory conditions. To fit the usual laboratory equipment and to meet the time limitations of most first courses in the subject, the authors suggest the following list of thirty-five experiments as affording a good training in those 1 2 GENERAL SUGGESTIONS fundamentals of the science most suitable for laboratory in struction : FUNDAMENTAL COURSE Mechanics: Exercises 3, 4, 5, 8, 9, 10, 11, 19, 23, 25, 26, 27. Sound : Exercise 35. Light: Exercises 37, 38, 39, 42, 43, 46 A, or 46 B and 47. fiectf : Exercises 51, 58, 59, 61, 62. Magnetism and Electricity : Exercises 66, 68, 69, 70, 80, 81, 82, 83, 84, 85, 89. The following ten exercises will supplement the above, particularly for those students whose ability enables them to do a maximum amount of work : Mechanics, 6, 13 or 14, 28, 29 ; Heat, 57 ; Sound, 34 ; Magnetism and Electricity, 72, Light, 44; 78 (or other experiment on resistance), 90. The following sixty exercises are suggested as a more extended course for those institutions favored with about double the laboratory time usually allotted to the first course : EXTENDED COURSE Mechanics: Exercises 1, 3, 4, 5, 8, 9, 10, 11, 15, 16, 17, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30. Sound : Exercises 32, 34, 35. Light : Exercises 37, 38, 39, 42, 43, 44, 46 A, or 46 B and 47, 48. Heat: Exercises 51, 52, 57, 58, 59, 60, 61, 62, 63. Magnetism and Electricity: Exercises 65, 66, 68, 69, 70, 72, 73, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90. /The authors recommend the following list of experiments /tor girls, especially for those not intending to go beyond the / high school. Most of these experiments have been selected be- / cause of their close relationship to the practical affairs of life. Mechanics: Exercises 1, 2, 3, 6, 8, 9, 12 (or 13 or 14), 17, 18, \ 23,26,27,28. VI TO THE INSTRUCTOR 3 Sound: Exercises 34 (or 35), 36. Light : Exercises 37, 38, 39, 49, 50. Heat: Exercises 51, 52, 59, 60, 61, 64. Magnetism and Electricity : Exercises 65, 68, 70, 79, 80, 82, 83, 84. A number of interesting and valuable experiments do not appear in any of the preceding lists, but it is hoped that some of them will be taken from time to time either as substituted or as additional exercises. A limited amount of variation from year to year adds interest and vitality to any laboratory course. Many of the experiments just referred to will meet the needs of those instructors who desire to give more time" to certain divisions of the subject. Order of Experiments. The order in which the divisions of the subject are taken should depend upon the aim of the course and the conditions under which it is given. In their own work the authors find the most satisfactory order to be Mechanics, Heat, Sound, Electricity, and Light. In most syllabi, however, the subj ect of Light precedes that of Electricity. In the view of many, the experiments on Heat are best adapted to the student's powers after he has finished the experiments in Mechanics. >Time required for Experiments. A majority of the experi- ments are designed to take from 80 to 90 minutes of laboratory time, including the writing of the note-book record. Some of the shorter ones will require but half of that time, or a single school period. Even if a double laboratory period is not available for the longer experiments, the directions have been written so that the experiments can be done successfully in two single periods. The system recommended for the note- book record saves time in securing the observational data. Especial care has been taken not to overload the student with more manipulations and observations than would be reason- able for an average rate of work within the time allotment. 4 GENERAL SUGGESTIONS The Experimental Directions Aim. At first sight it may seem that the directions for the experiments have been written in a rigid form which may hamper the individuality of the teacher using them. With the possible exception of the placing of the tables of observa- tions and calculated results, it will be found that the directions and their requirements are in accord with the usages which have become generally established as leading to intelligent and efficient laboratory work. The five main divisions of the printed directions are "Introductory," "Experimental," "Calculated Kesults," "Dis- cussion," and "Conclusion." Certain suggestions as to these divisions appear in the paragraphs that follow. Introductory. The paragraphs under this heading in the printed directions serve several purposes. First, they awaken the student's interest in the problem to be studied by reference to applications of Physics more or less familiar to him. Sec- ondly, the introductory statements show the relation between the practical applications and the laboratory problem to be solved. In some cases the paragraphs furnish a little theoretical in- formation, necessary for the intelligent performance of the experiment. All that is required of the student is that he read and understand this introductory matter usually a task of a few minutes. It is not expected nor is it desired that the in- troductory matter be copied into the note-book. The authors offer no apology for the paragraphs introduc- tory to the experiments. They have simply put in written form those preliminary remarks that many instructors find desirable to make when the class assembles for the experiment. It is felt that the written form has the advantage of being al- ways available for the student's reference. Experimental. Whenever the length and character of the experiment permits, the laboratory problem is presented as a whole to the student. With the general plan in mind, ' he is able to do the experiment with greater self-reliance and effi- TO THE INSTRUCTOR 5 ciency than can be obtained from the slavish following of detailed directions with little grasp of their intent. In some experiments, however, detailed directions must be given to secure the successful imparting of a series of experi- mental facts. In such cases the divisions are made as few as possible and their meaning made clear by brief directions, a little supplementary information, and questions that the aver- age student should be able to answer from his experimental observations. The students are directed to place the data gathered in the experiment in a table of observations near the top of the left- hand page of the note-book record. The form for this table is usually furnished, and it is strongly recommended that the student write the form in the note-book before making any of the measurements. This procedure provides for the orderly recording of the data as soon as it is obtained, and insures the completion of the experimentation within the laboratory hour. There is economy also of the instructor's time, as he can quickly note the rate of progress of the individual and check inaccuracies in the readings. With most experiments only one set of readings is indicated in the tables of observations, but the instructor desiring more can increase the number of columns at the right. In the opinion of the authors, much time is wasted by requiring the duplication of readings by the elementary student of Physics, unless in work where personal errors are large. Drawings. After the observations are completed, the student is directed to make sectional or outline drawings from his apparatus so as to show that he understands its arrange- ment and operation. Many of the illustrations in this book have been made from drawings made by students in the regular course of their laboratory work. Such drawings will indicate to the users of this book the methods of representing labora- tory apparatus by simple outline drawings. The development of a simple scheme of sectional representation is within the power of any student and will prove most useful to him. 6 GENERAL SUGGESTIONS Descriptions. The table of observations and the sectional drawings render unnecessary long and elaborate descriptions of the experimental work. All that is asked is a brief but clear statement of the general method of the experiment and the recording of any experimental facts not shown by the draw- ings nor provided for in the table of observations. In the last few years it has become more and more recognized that the chief function of the laboratory note-book is to show the essentials of an experiment and not to provide useless drudgery for the student. Calculated Results. Preceding the table of calculated results occurring in many experiments, are found directions for mak- ing the calculations. The authors have not hesitated to fur- nish information to aid the student in making the calculations when these are rendered more intelligible thereby. The directions call for the placing of the table of calculated results at the top of the right-hand page of the note-book record. The calculations themselves should be made directly below the table. These requirements secure prominent and convenient locations for the making of the computations and the orderly recording of the results. The student can tell from the tabular form what is expected of him in the way of calculations and knows when his work is finished. The instructor is enabled to check quickly the recorded results and to point out during the laboratory period sources of error. Discussions. Under this division the student is directed to answer any italicized questions occurring in the experimental directions or the questions under the printed heading, Piscus- sion. Thus the theoretical considerations of the experiment are brought together ready for reference or correction. Conclusions. The student is either required to state for himself the formal conclusion justified by the experimental facts, or to complete a partial statement by filling in the in- dicated blanks. The latter method is preferred in those cases where a complete and well-worded conclusion is difficult for TO THE INSTRUCTOR 7 the student to formulate. The vital part of the statement must be furnished by the student and requires thought on his part. Method of Laboratory Work. Many of the advantages of having the note-book record follow a definite plan have been discussed under the topics preceding this. Tabular forms for the observations and the calculated results are appreciated by many instructors as leading to that economy of laboratory time which gives the best opportunity for experimentation and reflection. The forms for such tabulations may be written in the note-book prior to the laboratory hour and the general plan of the experiment studied. The authors believe that it is not only permissible, but highly desirable, for the student to know before he comes into the laboratory what he is to do. They require their own students to carefully study the experiment and to write the blank table of observations in the note-book before coming to the laboratory. Except in the case of very complicated experiments, the student is not allowed to have the experimental directions before him until he has taken all readings and completed his drawing and description. He is then allowed to refer to his direction sheet for guidance as to his calculations and conclusions. It has been found that under this plan the work in the laboratory is more intelligent and less of the " cook-book " order. Further- more, schools having only single laboratory periods may be certain of having the readings taken and the experiment described during the laboratory period, while calculated results and conclusions may be worked out the next day either in laboratory or classroom, or, if desired, done as part of the home lesson for the day following that of the laboratory period. No factor contributes more to the success of a laboratory course than having the apparatus tested and entirely ready for the student when he enters the laboratory. Then only is it possible for him to put the apparatus together and start its operation without loss of time, so that the readings can be made comfortably within the period. 8 GENERAL SUGGESTIONS Note-book Directions. On page 16 there will be found brief instructions intended for the student and relating to the form of the note-book record. Any orderly plan must have definiteness; so it becomes necessary to designate left-hand and right-hand pages for certain purposes. These directions may reverse the usage of some instructors, but it is hoped that they will realize it makes little difference whether the left-hand page or the right-hand page serves a certain purpose, so long as there is a definite systematic plan to make the note- book record a help to the student, and to make the ever present and laborious task of note-boot correction easier for the instructor. DIRECTIONS TO STUDENTS Balances Construction of Platform Balances. The platform balance 01 trip scale is a simple, equal arm lever in which the vertical displacement of either arm is indicated by a pointer swinging across a horizontal scale. When the pointer swings approxi- mately equal distances on each side of the center division on the horizontal scale, the two lever arms are balanced and the scale is said to be in equilibrium. Fig. 1. Platform Balance. The construction of the trip scale is shown in Figs. 1 and 2 on this and the following page. This convenient instrument for weighing is too often misused in the physical laboratory and poor results obtained with it. With the observance, how- ever, of a few simple precautions, rapid, accurate weighings can be made with this piece of apparatus. Adjustment of Platform Balances. Before weighing always see that both platforms are clean Then touch lightly one 10 GENERAL SUGGESTIONS Fig. 2. Sectional View of Balance. platform and note whether or not the pointer swings freely and equally on each side of the center line of the scale. The pointer should oscillate at least two divisions to the right and to the left. In too short swings the friction in the bearings makes the scale rela- tively less sensitive. Therefore the point- er's coming to rest at the center point is no sure indication that the two arms of the scale are balanced or in equilibrium. In case the pointer swings to a distinctly greater distance on one side of center, turn the thumb nut which is just below the center, so that the nut moves a little distance towards the side of the lesser swing. Again note the swings. When they are approximately equal on both sides of center, the scale is adjusted for weighing. Handling of Weights. Place the object to be weighed on the left-hand platform or pan and the weights on the right-hand platform. In adding or removing weights, prevent with the left hand the movement of the pans until the change of weights has been made. In this way avoid jarring the balance and injuring the knife-edges. For the first weight select the one which in your opinion is about equal to the object being weighed. If this weight is too small, take it off and replace it with the next larger one. Continue in this way until you have the largest weight which is lighter than the object. Then add the next smaller weight. Time-saving weighing means the systematic use of the next smaller or the next larger weight, as the case may be, until the scale is balanced. In practice the graduated beam with its rider enables one to TO STUDENTS 11 dispense with the smaller weights. If the beam is graduated for 5 grains, the 1-gram and the 2-grain weights are not used ; with a 10-gram beam, the weights below 10 grams are not necessary. By means of the graduated beam, these smaller weights are found by moving the rider to the right until the balance is in equilibrium. Note carefully on which side of the rider the reading should be made, and remember that the reading can be made to tenths of a gram. When the correct weight is obtained, count carefully the weights on the right-hand pan and add the weight indicated on the beam. Record this total weight at once in the labora- tory note-book. Return the weights to their block, or case, counting as you do so. Add the weight indicated on the beam and check the weight recorded in the note-book. Remove the object from its scale pan. A scale left with the arms unequally balanced soon loses its sensitiveness, owing to unnecessary wear on the bearings. Beam Balances. Another form of balance much used in the physical laboratory is the beam balance. The beam in this case rests at its center point on a knife-edge, or a wedge, sup- ported on a vertical stand. Pans are suspended on the ends of the beam either by hooks, or in the more expensive kinds by stirrups which rest on knife-edges. A vertical pointer indi- cates on a small graduated scale the oscillations of the beam. Some beam balances have on one arm of the beam a rider, which slides along a graduated scale and thus indicates the smaller weights. To avoid dulling the knife-edges, there is often a device which lifts the beam off the knife-edges when the balance is not in use. The pan arrest similarly lifts the bow and stirrup suspension from off the knife-edges on the ends of the beam. The specific gravity balance is usually a beam balance which has a shorter suspension for one of the pans. From a hook on the under side of this pan are suspended objects which are to be weighed in a liquid. 12 GENERAL SUGGESTIONS The hornpan balance is simply a beam balance, which is sup- ported vertically from a hook hung on a ring stand or held by the hand. Spring Balances. A spring balance measures the mass of a body by the elongation of a spiral spring. The weight is in- dicated on a graduated scale by a pointer attached to a draw- bar on the free end of the spring. Attached to the drawbar is a hook on which is suspended the object to be weighed. The spring balance is made to read correctly in vertical position, with the hook downward. The weight of the draw- bar and hook should be sufficient to bring the pointer to the zero mark on the graduated scale. If the pointer does not stand at zero with no load on the balance, a correction must be made to the weight registered on the scale in order to get the true weight of the object. The inconvenience of mak- ing these corrections may sometimes be avoided by wrapping about the shank of the hook a strip of sheet lead, sufficient in weight to bring the pointer to the zero point of the scale. The friction in a spring balance tends to make less accurate the readings in the first portion of the graduated scale. At the other end of the scale, when the spring is near its maximum stretch, the elongations are not quite proportional to the heavier weights added. Accordingly the most acciirate read- ings with a spring balance are those obtained in about the middle portion of the graduated scale. In some experiments the spring balance is used to measure the pull or force exerted upon its spring. When used for this purpose it is termed a dynamometer. Sensitiveness of a Balance. The sensitiveness of a balance may be defined as the smallest difference which is indicated by the balance with a given load. The trip scale should be sensitive to at least the tenth of a gram with an ordinary load, i.e. show a difference between 50.6 and 50.7 grams. A good hornpan balance indicates weights within the hundredth of a gram (1 centigram) while an accurate chemical balance is sen- sitive to a ten-thousandth of a gram (tenth of a milligram). TO STUDENTS 13 Relative Advantages of Platform and Beam Balances. The platform balance, while it is easy to keep clean and can stand much usage, is usually not so sensitive as the beam balance. The broad platforms, however, are very convenient for weigh- ing bulky, unstable objects, and the oscillations of its beam are easily controlled. The sensitiveness of a beam balance is gained at the expense of stability and durability, for the beam is easily displaced and the knife-edge suspension becomes dulled by use. On this ac- count great care should be taken not to jar the balance nor allow the beam to oscillate too rapidly. The weights should be placed gently upon the pans and removed when the pans are at rest (i.e. supported by the pan arrest or by the hand). Were it not for the awkwardness and carelessness of some students, the beam balance would always be most desirable for rapid, accurate weighings in the physical laboratory. Electrical Measuring Instruments The instruments used for measuring the strength or the pressure of an electric current have very delicate parts and may be easily ruined by either rough usage or excessive current. Before using any galvanometer or other meter the student should assure himself that it has the proper scale range and current-carrying capacity for the work in hand. He must further so connect his apparatus that the instrument will not be upset or pulled out of place by any change in connections made during the experiment. As the several instruments that the student may be called to use in his experiments differ in their sensitiveness, method of connection, and method of read- ing, each kind will be briefly discussed by itself. In reading all instruments, tenths of the smallest divisions should be esti- mated. Tangent Galvanometer. This consists of a compass needle mounted at the center of a hoop, on which is wound the wire 14 GENERAL SUGGESTIONS which is to convey the current. This is the most rugged ol the instruments, but the pivot is likely to be bent by dropping or violently jarring the instrument. Where there are a num- ber of binding posts, to permit the use of different numbers of turns of wire, find out from the instructor which posts to use and the number of turns of wire included between them. In order to read the instrument accurately, it should be so placed on the table that it will be possible to look directly down on the needle. The instrument should be carefully turned until the needle is in the plane of the coil. D'Arsonval Galvanometer. The moving part of this instru- ment is a light coil of wire, suspended between the poles of a permanent luagnet by a fine wire or ribbon through which the current passes. This suspension is exceedingly thin, so that even a slight shock to the instrument will break it and a comparatively small current will melt it. The instrument is commonly provided with a clamping device which takes the weight of the coil off the suspension when the galvanometer is not in use. In setting up the galvanometer, keep the coil clamped until you are ready to connect to the source of current. Then make sure that the instrument is leveled in such a way that the coil does not rub against any part of the instrument but hangs per- fectly free. The method of reading the deflections for the particular instrument you are using will be explained by the instructor. It is exceedingly important that only a very small current pass through the coil of the instrument. On this account, the galvanometer should have either a coil of high resistance in series with it or a low resistance shunt across the terminals for most experiments. Such additions to the instrument should be made either by the instructor previous to the laboratory hour or under his immediate direction by the student. Ammeter. The commercial form of this instruin-ent is usually a d'Arsonval galvanometer provided with a shunt of TO STUDENTS 15 such resistance that the deflections of the needle give the num- ber of amperes directly. The coil is pivoted instead of being suspended, but the instrument must be guarded against falls and shocks just as a fine watch would be. Before connecting the ammeter in circuit, be sure that its range is sufficient for the current to be measured. If the in- strument has more than one range, always connect for the largest range first, and then change the connections to those for a smaller range, if the readings indicate that this can be safely done. If the ammeter has an external shunt, be sure that the con- nections between the shunt and the instrument movement are tight. A loose contact will certainly make an incorrect read- ing and may burn out the instrument. Connect the terminals of the instrument .in series with the circuit. If connected in shunt with the other apparatus, the resistance of the instrument is so small that the movement will probably be burned out. In every electrical circuit, there should be a switch that can be opened instantly if there is the slightest indication of too much current for the instruments or any other part of the apparatus. Voltmeter. This is similar to the ammeter in construction, but has a high resistance in series with the movement instead of a shunt across the movement. The voltmeter measures pressure, while the ammeter measures current flow. The same precautions for handling and for the selection of a proper scale range are to be observed as in the case of the am- meter. Connect the voltmeter across (in shunt with) the circuit or that part of the circuit in which the voltage drop is to be measured. Resistance Box. The voltage applied to a resistance box should never be great enough to cause more than 0.1 ampere to pass through the box. 16 GENERAL SUGGESTIONS The Laboratory Note-book Unless other directions are given by the instructor, the fol- lowing plan should be followed in recording experiments in the note-book. Number of Experiment. Place to the left and at the top of the left-hand page. Date of Experiment. Place to the right and at the top of the left-hand page. Title. Place immediately below the number and date. Object. Place directly below the title. Tables of Observations. Place immediately below the object. In case the instructor desires the duplication of the observa- tions, make the necessary number of parallel columns at the right. Always record the measurements, as soon as made, in the tabular form. Decimals should be used, rather than com- mon fractions. The number, the date, the title, the object, and the table of observations should be written in the note-book before the experimental work is begun. Drawings. Place on the left-hand page clear sectional drawings showing the arrangement and operation of your ap- paratus. In making a sectional drawing, imagine a vertical plane passing through the middle of your apparatus ; then imagine your paper to be in the position of this plane. Draw lines where the paper would touch the intersected apparatus. Descriptions. Place these usually on the left-hand page and shorten your work by referring to your drawings. A simple, clear account of the general method of the experiment is prefer- able to an elaborate description. Table of Calculations. Place at the top of the right-hand page before making any of the calculations. Do the mathe- TO STUDENTS 17 matical work involved, immediately below the table, and record the results as soon as obtained in the tabular form. Discussion. Under this heading on the right-hand page, answer any italicized questions occurring in the experimental directions as well as the questions under the printed heading of " Discussion." If more room is necessary, continue on the next right-hand page. Conclusion. Place under this heading on the right-hand page, immediately following the Discussion. Introductory. It will pay you to read and understand this, before beginning the experimental work. It is not to be copied into the laboratory note-book. LABORATORY EXERCISES EXPERIMENT 1 Metric Units of Measurement OBJECT. To become familiar with the units of metric measure- ments commonly used in scientific work. APPARATUS. Meter stick ; scissors ; small graduate (50 or 100 c.c); large graduate (500 or 1000 cc); liquid quart meas- ure; small wide-mouth bottle; tumbler; platform balance ; metric weights; 1 Ib. weight. MATERIAL. "Oak tag," or some other kind of stiff paper; mucilage, or paste. Introductory : The Metric System is the official system of units of measurement in most civilized countries. It is the system used in scientific work in the United States. The unit 100 MILLIMETERS = 10 CENTIMETERS = 1 DECIMETER = 3.937 INCHES. nli ii iiiiifn INCHES AND TENTHS Fig. 3. of this system is the meter, and standard bars with this distance marked on them are preserved for reference by various governments. The Metric System is a decimal system and therein lies its great convenience. The meter is subdivided into 18 METRIC UNITS OF MEASUREMENT 19 ten parts, each of which is termed a decimeter ; the hun- dredth of a meter is a centimeter; the thousandth of a meter, a millimeter. From these fundamental units, the units of surface, volume, and weight are derived. The meter measures 39.37 inches. Experimental : At the top of the left-hand page of the laboratory note- book put the number and title of the experiment and the date. Then state the object of the experiment. Immedi- ately below this, put the following tabular form for the readings : OBSERVATIONS Length of note-book cover cm. Width of note-book cover cm. Metric equivalent of liquid quart .... cm. 3 Capacity of small bottle cm? Capacity of tumbler cm. s Weight of note-book ...... g. Metric equivalent of a pound ...... a. Units of Length. (a) Examine a meter stick, noting its subdivisions. In your laboratory note-book, just below the table of observations, rule horizontal lines of the fol- lowing lengths, labeling each line with its length : 1 decimeter, 1.1 decimeters, 1.5 decimeters, 5 centimeters, 2.5 centimeters, 1.3 centimeters, 1 centimeter. (6) Measure in centimeters and tenths of a centimeter the length of the cover of your laboratory note-book. Similarly measure the width. Record the dimensions. Units of Volume and Capacity. ( 1 Fig. 10. 20651- 38 LABORATORY EXERCISES Experimental : (a) The block is clamped to one end of the laboratory table and the stem of the pulley set into a hole bored diagonally into the opposite end. A piece of wire about 30 cm. longer than the table is cut off. This is clamped to the binding post, given a turn around the wooden cylinder, and attached to the weight carrier at the other end. Care must be taken that there are no kinks or sharp bends anywhere in the wire. The wire is then placed over the pulley and the needle attached at right an- gles to it with a drop of melted wax at a point near the pulley. The millimeter scale is then fixed in place beneath the the needle with the thumb tacks so that its divisions are parallel to the needle. A 2-lb. weight is next placed on the carrier to straighten the wire ; then it is removed and the zero reading of the needle taken, tenths of the smallest scale division being estimated. A lens may be used to advantage in estimating tenths. Weights are now added, a pound at a time, the amount of stretching force and the reading of the needle on the scale being noted and immediately recorded in tabular form near the top of the left-hand page. After each reading remove the weights and again note the zero reading. The force which causes the first con- siderable shifting in the zero point is known as the elastic limit. Continue the readings until the wire breaks. OBSERVATIONS ON WIRE, GAUGE No. STEETCHISO FORCE etc. ZERO READING ete. HEADING OF POINTER BREAKING STRENGTH etc. etc. TENACITY OF WIRE 39 (6) Replace the broken wire with another of different material, and add the weights one pound at a time until the wire breaks, without recording the elongations. Re- peat with as many wires as the instructor may designate. Record results in tabular form on the second left-hand page. OBSERVATIONS, PART (6) MATERIAL or WIRE GAUGE NUMBER BREAKING STRENGTH On the left-hand page of the note-book make a simple drawing of your apparatus, and write a simple description of how the experiment was done. On the right-hand page, at the top, place the calculated results for Part (a) in tabular form. CALCULATED RESULTS Stretching force 1 Ib. 2 Ib. 3 lb., etc. Elongation ......mm. mm. mm., etc. Curve. On a piece of cross section paper, plot a curve, laying off forces as abscissae (horizontal) and elongations as ordinates (vertical) to the scale given by the instructor. Compare the force at the point where the curve begins to turn with the elastic limit. Paste the cross section paper by one edge into the note-book. Discussion : Does the wire follow Hooke's Law in that "the dis- tortion (elorgation) is proportional to the stretching force," through any part of the test as shown by the curve ? If so, up to what point ? 40 LABORATORY EXERCISES Conclusion : (1) State the relation between the tension of a wire and its elongation (a) up to the elastic limit, (5) beyond the elastic limit. (2) Arrange the materials tested in the order of their tensile strength, placing the strongest first. EXPERIMENT 8 Relation between Pressure and Depth OBJECT. To find the relation between the depth of a sub- merged surface and the pressure upon it. APPARATUS. 1 A test tube loaded with shot, upon which melted paraffin has been poured, so that the tube will float vertically ; a paper centimeter scale, attached vertically to the inside of the tube with paraffin; weights 1 to 10 grams if a 6" x f" test tube is used and 5 to 20 grams if a 8" x 1" test tube is used ; battery jar or hydrometer jar ; cross section paper. Introductory : When a stick is thrown endwise into water, it springs back into the air. When a boat floats in water, there must be an upward pressure of the water on it to balance its weight. When more heavily loaded, it sinks more deeply, but the upward pressure must then also balance its weight. Experimental : A glass tube loaded so that it will remain upright will be floated in a jar of water. A scale on the inside of the tube will be used to measure changes in depth. This 1 The method of this experiment was called to our attention by Dr. H. C. Cheston of the High School of Commerce, New York City. RELATION BETWEEN PRESSURE AND DEPTH 41 --:.-- tube should float freely and should not be allowed to touch the sides of the jar. The scale readings are taken by sighting through the jar along the under side of the water surface. By add- ing small weights as indicated in the table below, the level of the bottom of the tube may be changed. By compar- ing the changes in depth and the changees in weight pro- ducing them, we may find how the upward pressure of the water (which balances the weight of the tube) varies with the depth of the surface on which it acts. Fi ^ n - Place your observations in a table near the top of the left-hand page. NUMBER or OBSERVATION 1 OBSERVATIONS WEIGHT Loaded tube alone ..... Loaded tube alone + 2 grams . Loaded tube alone + 4 grams . Loaded tube alone + 6 grams . Loaded tube alone + 8 grams . Loaded tube alone + 10 grams . SCALB READING cm. cm. cm. cm. cm. Make a drawing from your apparatus and write a simple description of the method of the experiment. Make the following tabulations at the top of the right- hand page: 42 LABORATORY EXERCISES NUMBERS CALCULATED RESULTS CHANGE OP CHANGE 01 PRESSURE DEPTH 1 2 grams .... cm. 1 3 grams .... cm. 1 4 grams .... cm. 1 5 . '. . . . grams .... cm. 1 6 grams .... cm. Curve on Cross Section Paper. The readings of change of pressure and change of depth should be plotted on cross section paper, depths on the perpendicular axis and pressures on the horizontal axis. Use a scale of 5 small spaces to 1 gram, and 2 small spaces to 1 mm. If the resulting graph is a straight line, we may conclude that twice the depth was caused by twice the pressure and so on, or that the pressure is directly proportional to the depth. Paste the cross section paper by one edge in the note-book. Discussion : At each observation in the experiment, what relation must exist between the total weight of the floating tube and the upward pressure of the water? Why is it not necessary to consider any sidewise pressures that may be exerted on the tube ? Conclusion : What is the relation between the pressure on a sub- merged surface and the distance of that surface below the surface of the liquid ? ARCHIMEDES' PRINCIPLE 43 EXPERIMENT 9 Archimedes' Principle OBJECT. To determine the relation between the loss of weight of a sinking solid and the weight of a liquid displaced by it. APPARATUS. Lump of coal with thread, or copper wire $22 at- tached ; overflow can ; catch bucket or beaker with wire loop for suspension ; spring balance (250 g.), or beam balance ; battery jar. Introductory : It is much easier to lift the anchor of a boat when the anchor is in the water than when it is out of the water. The displaced water balances part of the weight of the anchor, and so makes it seem lighter, because the upward pressure of the water on the bottom of the anchor is greater than the downward pressure on the top. The anchor displaces a volume of water its own size. We wish to compare the loss of weight of a body submerged in a liquid with the weight of the liquid displaced by it. This was first done by Archimedes, and the relation found is called Archimedes' Principle. Experimental : Use a piece of coal for the solid. By weighing it in air, with a spring balance, and then when immersed in water in a jar, the loss in weight of the lump can be found. When a can with a spout, called an overflow can, is rilled and placed on a level table, the water will run out to the level of the spout. By placing a weighed beaker under the spout and carefully lowering the coal into the can, the water which overflows may be caught and weighed. Comparing the weight of this displaced water with the loss of weight of the coal, will give the relation sought. 44 LABORATORY EXERCISES Record the following readings in tabular form near the top of the left-hand page : OBSERVATIONS Weight of coal in air , Weight of coal in water Weight of catch bucket Weight of catch bucket + displaced ivater Briefly describe what you did, illustrating each step with a drawing from your apparatus, similar to Fig. 12 (A, B, and (7). B A 1 T * jBfCK G^f \;^;~ :=-:i? rr^rirrij ^jin-rtRr c 3 r -4 zq Fig. 12. CALCULATED RESULTS Loss of weight of coal in water Weight of an equal volume of ivater Conclusion : State the relation between the loss of weight of a sink- ing body and the weight of a-liquid displaced by it. LAW OF FLOTATION 45 EXPERIMENT 10 Law of Flotation OBJECT. To determine the relation between the weight of a floating body and the weight of a liquid displaced by it. APPARATUS. Block loaded to float upright on water ; overflow can ; catch bucket or beaker with wire loop for suspension ; spring or beam balance. Introductory : The cork float on a fishline exerts no pull on the line. The weight of an ocean liner is supported by the upward push of the water. A boat is said to have a certain num- ber of tons displacement, depending upon its size and weight. What is the rela- <*> tion between this number of tons of water displaced and the weight of the boat ? Experimental : A method similar to that used in Experiment 9 will give us the relation between the weight of the wooden block and the weight of the liquid displaced by it. Place the table of observations near the top of the left-hand page. Fig. 13. OBSERVATIONS Weight of block Weight of catch bucket^ empty . Weight of catch bucket + displaced water 46 LABORATORY EXERCISES Write a simple description of the steps in the expert ment, illustrating each with a drawing from your apparatus. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS Weight of water displaced by floating body . . g. f z, {floating body .... g. Comparison of weights \ , . 7 , i displaced water ... g. Conclusion : The weight of a floating body and the weight of the liquid displaced by it are . EXPERIMENT 10 (Alternative) Law of Flotation OBJECT. To determine the relation between the weight of a floating body and the weight of the liquid displaced by it. APPARATUS. A wooden bar 20 cm. long and 1 cm. square with metric scale attached and loaded so as to be almost sub- merged when floating upright in water; 1 hydrometer jar or battery jar ; platform balance ; metric weights. Introductory : The cork float on a fishline exerts no pull on the line. The weight of an ocean liner is supported by the upward push of the water. A boat is said to have a certain num- ber of tons displacement, depending upon its size and 1 The ordinary wooden hydrometer can be made available by drilling a hole in the lower end, adding lead shot, and closing with a cork plug. The weight of the bar should be so adjusted that the bar will float almost submerged. Finally put a light coat of paraffin over the end which was opened. LAW OF FLOTATION 47 weight. What is the relation between this number of tons of water displaced and the weight of the boat ? Experimental : The wooden bar is to be weighed and then floated in the water of jar so as to note the depth to which it is submerged. The metric scale on the bar gives the length of the column of water dis- placed and, like the bar the column of displaced water, is 1 centimeter square. Therefore the reading on the metric scale is numerically equal to the number of cubic centimeters of displaced water. Since a cubic centimeter of water at ordinary temperatures weighs approximately a gram, the weight of the displaced water can eas- ily be found. A comparison of the weight of the floating bar and the weight of the displaced Fig. 14. water will bring out the principle of flotation. OBSERVATIONS Weight of bar g. Length of column of displaced water . . . cm. Make a drawing of the floating bar from your apparatus and write a simple description of the experimental method. CALCULATED RESULTS Volume of water displaced by floating body . cm.* Weight of water displaced by floating body . g. \ floating body . . g. Comparison of weights < ,. 7 , . [ displaced water . . g. Conclusion : The weight of a floating body and the weight of the liquid displaced by it are . 48 LABORATORY EXERCISES EXPERIMENT 11 Specific Gravity of Solids OBJECT. To find the specific gravity of various solids. APPARATUS. Spring balance, or beam balance arranged for weighing in water ; battery jar ; pieces of coal, glass, and marble, or other solids desired. Introductory: Lead is a very heavy metal. While a pailful of water weighs only about 20 pounds, the weight in pieces of lead that would just fill the pail would be about 225 pounds. Lead weighs about 11.2 times as much as the same volume of water. We say that the " specific gravity " of lead is 11.2 times. The specific gravity of a substance is the num- ber of times a piece of the substance is as heavy as the same vol- ume of water. Experimental : It will be necessary to get the weight of a lump of coal and the weight of the same vol- ume of water. The weight of the coal can be found directly with a spring balance, and Archimedes' Principle will help us in getting the weight of an equal volume of water. If the coal is weighed while immersed in water, it will weigh less than A A B J^ T I /^ , ) ..( } Fig. 15. SPECIFIC GRAVITY OF SOLIDS 49 in air by an amount equal to the weight of water having the same size (volume) as the coal. The specific gravity of the other solids furnished may be found in the same way. Record the weighings in tabular form near the top of the left-hand page. OBSERVATIONS COAL MAKBLK GLASS Weight of body in air . . Weight of body in water . Then make drawings from your apparatus and write a simple description of how the experiment was done. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS COAL MARBLE GLASS Weight of water size of solid . Weight of solid Specific gravity of solid . . Conclusion : The specific gravity of coal is times; the specific gravity of marble is times; the specific gravity of glass is times. 50 LABORATORY EXERCISES EXPERIMENT 12 Specific Gravity of a Liquid (Bottle Method) OBJECT. To obtain the specific gravity of a solution of copper sulphate with a specific gravity bottle. APPARATUS. Specific gravity bottle ; spring balance (250 g.) with scale pan, or beam balance ; bottle or jar of copper sulphate solution provided with a siphon delivery tube, ending with rubber connection, pinchcock, and glass jet tube (Fig. 17). MATERIAL. Water; saturated solution of copper sulphate; 1 small cloths for wiping. Introductory : If we find the weight of a gallon of water and of a gallon of alcohol, we can directly deter- mine the specific gravity of the alcohol by finding how many times it is as heavy as water. This is a general method for finding the specific gravity of any liquid. Experimental : We use small spe- cific gravity bottles having perforated glass stoppers, as in this way we can Fig. 16. Fig. 17. Jar and siphon for solution. 1 A hot saturated solution should be made and allowed to cool, or a cheesecloth bag full of copper sulphate crystals should be suspended in the top of a jar of water and allowed to stand at least twenty-four hours, or until no more copper sulphate will dissolve. SPECIFIC GRAVITY OF A LIQUID 51 obtain very exactly equal volumes of the two liquids. The weight of the specific gravity bottle must first be found. Then it is to be weighed full of water and next full of copper sulphate solution. By comparing the weight of the copper sulphate solution filling the bottle with the weight of the water filling the same space, the specific gravity of the copper sulphate solution may be found. CAUTION. Using the wiping cloths if necessary, see that the bottle is dry on the outside before weighing and avoid handling it except by the neck, for the heat of the hand is likely to drive out some of the liquid through the stopper, after it has been fitted. After the water weighed has been emptied out, rinse the bottle with a little of the sulphate solution. Record the weighings in tabular form near the top of the left-hand page. OBSERVATIONS Weight of scale pan and empty bottle .... g. Weight of pan and bottle fitted with water . . g. Weight of pan and bottle filled with copper sul- phate solution g. Make drawings from your apparatus and write a short description of how the experiment was done. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS Weight of water filling bottle g. Weight of copper sulphate solution filling bottle . g. Specific gravity of copper sulphate solution . . times Conclusion : The specific gravity of copper sulphate solution is times. 52 LABORATORY EXERCISES EXPERIMENT 13 Specific Gravity of a Liquid (Hydrometer Method) OBJECT. To find the specific gravity of a copper sulphate solu- tion by the hydrometer method. APPARATUS. Hydrometer jars ; square wooden hydrometer graduated in millimeters; glass hydrometer for heavy liquids (1 to 2). MATERIAL. Water ; saturated solution of copper sulphate as in Experiment 12. Introductory: A boat, passing from fresh water into the ocean, rises a little, as the boat displaces its own weight in each case, and the salt water, being more dense, has less volume for the same weight. An electric light bulb in concen- trated sulphuric acid floated with 100 c.c. of its volume submerged ; in alcohol, which is half as dense as sulphuric acid, the same bulb would sink until 200 c.c. were sub- merged. We see, then, that the greater the specific gravity of a liquid the less portion of a given floating body will be submerged in it. More exactly, the volumes of a floating body submerged in two liquids are inversely proportional to the specific gravities of the two liquids. Experimental : (a) A graduated float used for obtaining the specific gravity of liquids is called an hydrometer. The hydrom- eter to be used is a loaded stick 1 cm. square and graduated in centimeters and tenths. If we now immerse this in water (Fig. 18) and record the depth to which it sinks, and then do the same with a copper sulphate solution SPECIFIC GRAVITY OF A LIQUID 53 (Fig. 19), the hydrometer will sink deeper in the less dense liquid. The volume of each liquid displaced may be measured by the depth of the submerged part of the hydrometer, since each centimeter of length means 1 c.c. of volume. If, then, we divide the length submerged in in water by the length submerged in copper sulphate, we shall obtain the specific gravity of the copper sulphate solution. Fig. 18. Fig. 19. Fig. 20. (J) Direct-reading hydrometers are made of glass tubes loaded so as to float upright and provided with a scale which gives the specific gravity directly (Fig. 20). After completing calculations on part (a), ask the instructor for such a hydrometer, and with it find the specific gravity of your solution, as a check on your results. Record the observations in tabular form near the top of the left-hand OBSERVATIONS Reading of bar in water Reading of bar in copper sulphate solution Reading of glass hydrometer in copper sulphate solution .... cm. cm. 54 LABORATORY EXERCISES Make drawings from your apparatus showing the posi tion of the wooden hydrometer in the two liquids and the position of th*e glass hydrometer in the copper sulphate solution. Accompany these drawings with a short de- scription of the method of work. CALCULATED RESULT Specific gravity of copper sulphate solution as determined by wooden hydrometer . . times Discussion : Explain why the volume of water displaced was divided by the volume of copper sulphate solution displaced. Conclusion : The specific gravity of the copper sulphate solution by this method (wooden hydrometer) is -- - times by the bottle method (Experiment 12) is times by the direct reading of the glass hydrom- eter is times SPECIFIC GRAVITY OF A LIQUID 55 EXPERIMENT 14 Specific Gravity of a Liquid (Hare's Method) OBJECT. To find the specific gravity of alcohol and of a salt solution by Hare's method. APPARATUS. Two 90 cm. lengths of \" glass tubing ; lead or glass T-tube, or Y-tube ; 2 rubber connections ; black rubber tubing of length convenient for suction ; screw compressor ; ring stand and clamp for supporting T-tube or Y-tube ; 2 tumblers (preferably of thin glass and with nearly vertical sides), or 2 oeakers. MATERIAL. Distilled water, if available ; saturated solution of common salt, and grain alcohol in stock bottles provided with siphon tubes about -$" bore. Introductory : The simple barometer is nothing more than a long tube, closed at one end and filled with mercury, which is then inverted in a dish of mercury. A mercury column about 76 centimeters in length remains standing in the tube. This column is held up by the pressure of the atmosphere. It has also been determined experimentally that the pressure of the air supports a much longer column of water approximately 34 feet. We know that mercury, volume for volume, is much heavier than water, or, as we say, has a greater specific gravity. The fact that the atmosphere holds up columns of liquid whose length varies with the particular liquid taken, has been utilized in an ingenious method for determining the specific gravity of liquids. 56 LABORATORY EXERCISES Experimental : The apparatus (Fig. 21) consists of two long parallel tubes with their lower ends dipping into tumblers of liquids. The upper end of each is joined by a rubber connection to an arm of a T-tube. To the center tube of the T is attached a rubber tube to be used for suc- tion, which can be closed by a screw compressor. (a) Half- fill one tumbler with water and the other with a sat- urated solution of salt. With the rubber tubing open, compare the water levels inside and outside the long tube. Ac- count for this condition of levels. Is it also true for th'e levels of the salt solution ? Suck out a little air through the rubber tube, noting the be- havior of the liquids. What pres- sure causes the liquids to rise in the tubes ? Again remove air by suction until the water column is pushed up nearly to the top of its tube. Pinch the rubber tube tightly and close the screw compressor. Note the relative height of the two liq- uids. The pressure on the upper surfaces of the two liquids is the same. How does this pressure compare with the outside air pressure ? What pressure forced the liquids Fig 21. SPECIFIC GRAVITY OF A LIQUID 57 up into the tubes ? How does this pressure compare with the downward pressure of each liquid? Compare, then, the downward pressure of the water column with that of the salt solution. Measure with a meter stick the length of the water column above the level of the water in the tumbler. Obtain similarly the length of the column of the salt solution. Record the measurements in tabular form near the top of the left-hand page. (5) Open the compressor and allow the liquids to run back into their tumblers. Return the salt solution to its stock bottle and rinse out the tumbler. Detach the long tube used for the salt solution, and, after washing, attach it again. Put grain alcohol into the empty tumbler and repeat the experiment so as to obtain the length of the water and the alcohol columns, taking care not to suck the alcohol up into the mouth. Tabulate the measurements near the top of the left-hand page. Return the alcohol to its stock bottle. OBSERVATIONS Part (a) : Length of the water column . . . . . . cm. Length of the salt solution column ... cm. Part (6) : Length of the water column cm. Length of the grain alcohol column .... cm. Make an outline drawing of the apparatus used, and write a simple description of the general method of the experiment. With the water and the salt solution, the downward pressure per square centimeter of each, balances the same amount of atmospheric pressure. The two columns must 58 LABORATORY EXERCISES then have the same weight. Being of equal cross section, their lengths are proportional to their volumes. But the greater the specific gravity of a liquid, the smaller the volume for a given weight. Are the relative weights, then, directly or inversely proportional to the heights of the columns ? With this relation in mind, calculate the spe- cific gravity of the salt solution and of the alcohol, relative to water. Record the results in tabular form at the top of the right-hand page. CALCULATED RESULTS Specific gravity of the salt solution . . = times Specific gravity of the alcohol .... = times Discussion : Answer under this heading on the right-hand page the italicized questions occurring in the directions. Conclusion : The specific gravity of the salt solution is times ; the specific gravity of the alcohol is times. EXPERIMENT 14 (Alternative) Specific Gravity of Liquids (Balancing Columns) OBJECT. To find the specific gravity of (a) carbon tetrachloride, (&) grain alcohol, by the method of balancing columns in a U-tube. APPARATUS. 2 Mohr burettes (50 c.c.) connected by a piece of thick-walled rubber tubing of sufficient length ; Hofmann screw compressor ; ring stand ; two burette clamps ; 2 glass ' funnels, 1\ n ', or tops of two thistle tubes ; beaker; medicine dropper. SPECIFIC GRAVITY OF LIQUIDS 59 MATERIALS. Mercury ; distilled water if available ; carbon tetrachloride ; grain alcohol. (Other liquids, such as glycerine kerosene, etc., as the instructor desires.) Introductory : When mercury fills the lower rounded portion of a U- tube, the mercury stands at the same level in the two arms, since the downward pressure of the air is the same on the two mercury surfaces. When a certain volume of water is poured into one arm of this same tube, and an equal volume of kerosene into the other arm, the mercury level in the water arm is lower than that in 'the kerosene arm. Since the mercury is free to move, the given volume of water must press down with greater weight on the mercury than does the same volume of kerosene. Accordingly, volume for volume, the kerosene weighs less than the water. Usually the specific gravity is found by calculating the ratio be- tween weights of equal volumes. Since this is so, might not the inverse ratio between the volumes of equal weights give the specific gravity ? Experimental : As we have seen, equal weights may be measured by the downward pressure of liquids. The equal weights can be obtained by pouring just enough of each liquid into its arm of the U-tube, so as to make the two mercury surfaces stand at the same level. All that remains is the measurement of the volumes of the two liquids and the finding of the ratio, remembering that it is an inverse one. Clamp the two burettes at about a third of their length from their lower ends and in a vertical parallel position with the 50-c.c. marks horizontally opposite each other. 60 LABORATORY EXERCISES Slip the screw compressor over the rubber connecting tube and attach the ends of the tube to the burettes. Pour mercury through a thistle tube top or funnel at the top of one burette until the mercury surface in each burette stands at the 50-c.c. graduation, or some mark a short distance above (Fig. 22). Squeeze out the air bubbles in the connect- ing tube before taking the zero reading of the mercury levels. (a) Record the zero reading of the burettes in the table of obser- vations. Then close the screw com- pressor on the connecting tube. Into the right-hand burette pour enough carbon tetrachloride to half fill the burette. Add about the same volume of water to the other burette. Cautiously open the compressor a lit- tle, noting whether the tetrachloride column is balanced by the water. If not, close the compressor, add more water, and test again. Con- tinue in this manner until the water balances the tetrachloride, as shown by the mercury remaining at the same levels when the compressor is opened wide. A medicine dropper Fi 22 i g convenient for adding the last portions of water needed. Read and record the top levels of the balancing columns. Raise the tetrachloride burette so that the mercury just runs into the connecting tube. Over this end of the tube SPECIFIC GRAVITY OF LIQUIDS 61 close the screw compressor and slip off the rubber tube, so that the tetrachloride can empty into a beaker placed below the burette. Pour the tetrachloride into its stock bottle. (6) Rinse out the open burette with a few cubic centi- meters of alcohol (or other liquid to be used) and again connect the rubber tube. Then obtain as in (a) a column of alcohol which balances the water column in the left-hand burette. Record all readings in a tabular form near the top of the left-hand page. OBSERVATIONS Part O) : Reading of mercury levels cm. 3 Heading at top of water column cm. 3 Reading at top of tetrachloride column . . . cm. 3 Part (6) : Reading of mercury levels cm. 3 Reading at top of water column cm. 3 Reading at top of alcohol column cm. 3 Make an outline drawing of your apparatus and de- scribe briefly how the experiment was done. Place the table of calculated results at the top of the right-hand page. The specific gravities are to be calcu- lated with reference to water. CALCULATED RESULTS Part (a) : Volume of the water column cm. 3 Volume of tetrachloride column cm. 8 Specific gravity of tetrachloride . . = times Part (6) : Volume of water column cm. 8 Volume of alcohol column cm. 3 Specific gravity of alcohol .... = times 62 LABORATORY EXERCISES Discussion : Why is the specific gravity in this experiment the in- verse ratio of the volumes of the balancing columns ? Conclusion : The specific gravity of carbon tetrachloride is times. The specific gravity of alcohol is times. EXPERIMENT 15 Density of Air OBJECT. To determine the approximate density of air in the room. APPARATUS: Air pump ; round-bottom flask (250 c.c.) with a tightly fitting 1-hole rubber stopper carrying a glass inlet tube with a piece of. thick-walled rubber tubing attached; screw compressor ; beam or horn pan balance weighing to 0.01 gram ; metric weights ; graduate ; large battery jar, or pail. Introductory : It is very evident that lead has weight. Even a small child knows that a tumbler of water is heavier than the empty glass. We know that solids and liquids have weight, but does the air which surrounds us have weight ? If balloons are lighter than air, the air must have weight. It would be interesting to find out just how dense air is, that is, the number of grams to a cubic centimeter. Experimental : A flask may be weighed full of air and then the air partially pumped out. Then the exhausted flask may be weighed. The difference between the two weights is the weight of air pumped out of the flask. The volume of DENSITY OF AIR 63 Fig. 23. this air may be found by measuring the water which will run into the exhausted flask. With the weight and volume of the air known, the density (grams per cubic centimeter) may be found. Make all weighings to the nearest cen- tigram. In all weighings of the flask, in- clude the rubber stopper with its tubing and screw compressor, and any wire sus- pension used with the balance. See that all joints between rubber and glass are tight before exhaustion. Allow at least live minutes for the exhaustion of the flask, and be sure the screw compres- sor is tightly closed before the removal of the rubber tube from the pump. Immerse most of the flask in water and open the bcrew com- pressor a little at a time under water. As soon as no more water will run in, move the flask so that the level of the water on the in- side is the same as that on the outside (Fig. 24). Pinch the rubber tube with the compressor so as to close it, and remove the flask from the water. Set it in a secure upright position on the table. Open the compressor so as to allow the water in the small tube to run down into the flask and then re- move the stopper and its connections. Fig. 24. 64 LABORATORY EXERCISES Measure with a graduate the volume of water in the flask. Record the measurements in tabular form near the top of the left-hand page. OBSERVATIONS Weight of flask filled with air g. Weight of flask, air exhausted g. Volume of air exhausted cm. 3 Record, if so directed by the instructor, the temperature of the room and the barometric pressure. Briefly describe the steps in the experiment, illustrat- ing with drawings from your apparatus. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS Weight of air exhausted g. Volume of air exhausted cm. s Density of air grams cm* Discussion : After the water had run into the flask, the water levels were made the same, so that any air not pumped out of the flask would be at the same pressure as the air in the room. What is the necessity for this precaution ? Would the results obtained for this experiment be exactly the same on different days ? Give reasons for your answer. Conclusion : The density of the air in the laboratory at the existing conditions was grams per cubic centimeter. DENSITY OF AIR 65 EXPERIMENT 15 (Alternative) Density of Air OBJECT. To determine the approximate density of air in the room. APPARATUS. Incandescent lamp bulb; Bunsen burner ; blow- pipe ; small battery jar ; small funnel and graduate ; horn pan balance weighing to 0.01 gram or better; metric weights; small squares of adhesive plaster. 1 Introductory : It is very evident that lead has weight. Even a small child knows that a tumbler of water is heavier than the empty glass. We know that solids and liquids have weight, but does the air which surrounds us have weight ? If balloons are lighter than air, then air must have weight. It would be interesting to ascertain just how dense air is, that is, the number of grams to a cubic centimeter. Experimental : The bulb of an incandescent lamp is empty save for the filament and a very slight trace of gas which was not exhausted. The bulb then can be weighed empty. By making a small hole, t*he air will rush in and fill the bulb. Another weighing gives the weight of the bulb filled with air. The difference between the 'two weighings is the weight of the air in the bulb. The volume of this air may be found by filling the bulb with water and then measuring the water with a graduate. With the weight 1 Note to Instructor. If the supply of burnt-out bulbs is limited, the experiment may be done in small squads, each student making the weighings and measurements for himself. In small classes the instructor may prefer to make the first air hole with the blowpipe. 66 LABORATORY EXERCISES Fig. 25. and volume of the air known, the number of grains per cubic centimeter can be calculated. Filling the Bulb with Air. Use the tiny point of a blowpipe flame, but approach the portion to be heated very gradually with the flame so as to avoid the sudden cracking and collapsing of the bulb. Heat a small area near the top of the bulb where the diameter is greatest (Fig. 25). As the glass softens at the tip of the blowpipe flame, the pres- sure of the outside air will make a hole. Any bits of glass which may be chipped off will tend to be drawn inward o that there will be no loss of weight due to the glass. Only a tiny hole is needed to admit the air. Filling the Bulb with Water. After the bulb has been weighed full of air, heat it with the tip of a blow- pipe flame so as to make a little hole in the glass an inch or so from the base of the lamp. When the heated glass is cool, immerse the bulb upright in the water of a battery jar so as to leave the first air hole made just above the surface of the water (Fig. 26). When the bulb is nearly full, incline the bulb, so that the rest of the space can fill with water. Then take the small square of adhesive plaster and stick over the lower hole, holding it in position for a couple of minutes with the finger. Now cover the upper air hole with the finger and remove the bulb from the water. Holding the bulb nearly upright over a funnel sup- ported in a graduate, pierce through the adhesive plaster just over the lower air hole. When the finger over the Fig. 26. DENSITY OF AIR 67 upper air hole is removed, the water will run down into the funnel. Remember that the outward flow may be stopped at any time by closing the upper hole with the finger. Record the measurements in tabular form near the top of the left-hand page. OBSERVATIONS Weight of incandescent bulb empty . . . , . g. Weight of bulb filled with air g. Volume of air filling bulb cm. z Record, if so directed, the temperature of the air in the room and the barometric pressure. Describe briefly the steps in the experiment and illus- trate with drawings from your apparatus. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS Weight of air filling bulb Volume of air filling bulb ..... Approximate density of air ..... Conclusion : The approximate density of air in room at existing con- ditions was grams per cubic centimeter. 68 LABORATORY EXERCISES EXPERIMENT 16 Boyle's Law OBJECT. To find how the volume of a gas varies with the pres- sure exerted upon it. APPARATUS. Barometer ; Boyle's Law apparatus as furnished by dealers in scientific instruments. The two forms recommended are : ( 1 ) the apparatus with the closed tube ending in glass stop- cock, and the open tube connected with the closed tube by heavy- walled tubing ; (2) the apparatus with both tubes dipping into a mercury reservoir, the closed tube sealed at the upper end, and a small bicycle pump to produce pressure in reservoir, so as to make mercury rise in the two tubes. 1 MATERIAL. Mercury, if not supplied with the apparatus. Introductory : A bicycle pump takes in air and makes it occupy a much smaller space. We know that the air in the inflated tube is under much greater pressure than before. Oxygen is sold in steel cylinders filled under pressure. When the valve is opened, many jars of oxygen may be obtained from one tank for experiments in the chemical laboratory. The total volume of the jars filled is far greater than that of the cylinder, for the oxygen is under much less pressure in the jars than in the steel tank. The two instances of 1 Note to Instructor. The directions for this experiment have been written so that either of the two forms of apparatus may be used. Both forms are on hand in many schools. A good type of the first apparatus may be obtained from the C. H. Stoelting Co., Chicago (list number 1151) ; the second form with an improved mercury reservoir is made by the L. E. Knott Apparatus Co., Boston (list number 41-105). The authors regard the J-tube form as very desirable for demonstration purposes, but less fit for the laboratory experiment, as most students are unable to handle it without spilling the mercury required. BOYLE'S LAW 69 the inflated tire and the filling of jars with oxygen show that there is some relation between the volume of the gas and the pressure exerted on it. Whether or not there is any regularity in this relation, may be ascertained by experiment. Experimental : Specific directions for handling the apparatus will be given by the instructor. The volume of air used is that inclosed above the mercury in the closed tube. The mercury in the open tube is used for varying the pressure upon the inclosed air. When the mercury levels are the same in the two tubes, the inclosed air is under atmospherio pressure. When the mercury level is higher in the open tube, then the inclosed air is under more than atmospheric pressure, for a column of mercury equal in height to the difference in levels is adding its pressure to the atmospheric pressure. A lower level in the open tube means a pressure less than the atmospheric. The pressure is expressed in centimeters of mercury. If the bore of the closed tube is of uniform diameter, the length of the inclosed air column may be taken as the measure of its volume and recorded in centimeters. Make a number of readings, as directed by the in- structor. The difference of the mercury levels in the open tube between successive readings, should be about 10 cm. One reading should be made with the mercury at the same level in the two tubes. As soon as the readings are made, record them in tabu- lar form at the top of the left-hand page. Write a simple description of the method of using the apparatus and make an outline drawing of it, showing the essential parts. 70 LABORATORY EXERCISES OBSERVATIONS NUMBER OP READING Oow MN OF INCLOSED AIR MERCERY LEVBL OPEN TUBE Top Bottom 1 cm. cm. cm. 2 cm. cm. cm. etc. . = cm. Barometric pressure at --------- on --------- was ----- mm. = (.time) (date) Place the calculated results in tabular form at the top of the right-hand page. The difference in the mercury levels can be found from the quantities in the last two columns of the table of observations. The pressure of the inclosed air is atmospheric pressure plus or minus (as the case may be) the difference of mercury levels. In recording the product of the pressure by the volume, omit the decimal fractions. CALCULATED RESULTS NUMBER OF READING DlFFEEENCE IN LEVELS PRESSURE OF INCLOSED AIR VOLUME OF INCLOSED AIR PRESSURE X VOLUME 1 cm. cm. cm. 8 2 cm. cm. cm. 8 etc. Discussion : Is the product of the pressure and the volume approxi- mately constant ? Why should the temperature of the inclosed air not change while the readings are being made? Would a variation in the barometric pressure during the experiment affect the result ? Conclusion : Complete the following statement : At a constant temperature, the volume of a given mass of gas varies as the pressure sustained by it. MEASUREMENT OF GAS PRESSURE 71 EXPERIMENT 17 Measurement of Gas Pressure OBJECT. To measure the pressure of the laboratory gas supply. APPARATUS. Water manometer, consisting of a U-tube (8") with one arm carrying a tightly fitting 1-hole rubber stopper with glass elbow tube ; l block with slot or groove for supporting U-tube ; foot rule or a metric scale ; rubber tubing for connecting ma- nometer with gas cock ; barometer. Introductory : The bag of a balloon connected with a gas main, fills and rounds out as the gas rushes in. One can feel the gas pressing out when a stopcock is opened from the gas supply in the laboratory. The balloon fills and the gas rushes into the room despite the fact that the weight of the air is pressing around the bag of the balloon and against the opening of the gas cock. This pressure, which is effective against the atmospheric pressure, may be de- scribed as the effective pressure of the gas supply. How much is the effective pressure of the gas delivered to our homes and school ? Experimental : Enough water is added to the U-tube to fill it about halfway up, and then the stopper carrying the elbow tube is pressed tightly into one arm of the tube. The water levels in the two arms are at the same height, since the air presses down on both water surfaces equally. The elbow tube is connected by a rubber tubing with 1 Instead of the U-tube, a U-shaped bend of glass tubing with the arras about 8 " long, may be used. A Skidmore stand is very convenient for supporting the U-tube. 72 LABORATORY EXERCISES the gas supply. The gas stopcock is slowly turned on and the difference in the height of the water levels meas- ured. This measurement should be made as soon as the rising water level reaches its greatest height. OBSERVATIONS Atmospheric pressure (barometer reading} . . in. Difference in height of water levels .... in. Time when readings were made If the measurements were made in centimeters, change them to inches by multiplying by 0.3937. Write a simple description of the experiment and make a drawing showing how your apparatus indicated the gas pressure. The difference of the water levels due to the increased pressure is independent of the cross section of the U-tube, therefore we can consider its cross section to be 1 square inch. A pressure of 14.7 pounds to the square inch holds up a water column 33.57 feet in length. From this equivalent, calculate the pressure in pounds per square inch of a column of water equal in height to the differ- ence of levels measured in the U-tube. This will give the effective pressure of the gas. A pressure of 14.7 pounds to the square inch holds up Fig. 27. MEASUREMENT OF GAS PRESSURE 73 a mercury column 30 inches in length. From this rela* tion, calculate the pressure in pounds per square inch which is equivalent to the observed barometric reading. Adding the effective pressure to the atmospheric pres- sure gives the total pressure of the gas, that is, the pressure per square inch within the gas pipes. Record the calculated results in a table at the top of the right-hand page. CALCULATED RESULTS Effective pressure of gas per sq. in. . . . Atmospheric pressure per sq. in Total pressure of gas per sq. in Discussion : Why is it not necessary to remove the air in the arm of the U-tube connected with the gas supply? What is the gas pressure stated to be in your town or city ? What does this mean ? Conclusion : The effective pressure of the gas in the laboratory at on was pound per square inch. The total (time) (date) pressure per square inch in the gas pipes was pounds. 74 LABORATORY EXERCISES EXPERIMENT 18 Water Pumps OBJECT. To study the parts and the operation of the simple lift pump and the force pump. APPARATUS. Glass models of a lift pump and a force pump ; 3 feet of glass tubing (^") with a short piece of rubber tubing ' attached ; battery jar. Introductory : The ordinary suction or lift pump has been used for over two thousand years. Although both the lift pump and the force pump are articles of familiar appearance, few can give an intelligent explanation of their operation. In these cases, as in other apparently simple devices, the study of the principles upon which they are based proves fascinating. Experimental : CAUTION. Handle the glass models with great care. Do not spill water around the laboratory. (a) Place in a jar of water the lower end of a long glass tube which has a short rubber tube on the upper end. Compare the water levels in the tube and in the jar. Account for the relative levels. Suck out through the rubber tube most of the air in the glass tube, noting the action of the water. Pinch tightly the upper end of the rubber tube. Does the water run back ? What pressure holds up the column of water in the glass tube? Release the pressure on the rubber tube. What happens? Explain. Why is it necessary to remove some of the air in a tube if we want water to be pressed up in it ? WATER PUMPS 75 Make three simple diagrams which will show what was done in this part of the experiment and indicate the results. (i) The Lift Pump. Examine a glass model of a lift pump, noting the suction tube, the bar- rel, the piston, the two valves, and the spout. Make an outline drawing, labeling the parts. Starting without any water in the pump, im- merse the suction tube in a jar of water and operate the pump till it is in full action, noting the action of the inclosed air, the water, and the two valves on each successive stroke. Record the observations in tabular form on the left-hand page. What is the main thing accomplished by the first few strokes of the pump ? Fig. 28. OBSERVATIONS ON THE LIFT PUMP STROKE VALVE ACTION OP AIE ACTION OF WATER ACTION AND USE OK VALVK 1st Up Lower 1st Up Upper 1st Down Lower 1st Down Upper 2dUp Lower 2dUp Upper etc. etc. (c) By a rubber connection attach a long glass tube to the suction pipe of the lift pump. Dip the free end of the long tube into a jar of water placed on the laboratory floor. Can you pump water from the floor? What limits the vertical distance through which water can be taken by a lift pump even though it were mechanically perfect ? 76 LABORATORY EXERCISES (i?) The Force Pump. Examine the glass model of a force pump, noting its parts. Try its action. Make two diagrams showing the action of the pump one for the up stroke, the other for the down. Show water levels, and use arrows to indicate the direction of water flow. Will the force pump or the lift pump raise water to a higher level ? Why is this so? Do not write a description of the work done, as the drawings and tabulations show this. A few explanatory statements may be added if necessary. Discussion : Under this heading, on the right-hand Fig. 29. page, answer the italicized questions in the experimental directions. Is the action of these pumps due to pressure or to " suc- tion." Which type of pump is a bicycle pump ? Explain. Why is a little water sometimes poured in at the top of a pump just before working the handle? (Class Dis- cussion.) THE PRINCIPLE OF MOMENTS 77 EXPERIMENT 19 The Principle of Moments OBJECT. When three parallel forces are in equilibrium, to com- pare (a) the forces in one direction with the force in the opposite direction; (&) the clockwise moments with the counterclockwise moments. APPARATUS. Meter stick ; loops of strong cord ; 3 spring balances (2000 grams), with hooks for suspending them, or clamps for fastening the balances to the edge of the table top (Fig. 35). 1 Introductory : When a team of horses is drawing a wagon, their com- bined force forward is exerted to overcome the resistance of the wagon pulling backward. When two boys carry a heavy weight suspended from a stick, the boys pull up- ward and the weight pulls downward. If the boys have not equal strength, the weight will be shifted toward one of the boys. Which one? In each of these cases, we have three forces parallel to each other, two in one direction and one in the opposite. These forces are in equilibrium when the stick is balanced. If one boy should lift more than he had been lifting, the stick would turn toward him. The turning effect of a force is called the moment of the force. We can imitate either of these cases by attaching three spring balances to a meter stick, so that two pull in one direction and one in the other. We can then compare (a) the pull of the two forces in one direction with that 1 This experiment can also be conveniently done by using two balances suspended vertically with a weight between, supported by a loop on the meter stick so that the weight may be moved to positions of equilibrium. If this modification is made, allowances must be made for the pull on the balances due to the weight of the meter stick. 78 LABORATORY EXERCISES of the single force in the other, and compare (6) the turn- ing effect or moment of the force at one end with that of the force at the other end of the stick. Experimental : The apparatus will be arranged as shown in the diagram (Fig. 30). The amount of each force may be read on the balance. First each outside cord should be placed 10 cm. from its end of the meter ~ stick and the third cord in the center. See that all cords are parallel. The highest reading on ] any balance should not be more than 1600 grams. When all is adjusted, the reading of each balance and the position of each Fig. 30. string on the meter stick should be recorded (I). One end balance may then be shifted so that it is half as far from the center as the other. After adjustment, readings should again be taken (II). The total force in one direction may then be compared with the total force in the other, as indicated in the table for the right-hand page. The moment of a force is found by multiplying the force by its lever arm. The lever arm is the perpen- dicular distance from the fulcrum a-bout which the force is trying to turn the body, to the force. In this experiment, the distance between each of the outer cords and the center cord will be the lever arm for the force ipplied by the cord, if the cords are at right angles to the meter stick. The moment of each of the end forces around the center cord is to be computed. THE PRINCIPLE OF MOMENTS 79 Record the readings in tabular form near the top of the left-hand page. OBSERVATIONS i ii Reading of balance A Reading of balance B Reading of balance C Point of application of force A . Point of application of force B . Point of application of force . Make a drawing of your apparatus and write a simple description of how it was used. Place the table of calcu- lated results at the top of the right-hand page. CALCULATED RESULTS i ii Combined Force of A and B . . . Force of O Moment of A ab out C Moment of B about O Discussion : Is the moment of A about C clockwise or counter- clockwise ? Is the moment of B about clockwise or counterclockwise ? Conclusion : Complete the following with a statement about the amount of force in each direction : When three parallel forces act on the same body to pro- duce equilibrium, then Complete the following by comparing with the moment of the third force around the second, both as to magnitude and direction : When three parallel forces act on the same body to produce equilibrium, the moment of one of them about the second is___ 80 LABORATORY EXERCISES EXPERIMENT 20 The Lever Arm of a Force OBJECT. To determine the lever arms of non-parallel forces. APPARATUS. Meter stick, with a hole on the center division near one edge, drilled slightly larger than the shank of a f " screw eye; short piece of board about f" stock ; screw eye, " ; fish line; four clamps; half meter stick; draughtsman's triangle, 90, 60, and 30. Introductory : In using such a lever as a crowbar, pump handle, or hammer, it is seldom that the forces exerted on and by the lever are parallel to one another. Under such circum- stances, it would be desirable to know whether the lever arm is to be measured along the lever or at right angles to the applied force. f&-^ Fig. 31. THE LEVER ARM OF A FORCE 81 Experimental : The meter stick is to be attached by the screw eye to a short board held firmly by two clamps to the edge of the laboratory table. The meter stick must be free to rotate around the shank of the screw eye as a ful- crum. The hook of each bal- ance is to be attached by a loop to the meter stick. The other end of each bal- ance is to be clamped to the edge of the table op- posite the meter siick. These two balances are to be clamped so that they make acute angles with the meter stick. One angle should be nearly a right angle and the other decidedly acute, as shown in Fig. 31. Perpendicular distances may be measured by using a triangle and a half meter stick, as shown in Fig. 32. Make the following readings and record in tabular form near the top of the left-hand page of note-book. OBSERVATIONS Reading of balance A g. Reading of balance B g. Point of application of force A ..... cm. Point of application of force B cm. Position of fulcrum on meter stick . . . . cm. Perpendicular distance, fulcrum to force A . cm. Perpendicular distance, fulcrum to force JB . cm. Make one drawing showing the arrangement of your apparatus and another drawing showing the method of 82 LABORATORY EXERCISES measuring the perpendicular distance of a force from the fulcrum. Write a simple description of Jiow the experi- ment was done, referring to the drawings. Place the table of calculated results at the top of the right-hand page and make all the calculations on that page. CALCULATED RESULTS Distance along stick from fulcrum to a . . . cm. Distance along stick from fulcrum to b . . . cm. Force A x meter stick distance from fulcrum . Force B x meter stick distance from fulcrum . Force A. x perpendicular distance from fulcrum Force B x perpendicular distance from fulcrum Discussion : Which pair of products, in the table above, more nearly agrees with the principle of moments ? Conclusion: How should the lever arm of a force always be measured? EXPERIMENT 21 Composition of Several Parallel Forces OBJECT. When a number of parallel forces are in equilibrium, to compare (a) the total force in one direction with the total force in the opposite direction; (6) the clockwise moments with the counter-clockwise moments. APPARATUS. Meter stick ; four or more spring balances (2000 g.), with cords and clamps. COMPOSITION OF SEVERAL PARALLEL FORCES 83 Introductory : A floor or bridge beam is frequently supported at more than two points and has a number of different persons or objects exerting their weights on it at various points. It is interesting to determine whether the principle of moments which has been tested for two forces acting about the point of application of a third as a fulcrum, will apply to this case also. Experimental : Four or more spring balances, as the instructor may direct, are to be attached by cords to a meter stick, as in 1000 g TOO g ^750(7 Scale 1cm =500 (7 1800 fj Fig. 33. the experiment on the Principle of Moments (see Fig. 30, page 78). The balances should then be strained and clamped in place in such a way as to make all the cords parallel, and at right angles to the meter stick. The amounts of various forces and their lever arms are to be recorded near the top of the left-hand page in the form of a diagram like that shown in Fig. 33. Letter the forces in order from left to right. 84 LABORATORY EXERCISES Take for the center of moments some point which is not the point of application of any of the forces. The line representing each force should be drawn to a scale to be designated by the instructor and the exact amount of the force should be noted at the right of the line repre- senting it. The lever arms are indicated by dimension lines as shown. No drawing of the apparatus will be necessary. A short description, however, of the experi- mental method should be written. Place a table like the following at the top of the right- hand page and make all calculations on that page: CALCULATED RESULTS CLOCKWISE MOMENTS COUNTERCLOCKWISE MOMENTS Moment of A etc. Total clockwise moments . Sum of forces as A, C, E, etc. Sum of forces as B, D, etc. Moment of B . . . . etc Total counterclockwise moments Conclusion : Fill in the blanks in the following statement so that it agrees with your results: When a number of parallel forces act on a body, it is in equilibrium when the of the forces in one direction equals the of the forces in the other direction, and the total moments equal the total moments about any point taken as fulcrum. FOUR FORCES AT RIGHT ANGLES 85 EXPERIMENT 22 Four Forces at Right Angles OBJECT. When four forces at right angles in one plane produce equilibrium, to compare (a) the force in any one direction with the force in the opposite direction ; (&) the clockwise moments with the counterclockwise moments. APPARATUS. Composition-of-force board with under side rest- ing on four steel balls or marbles ; four pegs ; four spring balances (2000 g.) with cords and clamps ; meter stick or other metric ruler. Introductory : Four boys of different ages might pull on the four sides of a piece of burlap so as to stretch it parallel to the top of a barrel of vegetables while their father finished the heading by putting on a hoop. Each boy probably took hold of the burlap at the center of his side, but one or more of them soon found it advisable to move his hands to one side or the other of the center, so as to prevent the burlap from being drawn out of his hands. When the burlap was properly stretched, four pulls or forces were acting at right angles in one plane. Did the principle of moments come to the aid of the smaller boys in the family so that they could do their share of the stretching? Experimental : The hook of each spring balance is to be attached by a cord to a peg on the composition-of-force board. The pegs should be arranged so that no two of them will be in the same row of holes across the board in either direction. The other end of each spring balance is to be securely clamped (see Fig. 35 on page 89) so that both the cords holding it are parallel to a row of holes (Fig. 34). This LABORATORY EXERCISES latter figure shows the method of attachment of the bal ances to the board, but not the correct location of the pegs. The strain on each balance should be at least 500 grams, and the board, which is free to move on its roller bearings, should be brought to rest by the equilibrium of the four forces at right angles pulling on it. The amounts of the va- rious forces and their lever arms are to be re- corded in the form of a diagram on the left-hand page. Draw, in about the middle of this page, a square, 7 centimeters on a side, and divide each side into centimeter divisions, and lightly rule such cross lines as will locate the positions of the four pegs or points of application of the several forces. Take for the center of moments some point which is not the point of application of any of the forces. To a scale designated by the instructor, draw a line representing the direction and the exact amount of each force. Indicate the amount of each force by figures placed to the right of the line representing it. The lever arm of each force is to be indicated by a dimension line as in Fig. 33, on page 83. CALCULATED RESULTS Fig. 34. CLOCKWISE MOMENTS COUNTERCLOCKWISE MOMENTS Moment of Moment of etc .... Total clockwise moments . Total counterclockwise moments . ~ PARALLELOGRAM OF FORCES 87 Unless the instructor so directs, make no drawing of the apparatus. A short description of the experimental method, however, should be written. Place a table, like the one on page 86, at the top of the right-hand page and make all calculations on that page. Conclusion : State, when four forces at right angles in one plane pro- duce equilibrium : (a) the relation of the force in one direction to the force in the opposite* direction ; (6) relation of the clockwise moments to the counter- clockwise moments about any point taken as a fulcrum. EXPERIMENT 23 Parallelogram of Forces OBJECT. To find the relation between three forces acting on a body at a point, in order that they may be in equilibrium. APPARATUS. 3 spring balances (2000 g.) ; fish line or other light, strong cord ; 3 Stone clamps or other means of hold- ing balances in place ; 30 cm. ruler. Note. Pencils used in this exercise should be hard, with long, sharp points. Introductory : If two boys were to kick a football, one east and the other north, at the same instant, the ball would not go in either direction, but would take . a course somewhere .be- tween north and east. The general direction that it would take would depend upon which force were greater. To prevent the football from moving, it would be necessary 88 LABORATORY EXERCISES to apply a third force which should have the proper direc- tion and amount to just neutralize the other two. We wish to find the relation between three forces at an angle to each other, acting on a body at a point in such a way as to keep the body at rest. With the football it would be possible for a single force to be substituted for the forces applied by the two boys. Such an imaginary force is known as a resultant force, and the two forces which it replaces are component forces. The single force that would keep the ball from moving is called the equilibrant force. Our problem is to find (a^ how the resultant force is related to the component forces in direction and magni- tude ; (5) how the resultant force is related to the equili- brant force. Experimental : Connect the three spring balances by three cords that meet at a point A. Fasten these balances in place by clamping the attached wires. Pull on the third balance until the pointer on one of the balances is near the end of the scale and then clamp the third balance in place. Place the right-hand page of the note-book under the cords with the center of the page under the point A. Mark two points directly beneath each cord. Remove the book and through each pair of points draw a line which represents in direction the force. Note and record on the diagram, the reading of each balance, calling the balances B, C, and D. Measure from A along each line a distance to represent the magnitude of the force, using a scale of 1 cm. to 250 grams. Place at the end of each line an arrowhead to show the direction of the force. Select one force as the equilibrant and lay off from A the resultant equal and opposite to the equilibrant. On the two lines representing the components, erect a parallel- PARALLELOGRAM OF FORCES 89 ogram and draw the diagonal from A. Determine the magnitude of the force which this diagonal would repre- sent. Compare it with the resultant which you laid off and drew. Mark on the drawing the lengths of the lines and the readings of the balances. No table of results is necessary Fig. 35. on the left-hand page, but write a simple description of the method of the experiment. The drawing has already been placed on the right-hand page. On the second right-hand page place the table of calcu- lated results. CALCULATED RESULTS Magnitude of resultant g. Magnitude represented by diagonal .... g. Discussion: (1) What single force would alone produce the same effect as the two forces represented by the sides of the 90 LABORATORY EXERCISES parallelogram? (2) Compare the resultant and the diag- onal of the parallelogram in direction and in magnitude. Conclusion : Three forces are in equilibrium when the of two of them is in magnitude and in direction to the . EXPERIMENT 24 Resolution of Forces OBJECT. Given the resultant of two forces and one of the forces, to find the other force. APPARATUS. 2 spring balances (2000 g.) ; 500-gram weight ; fish line ; upright, with ring for cord and notch for boom ; light hard-wood boom, about 25 cm. long, with a brad in the end. Introductory : When a load is hanging from the boom of a derrick, its weight is sustained jointly by the tension of the rope sup- porting the end of the boom and the outward thrust of the boom. These two forces may then be considered as the component forces, whose resultant balances the weight of the load. If we know the pull on the cord supporting the boom and the weight of the load, we can calculate the thrust of the boom outward. Experimental : (a) The apparatus is to be set up as shown in Fig. 36. The boom should be horizontal, and when it has been made so, a turn of the cord around the brad in the end of the boom will keep it from slipping. When all adjustments have RESOLUTION OF FORCES 91 Fig. 36. been made, hold the note-book with the right-hand page against the boom, and indicate the direction of the forces by dots under the cords and a line drawn along the top of the boom. Place a dot at the end of the boom, immediately under the brad. Leave the apparatus undis- turbed while per- forming the oper- ations of part (6). (J) Replace the note-book on the table. From the dot marking the com- mon point of application of the forces, draw lines through the dots that were placed under the cords. From the common point of application, continue outward some dis- tance the line drawn along the boom. Lay off on the line representing the tension, a distance corresponding to the reading of the balance, using a scale of 100 grams to the centimeter. Mark the end of the measured distance with an arrowhead, indicating the direction of the force. Do the same on the line representing the weight. Mark beside each line the exact number of grams represented. The weight is the equilibrant of the tension of the cord and the outward push or thrust of the boom against the cord. Therefore draw a line upward from the point of application equal in length to the line representing the weight. With this line as a diagonal and the line repre- senting the tension as one side, complete a parallelogram having a side extending outward from the point of applica- tion, as a continuation of the line drawn along the boom. 92 LABORATORY EXERCISES This side will represent the thrust in direction and magni- tude. From the length of this side, the outward thrust of the boom may be calculated, using the scale employed in laying off the other lines. (c) Hook a second spring balance between the cord and the boom and pull horizontally until the boom just slips out of the notch in the upright. Read the balance at this point and record below the drawing on the right- hand page : Force required to pull out boom .... g. Since action and reaction are equal, the inward compo- nent of the stretched cord on the boom must equal the out- ward thrust of the boom on the cord. Make a simple sketch of your apparatus and write a brief description referring to the sketch. Discussion : May the resultant of two forces ever be less than one of them? Is a rope that is just strong enough to lift a weight vertically, strong enough to lift that weight by means of a horizontal boom derrick ? Conclusion : Given the resultant of two component forces and one of the components, state how the other component may be found. FORCE AT THE CENTER OF GRAVITY 93 EXPERIMENT 25 Force at the Center of Gravity of a Body OBJECT. To find what is the gravitational force acting at the center of gravity of a body. APPARATUS. Half meter stick loaded at one end; 1 ruler or other fulcrum properly supported (see Fig. 37) ; 200-gram weight with loop of cord attached; spring balance, or platform balance ; metric weights. Introductory : When we shut a heavy door, we push near the outside of the door and not near the hinge. A small rjoy can balance a large boy on a seesaw, loy sitting farther out on the board. When a body is to be turned about an axis, the turning power depends upon how much force is exerted and how far from the axis the force is exerted. The turning power of a force is called the moment of that force and is measured by the product of the force and its distance from the axis. The moment of the small boy on the seesaw is equal to the moment of the large boy. If we know the moment of the large boy and the distance of the small boy from the fulcrum, we can calculate what the small boy weighs. If both boys get off, the board can be balanced so it will not touch at either end. The point at which a body must be balanced in order to sup- port it is called the center of gravity of the body. Experimental : The body will be a half meter stick loaded at one end. This is first to be balanced over a fulcrum in order to find 1 The loading may be done by attaching a strip of brass, iron, 01 lead to one end of the half meter stick, at right angles to the stick. 94 LABORATORY EXERCISES the center of gravity (Fig. 37, A*). Then a 200-gram weight will be hung about 10 cm. from the free end of the bar and the bar again balanced. By measuring the distance of the 200-gram weight from the fulcrum and multiplying this distance by the weight (200 g.), the moment of the 200-gram weight is obtained. Fig. 37. This moment equals the moment of the force at the center of gravity about the fulcrum. Then the force at the center of gravity is calculated. A second trial should be made with the weight at some other point on the stick, as 20 cm. from the end. Finally the loaded stick is weighed. All observations as soon as made should be recorded in tabular form near the top of the left-hand page. OBSERVATIONS Position of center of gravity of loaded i 2 stick Position of 2QQ-g. weight Position of fulcrum for equilibrium . Weight of loaded stick FORCE AT THE CENTER OF GRAVITY 95 Make drawings showing how your apparatus was used and write a simple description of how the experiment was done. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS i a Distance of weight from fulcrum (Z) x ) Distance of center of gravity from fulcrum (J9 2 ) .....'. Moment of weight about fulcrum (200 xDj) Moment of force at center of gravity Calculated force at center of gravity Discussion : Define moment of force. Explain the calculation of the moment of the force at the center of gravity and the cal- culation of the amount of this force. Conclusion : What gravitational force acts at the center of gravity of a body. (Compare the last item in both tables.) 96 LABORATORY EXERCISES EXPERIMENT 26 The Pendulum OBJECT. To observe the effect on the number of vibrations of a pendulum in one minute of (a) change in mass, (&) change in amplitude, (c) change in length. APPARATUS. A wood and a metal ball each about 1 inch in diameter and having a light cord about 125 cm. long attached; a support consisting of a split cork in a burette clamp, or a special pendulum clamp, so placed that the pendulum may swing freely in front of the laboratory table ; metronome or laboratory clock with telegraph sounder. Note. Some instructors prefer to have all pendulums in the room released at a given signal and stopped on signal at the end of the minute, as confusion is thereby lessened and the student's mind is concentrated on the counting. Introductory : When a clock goes too fast, should the pendulum be shortened or lengthened ? We see pendulums made of different materials. Does this affect the length of their beats ? Does it take a pendulum longer to swing through a long arc than a small one ? These are some of the ques- tions the experiment will help to answer. By a vibration of a pendulum is meant a swing from one end of its arc to the other. The period of the pendulum is the time that one vibration takes. A seconds pendulum is one that swings from one end of the arc to the other in just one second ; a half seconds pendulum makes one vibration in one half second ; etc. The frequency of the pendulum is the number of vibrations per minute. Experimental : There will be furnished a metal and a wooden ball of the same size, attached to a light cord over a meter THE PENDULUM 97 long. As the suspending cord is very light, we neglect its weight and consider the length of the pendulum as the distance from the lower edge of the support to the center of the suspended ball or "bob." For the first test, adjust the length of the pendulum with the wooden ball to 100 cm. Count and record the number of vibrations made / \ in one minute swinging / through a small arc. Re- > place with the metal pen- / duluni and find how many / vibrations that makes in one minute swinging through | , the same arc. Comparing these numbers will show / whether or not the material / of the pendulum affects the / period of vibration. Now swing the metal bob Fig. 38. through an arc twice as great as before, counting the number of vibrations per minute. Make the length of the pendulum 50 cm. and find the number of vibrations per minute. Repeat with lengths of 36 cm. and 25 cm. Record all observations in tabular form near the top of the left-hand page. OBSERVATIONS Vibrations per minute, bob wood, length 100 cm., arc small Vibrations per minute, bob metal, length 100 cm.^ arc small . 98 LABORATORY EXERCISES ions per minute, bob metal, length 100 cm., arc large .............. Vibrations per minute, bob metal, length 50 cm., arc small .............. Vibrations per minute, bob metal, length 36 cm., arc small .............. Vibrations per minute, bob metal, length 25 em., arc small .......... .... Make a drawing of your apparatus and describe briefly how the experiment was done. Place the table of calculated results at the top of the right-hand page and directly below make all the calcula- tions called for. CALCULATED RESULTS LENGTH PLRIOD 100 cm. 50cm. 36cm. 25 cm. Conclusion: (a) Does the mass of the pendulum affect the period ? (6) Does the amplitude (if comparatively small) affect the period ? (c) Is there any simple relation between the period and the length ? between the square of the period and the length ? THE INCLINED PLANE 99 EXPERIMENT 27 The Inclined Plane OBJECT, (a) To compare the work done in raising a load by means of an inclined plane and in raising it vertically; (b)to determine the mechanical advantage from the length and height of the plane. Note. Only the case when the force is parallel to the plane is con- sidered in this experiment. APPARATUS. Inclined plane properly supported ; car with cord attached ; 500-gram weight or other load ; spring balance (2000 g.). Introductory : Safe movers roll a safe into a wagon along a sloping plank. Does this require less force than to lift the safe directly into the wagon ? Is less work done by rolling it up the incline than by lifting it directly ? The plank is an example of the use of the inclined plane. We wish to answer the above questions by using a car on an inclined board in the laboratory. We also wish to find out the mechanical advantage of the plane. This is the number which is obtained by dividing the resistance by the effort. In the inclined plane the mechanical advantage may be found also from the dimensions of the plane. We shall seek to find what dimensions are used and what division is made to obtain the mechanical advantage. Experimental : An iron car loaded with a 500-gram weight will be used and it is to be pulled up an inclined plane by means of a cord attached to a" spring balance. This balance thus measures the force employed to draw the car up the plane. 100 LABORATORY EXERCISES The combined weight of the car and its load is the weight lifted by the use of the plane. It may be found with the spring balance. The dimensions of the plane are to be measured, as shown in Fig. 39. Correction is to be made for some friction. This may be eliminated by averaging the reading of the balance when the car is moving uniformly up the incline with the Fig. 39. reading when it is moving uniformly down the plane. Decide in each case whether the friction is a help or a hin- drance. The work done along the plane is measured by the product of the balance reading and the length of the plane (to A). The work done in raising the weight an equal distance is measured by the product of the weight lifted and the height of the plane (at A). Record the observations in tabular form near the top of the left-hand page. OBSERVATIONS Weight of car and load . . Force required, car ascending Force required, car descending Length of plane .... Height of plane .... 9- 9- cm. cm. THE INCLINED PLANE 101 Make a simple sketch of your apparatus and write a short description of the method of the experiment. Place the table of calculated results at the top of the right-hand page. CALCULATED RESULTS Average force used g. Work = weight lifted X height of plane . . ,. g.cm. Work = f orce x length of plane g.cm. Mechanical advantage = ^ .'.... force Length of plane Height of plane Conclusion : (a) Compare work done in lifting the load vertically from the table to the level of A, with the work done in raising it the same vertical distance by rolling it along the plane. (J) What relation between the height and length of the plane equals the mechanical advantage ? 102 LABORATORY EXERCISES EXPERIMENT 28 Pulleys OBJECT. To study the operation of pulleys and to find theii mechanical advantage. APPARATUS. 1 single fixed pulley and 1 double fixed pulley with stems for clamping or attaching ; single movable pulley ; an additional movable pulley or a movable double pulley with hooks for suspending pan or weights ; support for fixed pulley ; balance pan 1 ; metric weights ; spring balance (250 g.) ; meter stick; light, strong flexible cord (fish line). Introductory : The block and tackle is a familiar sight in large cities, as it is used for moving pianos and safes in and out of high buildings. In the country it is used for pulling stumps and handling logs. On the water front, the pulley in some form or combination is employed for loading the heaviest articles of the cargo. Pulleys would not be so widely used unless they brought some mechanical gain to their users. The me- chanical advantage of a machine may rest in changing either the direction or the magnitude of the force applied to it. Wherein lies the gain when pulleys are used? 1 The balance pan for Part (a) is made by first finding with a sensitive spring balance the error in indicated weight arising from the use of the balance tested in an inverted position. The pan is made from thin sheet copper and holes punched in the corners for the fine copper wire used as suspension cords. The weight of the pan and its suspension should equal the weight error found for the balance. It can be adjusted by filing or punching. PULLEYS 103 Experimental : (a) The Fixed Pulley. A spring balance should be used with the hook downward, as the weights of the hook and the drawbar were acting on the spring when the mark for the zero point was located. In an inverted position the balance will not read correctly. To compensate for the error arising in this manner, in this experiment, the balance pan with its supporting cords has been made equal in weight to the drawbar and hook. The apparatus should be arranged as in Fig. 40. A weight is placed in the pan and the spring balance is pulled vertically down- ward so as to raise the load at a steady rate, the force or effort necessary being read at the same time on the spring balance. Then the balance reading is again taken as the load descends at a uniform rate. The friction increases the balance reading as the load ascends and decreases the reading for the load de- scending. An average of the two readings may be con- sidered as the force or effort which will just equal the resistance to be overcome before the load will move. Take readings with 100 grams and 200 grams as the loads, and record in tabular form. Note the distance through which the load is raised as compared With the distance through which the effort moves. Compare the load with the effort. What is the only mechanical gain in using a single fixed pulley ? (6) Single Movable Pulley. The apparatus is arranged as in Fig. 41. The total load in this case includes the weight of the pan and the weight of the pulley block. These are weighed separately and the weights recorded. 104 LABORATORY EXERCISES Readings are made with the 100-gram and the 200-gram weights as in (a). How does the distance through which total load (resistance) moves compare with the effort distance? What is the Fig. 41. Fig. 42. Fig. 43. mechanical advantage of a single movable pulley ? Wliat is sacrificed to gain this ? (c) Combinations of Pulleys. A single fixed and a single movable pulley are arranged as in Fig. 42. This is the arrangement used in the movable scaffolds of house painters. Only one set of readings is made that with a load of 200 grams. What additional advantage does this combination of pulleys have over the single movable pulley ? Next, two fixed pulleys (a double pulley) and a single movable pulley are combined by the proper adjustment of cords. Readings are taken with the 200- and the 500-gram weights. The vertical distance through which the load moves from the table top is carefully measured as is also the distance covered by the effort at the same time. Note also the number of cords which support the movable block. Then a fixed pulley is combined with two movable pulleys PULLEYS 105 (or a double pulley), and a similar set of readings taken with weights of 200 and 500 grams. Make for (a), (5.), and (c) simple diagrams showing the arrangement of the load, the pulleys, and the spring balance. Indicate clearly the number of cords which support the movable pulley blocks. Write simple descriptions of the work done in each part of the experiment, shortening the descriptions by references to the diagrams. OBSERVATIONS TRIALS PULLEYS USED WEIGHTS OF BALANCE READING Load Pan Movable Block Up Down 1 and 2 1 fixed 100 g. 3 and 4 1 fixed 200 g. 5 and 6 1 movable 100 g. 7 and 8 1 movable 200 g. 9 and 10 1 fixed and 1 mov. 200 g. 11 and 12 2 fixed and 1 mov. 200 g. 13 and 14 2 fixed and 1 mov. 500 g. etc. etc. etc. For Part (r v\i>ARD\2 /UNKifowN\2 OF UNKNOWN \DISTANCK / \DISTANCE / Candle power determined for unknown.. 136 LABORATORY EXERCISES Discussion : Demonstrate the relation between the distance and the intensity of illumination. How would you determine the candle power of a lantern ? Conclusion : The candle power of lamp No. is . EXPERIMENT 37 (Alternative) Measurement of Candle Power OBJECT. To determine the candle power of a lamp by means of the Rumford photometer. APPARATUS. Ring stand ; vertical screen ; meter stick ; 2 incandescent lamps, one of known candle power. If electricity is not available, a standard candle and an oil lamp may be used. The ordinary paraffine candle " 6's " or " 12's"are about 1.25 candle power. A small lantern is a very desirable form of the oil lamp for this experiment on account of its candle power and its safety for laboratory use. Introductory: A 16 candle power lamp is one which gives 16 times as much light as one standard candle. If a candle and a lamp are both placed on the same side of a rod, they will each cast a shadow of the rod on a screen placed behind it. Each will then illuminate the shadow cast by the other. If the shadows are equally dark, then the screen receives the same intensity of illumination from both lights. The greater candle power of the incandescent MEASUREMENT OF CANDLE POWER 137 lamp, however, permits it to be much farther from the screen than the candle. If the latter is 20 m. from the screen, then the distance of the lamp will be found to be 80 m. It is interesting to note that the square of these dis- tances from the screen have the same ratio as the rela- tive candle power of the two lights : ILLUMINATING ILLUMINATING SQUARE OF CANDLE SQUARE OF LAMP POWKB OF CANDLB POWKB OF LAMP DISTANCE FEOM SCREEN DISTANCE FROM SCUEKN 1 : 16 :: 400 : 6400 Hence the ratio of the illuminating power of the two lights equals the ratio of the squares of their respective distances from the equally illuminated screen. The photometer which determines candle power by means of shadows cast upon an opaque screen is the Rum- ford photometer. Experimental : 1. Place the upright rod of the ring stand about 10 cm. from the vertical screen. 2. Place the lamp whose candle power is to be deter- mined at a distance of about 120 cm. from the screen. 3. Place the standard lamp (or candle) in such a posi- tion that the two shadows of the rod formed on the screen shall be of the same intensity. These shadows should be near each other, but should not overlap. Measure with the meter stick the distance of the stand- ard lamp to the nearer of the two shadows, and the dis- tance from the unknown lamp to the other shadow. Record the results in tabular form near the top of the left-hand page. Why was the distance measured in each case to the nearer of the two shadows ? 138 LABORATORY EXERCISES 4. Repeat the above test with the unknown lamp (or candle) successively at 100 cm. and 80 cm. from the screen. In case two incandescent lamps are compared, their sockets should be connected to the same current outlet. OBSERVATIONS NUMBER OF TRIAL DISTANCE OF UNKNOWN FBOM SCREEN DISTANCE OF STANDARD FROM SCREEN 1 cm. cm. 2 cm. cm. 3 cm. cm. Candle power of standard . Make a drawing showing the essential parts of the photometer, and describe how you used it. Using the ratio method given in the " Introductory," calculate the candle power of the unknown lamp, placing the calculated results in tabular form at the top of the right-hand page. CALCULATED RESULTS NUMBER OF TRIAL /STANDARD \' V DISTANCE / /UNKNOWN\' V DISTANCE / CANDLE POWER OF UNKNOWN 1 2 3 Average ' Discussion : Demonstrate the relation between the distance and the intensity of illumination. LAW OF REFLECTION OF LIGHT 139 Conclusion : The candle power of is (name lamp) EXPERIMENT 38 Law of Reflection of Light OBJECT. To determine the relation between the angle of in- cidence and the angle of reflection. APPARATUS. Glass or metal mirror ; clamp or block for holding mirror ; sheet of clear glass the same size as the mirror ; pins ; ruler ; protractor. Introductory : When sunlight falls upon a mirror, the light is reflected in a definite direction. The relation between the direction of the light before and after it strikes the mirror is stated in the law of reflection. We can locate a particular re- flected ray by sighting along a ruler at the image of the object that is reflected. A line drawn along the edge of the ruler will mark the direction of the reflected ray. Experimental : (1) Draw a line across the middle of the right-hand page of your note-book. Mark it MM. Place the mirror perpendicular to the page with its reflecting surface on this line. Stick a pin upright in the page in front of the mirror and mark its position P. (2) Placing the head on the level of the page and opposite one of the lower corners of the book, sight along a ruler placed on the page at the image of the pin, as seen in the mirror. When the edge of the ruler is exactly in 140 LABORATORY EXERCISES a line with the image of the pin, draw a line along the edge of the ruler. (3) Repeat the operations described in (2), with the eye near the other lower corner of the book. Fig. 54. (4) Remove the mirror and substitute a transparent sheet of glass, carefully placing its front edge on the line MM. Protect the page behind the mirror from the direct light of the windows. Looking through this transparent mirror, insert a pin to coincide with the image of P. Mark the position of this pin P'. Remove the mirror and pins. (5) Continue each of the lines drawn along the edge of the ruler as solid lines to the mirror line MM, and con- tinue them as dotted lines behind the mirror until they meet. Do these solid lines represent incident or reflected rays f From P draw a line to the intersection of each of the lines just drawn with the mirror line. Do these lines from LAW OF REFLECTION OF LIGHT 141 P mark incident or reflected rays ? Connect P and P' with a line, solid from P to the mirror and dotted from the mirror to P' . Mark the direction in which light is passing along each of the solid lines by an arrow on that line. (6) At the intersection of one of the solid lines with the mirror line, erect a perpendicular to the mirror line. The angle between the line coming from the pin to the mirror and this perpendicular line is called the angle of incidence. The angle between the reflected ray and this perpendicular is called the angle of reflection. Measure these angles with a protractor. Record in tabular form near the top of the left-hand page the measurements called for. OBSERVATIONS Angle of incidence Angle of reflection , Distance of pin from mirror cm. Distance of image from mirror cm. Angle between MM and PP' A simple sketch of the apparatus as seen from above should be made and the experimental operations described briefly. Discussion : Answer the italicized questions occurring in the ex- perimental directions. As seen in the mirror, from what point do the rays sighted along the ruler appear to come ? From what point do they actually come ? Compare the distance of the image of the pin as seen in the mirror with the distance of the pin itself. Conclusion : State the relation between the angle of incidence and the angle of reflection. 142 LABORATORY EXERCISES EXPERIMENT 39 Images in a Plane Mirror OBJECT. To compare an object with its image in a plane mirror with respect to size, distance, and form. APPARATUS. Glass plate for mirror ; wooden block with slot for holding mirror in vertical position ; half-meter stick, or foot ruler ; pins. Introductory : The plane mirrors which hang on our walls give rise to some interesting questions. Why does your image in the mirror seem to approach you as you walk toward the mirror ? Why do you sometimes move your hand in the wrong direction when attempting to adjust something on your head ? Why is a long mirror desirable when you want to see your apparel from head to foot ? An answer to these questions will be found in the study of the relations of the object to the image in a plane mirror. The image of an object is composed of the images of the points in that object. We can locate the image of each point in a transparent mirror by direct observation, as was shown in the experiment on the law of reflection. Experimental : Draw a line across the middle of the right-hand page of your note-book. About two inches below this line of reference make a drawing of a quadrilateral set obliquely to the line, no side of the drawing to be less than 1^ inches in length. Number the corners 1, 2, 3, and 4, as in Fig. 55. Place the front of the glass plate along the line of reference. Place a pin at point 1 of your drawing and IMAGES IN A PLANE MIRROR 143 set a second pin at the image of 1 as seen in the mirror. Mark the position of the image pin with a pencil dot and the figure 1'. Locate and mark the image of each corner in the same way. Connect these points by lines representing the images of the corresponding edges of the block. Shading the part of the note- book behind the mirror helps to secure a clear image in the Fi g- 5S - mirror. Compare the object and the image by means of the following measurements, which should be recorded in tabular form near the top of the left-hand page. OBSERVATIONS LINES 8-4 LINES 1-3 Length of lines in object Length of lines in image . ,. . . . POINTS 1 284 Distance of object" 1 * points from mirror .... POINTS 1' 2' 8' 4' Distance of image's points from mirror .... Write a brief description of the method of the experi- ment on the left-hand page. Conclusion: ( )n the second right-hand page, answer the following questions, using a complete sentence for each answer. 1. What relation exists between the object distance and the image distance of a point from the mirror line ? 2. Compare the size of the object and its image. 144 LABORATORY EXERCISES 3. Is the image formed by a vertical mirror erect or inverted ? (Before answering, consider your own image in a mirror.) Is the image of the pin in front of the mirror or behind it ? 4. In which direction do the hands of a watch appear to turn when viewed in a mirror ? 5. Are an object and its image in a plane mirror similar or symmetrical ? EXPERIMENT 40 Reflection in a Concave Mirror OBJECT. To study the form and location of the images formed by a concave mirror. APPARATUS. Concave spherical mirror of glass or metal, sup- ported in a vertical position ; two meter sticks so placed as to form a V with its apex beneath the center of the mirror ; two screens mounted so as to slide on the meter sticks one screen is opaque and the other has cut in it a round or square window, over which is pasted very thin paper, with ink lines ruled across it at right angles and an ink mark in one of the four spaces formed by the intersecting lines ; candle or incandescent lamp, to be placed behind the translucent window. Introductory : The beam of light from a headlight, where the burner is quite near the surface of a concave reflector, is shaped like a cone with its apex behind the reflector. The beam from a searchlight may take a conical shape like that from the re- flector. It may, however, be made parallel, or it may even be brought to a brilliant focus at some point in front of the searchlight. These changes in the shape of the beam are possible because the distance between the light and its REFLECTION IN A CONCAVE MIRROR 145 concave reflector can be varied. The position of the light when the reflected rays are parallel is called the principal focus and the perpendicular distance from the principal focus to the mirror is the focal length of the mirror. For every case of reflection from a concave mirror a definite relation exists between the distance of the object, the dis- tance of its reflected image, and the focal length of the mirror. Experimental : (a) In a darkened room, the translucent screen, lighted from behind, is placed on one of the meter sticks at a con- siderable distance from the mirror. The opaque screen, on the other meter stick, is then moved backward and for- ward until a position is found where the most distinct image Fig. 56. of the lighted window is formed. Record the distance of each screen from the mirror, also whether the image is larger or smaller than the object and whether the image is erect or inverted. Note in this and in each of the follow- ing cases whether there is any image back of the mirror, as in the case of the plane mirror. (i) Find another pair of positions for the screens where the image will now be larger than the object, if it was smaller before, or vice versa. The same items are to be recorded as before. 146 LABORATORY EXERCISES (V) Another pair of positions is to be found where the image will be as nearly as possible the same size as the object, and a similar record made. (<2) The lighted window is next, moved toward the mirror, until there is no image formed on the opaque screen at any distance, but an image appears to be formed behind the mirror. The position of the lighted screen and the general location and character of the image are to be recorded. (V) Finally the illuminated screen is removed, and the meter stick on which this screen rests is pointed through the window at some distant object outside. If the weather permits, the window should be open. The location of the image should be recorded. This image is at the principal focus of the mirror. All observations should be recorded in a table near the top of the left-hand page. Where distances are not meas- ured, record general position of object or image. OBSERVATIONS TRIAL OBJECT DISTANCE IMAGE DISTANCE IMAGE EKECT OB INVERTED IMAGE ENLARGED OR DIMINISHED a cm. cm. b cm. cm. c cm. cm. d cm. cm. e cm. cm. Make a simple outline drawing of your apparatus. A view from above, showing the location of the mirror, screens, and meter sticks, will be sufficient. Describe briefly your observations, stating particularly anything REFLECTION IN A CONCAVE MIRROR 147 you observe about the images which is not recorded in the table above. For cases (), (6), and (") to BC, and from the point of intersection with BC draw a line to (0). Place an arrow head on each line to show the direction of the light in each case. 158 LABORATORY EXERCISES At (0) erect a perpendicular to A O. With a protractor measure the angle of incidence (which is the critical angle if your work has been done correctly) and the angle of reflection in the glass. Record the readings of the pro- tractor on the figure. If time permits, repeat the process of finding the critical angle, using the next page of the note-book. No table of observations is necessary, as all observed results are recorded on the drawing. Write a brief but complete description of your work, referring to the draw- ing, and mention any conditions that were observed which are not shown by the drawing. No sketch of the apparatus is necessary. Discussion : Through what kind of a medium must light pass in order to be totally reflected at the transparent surface of that medium ? Under these circumstances, if the angle of incidence be greater than the critical angle, what happens to the light ? If the angle of incidence is less than the critical angle, what happens ? In total reflection, how does the angle of incidence compare with the angle of reflection ? Conclusion : The critical angle of glass is . STUDY OF A CONVERGING LENS 159 EXPERIMENT 46 A Study of a Converging Lens 1 OBJECT. To locate the principal focus of a converging lens and to study the images formed by such a lens, when the lens is at different distances from the object. APPARATUS. Double convex lens, 10 to 15 cm. focus ; opaque screen ; half-meter stick ; screen with translucent window (see description under " Apparatus," page 166) ; meter stick, mounted as shown in Fig. 61 ; lens and screen holders to slide along the meter stick ; incandescent lamp or other light ; strip of paper more than twice the focal length of the lens. Introductory : Converging lenses are among the most useful parts of optical instruments, such as cameras, telescopes, and pro- jection lanterns. The first experience of most boys with a converging lens is the handling of a "burning glass." The parallel rays from the far distant sun enter the lens, and are so bent in direction that they converge to a point. This point of convergence of parallel rays is the principal focus of the lens. The focal length of a lens is the dis- tance from the lens to the principal focus. When we look through a converging lens at an object, we see an image of the object. The relations of the ob- ject and image vary according to the position of the object with reference to the principal focus. The relations are not hard to find and are interesting, because they explain the use of the converging lens in some of its important practical applications. 1 This experiment is essentially qualitative in its character. Experi- ments 40 B and 47 provide for a quantitative treatment of the convex lens. Either one kind of work or the other should be selected, as the performance of all three experiments would involve unnecessary repetition. 160 LABORATORY EXERCISES Experimental : (I) The Principal Focus. If we assume that the rays from a fairly distant object are practically parallel, and that these rays on entering the lens converge to the prin- cipal focus, the location of a sharp image of the distant object on a screen tells us the position of the principal focus. Accordingly, set the lens on one of the main divi- sions of a half-meter stick, and move the screen until the most distant bright object which can be seen through the window is sharply focused on the screen. Note the distance between the lens and the screen (principal focus). Record this focal length in the table of observations near the top of the left-hand page. Take two more OzJ ^ readings, moving the lens and screen each ii v 7i i % . , , f ,. , . time. Record these readings, and the aver- age of the three, which will be considered the focal length. A simple and very convenient form of lens holder is shown in Fig. 60. (II.) Relations of Object and Image. On a strip of paper draw a line just twice the focal length of the lens in length ; in the middle of the line place a mark, the dis- tance of which from either end will be equal to the focal length. All distances in the remaining portion of the experiment are to be measured in terms of the focal length of the lens, by means of this marked line, and not by means of the numbers on the meter stick. At one end of the meter stick place an incandescent lamp or other light, and directly in front of the light a screen with a translucent window in it to serve as an object (Fig. 61). (a) Set the lens at its focal length from the illuminated screen. The object is now at the principal focus of the STUDY OF A CONVERGING LENS 161 lens. Move the opaque screen on the other side of the lens, and note whether or not an image is formed on this screen. The formation of an image means that the rays of light leaving the lens converge. If an image is not formed, the rays leaving the lens are either parallel or divergent. When the object is at the principal focus, what is the direction of the ray 9 leaving the lens ? (Recall the method of finding the principal focus.) (6) Move the lens nearer the illuminated screen than in (a). The object is now within the principal focus. Move the screen to ascertain whether or not an image is Fig. 61. formed. Look through the lens at the illuminated screen and describe its appearance. In this case what do you think is the direction of the rays leaving the lens ? Explain. (c) Place the lens so that the object is at a distance of twice the focal length. Place the screen at an equal dis- tance on the other side of the lens. Is the image on the screen erect or inverted ? J Is it larger or smaller than the object ? When the object is at twice the focal length from the lens compare (1) the relative distances from the lens of object and image, (2) the relative size of object and image. At 1 In case a sharp image is not formed at twice the focal length, find the shortest distance between the object and the screen at which a distinct image of the object can be formed on the screen. Compare the object and image distances with each other and with twice the focal length. 162 LABORATORY EXERCISES what distance from a camera lens would you place a drawing in order to obtain a photographic copy of the same size ? (d) Move the lens in a little toward the object, so that it is at a distance from the object greater than the focal length, but less than twice the focal length. Move the opaque screen until a sharp image of the illuminated screen is obtained on it. Alongside the line already drawn on your strip of paper, lay off another line whose length is the distance between the lens and the image in this case. On this line also mark the object distance. Compare the image distance with twice the focal length. Note the relative sizes of object and image. When an object is at a distance from a lens greater than the focal length, and less than twice the focal length, (1) state the gen- eral location of the image in terms of the focal length, (2) compare the image and object as to size. (e) Move the lens to a point whose distance from the object is equal to the image distance obtained in (rf). The object distance is now greater than twice the focal length. Slide the opaque screen into a position where a sharp image is formed. Note the relative sizes of object and image. Beside the line drawn in (S in the table, to distinguish this point. Continue the readings at half-minute inter- ^ vals, until solidification is com- plete, and then at one-minute intervals until a temperature of about 55 C. is reached. At the close of the experiment the tube and thermometer should be returned to the in- structor, without any attempt to remove the thermometer from the acetamid. (,; Fig. 77. COOLING THROUGH CHANGE OF STATE 215 Record the observations in tabular form near the top of the left-hand page. OBSERVATIONS Time in minutes . J 1 1 J 2 2 J, etc. Temperature in 0. , etc. An outline drawing of the apparatus and a brief descrip- tion of the operations should be placed immediately below the table of readings. Curve. On a sheet of cross-section paper, plot a curve from your readings. Allow two horizontal spaces (2 mm.) for a half minute, and one vertical space (1 mm.) for one degree. This curve is to be pasted by its edge to the top edge of the right-hand page. Discussion : Answer each question with a complete sentence. Is there any point where the temperature curve takes a sudden change ? Does this correspond to any change in the condition of the acetamid ? Does your curve indicate that acetamid has a definite melting (or freezing) point ? If so, at what temperature? Is this temperature main- tained while solidification is taking place ? Is heat required to keep a body at a temperature above that of the room ? As no heat is being applied externally, from what change in the acetamid must this heat come ? Conclusion : Does a substance give out heat or absorb heat during solidification ? 216 LABORATORY EXERCISES EXPERIMENT 60 Melting Points and Boiling Points t OBJECT. To learn the method of determining the melting points and boiling points of substances ; and to study the boiling points of a mixture of alcohol and water. APPARATUS. Ring stand ; ring ; two burette clamps ; asbestos square, or iron gauze with asbestos center; beaker (100 cm. 3 ) ; glass stirrer ; thermometer ; rubber band (section of rubber tub- ing ; capillary tubes ; l distilling flask (60 cm. 3 ) ; cork to fit flask and perforated to admit thermometer ; small Liebig condenser, or 2 ft. length of \" tubing, with cork stopper perforated to admit delivery tube of distilling flask ; glass beads or a few short pieces of glass tubing; small graduate (preferably 25 cm. 3 ) ; Bunsen burner. MATERIAL. Stearic acid ; naphthalene or moth-balls ; carbon tetrachloride ; grain alcohol. Introductory : The melting point of a substance is the transition tem- perature between its solid and liquid state. The boiling point marks the boundary between the liquid and the gaseous states. A considerable change in pressure is necessary to affect the melting point of a solid ; the temperature at which a liquid boils changes with even the ordinary variations of atmospheric pressure. Determinations of the melting point are valuable in that they indicate the purity of a" substance. A pure sub- 1 The capillary tubes are made by heating the middle of a short piece of glass tubing. When the tubing is soft in the heated portion, draw it out into a thin-walled tube about 1 mm. in diameter. With a file cut off lengths of 2" to 3" and seal the narrower end of each in the Bunsen MELTING POINTS AND BOILING POINTS 217 stance, melting at a certain definite temperature, melts below that temperature when it contains even a very small amount of another substance. Crystal- line solids are characterized by very definite melting points. Boiling points are very useful in the identification of liquids and as an indi- cation of their purity. In the purifica- tion or separation of liquids by distilla- tion, the observed boiling points are the guides to the steps in the process. Experimental : Melting Points. () Light the burner underneath the beaker of water (Fig. 78). Have a very small flame, so that the water will heat very slowly. Put the open end of a capillary tube into some stearic acid, so as to get a column of the solid several millimeters in length. Turn the tube upright and tap the closed end gently on the table, so that most of the solid falls to the bottom of the tube. Slip the tube through the rubber band (Fig. 78, #) on the thermometer so that the solid is in the position indicated in Fig. 78. Move the glass stirrer 1 up and down in the beaker until you see some of the small particles sticking to the capillary walls melt. Read the temperature and record it as the melting point of the stearic acid in a tabular form on the left-hand page. In case you heated the water too Fig. 78. Fig. 79. 1 The bottom of the glass stirrer is most conveniently made by bending the glass into a triangular form as shown in Fig. 79. 218 LABORATORY EXERCISES rapidly, let it cool a little and approach the melting point more cautiously, using a fresh tube of the stearic acid. (i) Determine in a similar manner the melting point of naphthalene (the principal constituent of moth balls). (c) Put 15 cm. 3 of carbon tetrachloride into a small distilling flask having the delivery tube pointing upward as you pour the liquid in. Then arrange the flask as in Fig. 70, and pass the delivery tube of flask through a cork fitting into a condenser, with a beaker to receive the dis- tillate. A few short pieces of glass tube in the flask will save time in bringing the liquid to a boil. Take as the boiling point of the carbon tetrachloride, the steady tem- perature obtained as the liquid distills off through the de- livery tube. Record. Remove the burner and empty the distilled and the un- distilled tetrachloride into the bottle indicated by the instructor. (cZ) After rinsing out the distilling flask and the beaker with a very little grain alcohol, pour into the flask 15 cm. 3 of alcohol and 14 cm. 3 of water. This gives a mixture which is very nearly 50 per cent alcohol. Have at hand a sheet of cross-section paper. Accord- ing to a scale given by the instructor, temperatures are to be plotted on the vertical axis and the volumes (cm. 3 ) of the distillate on the horizontal axis. Heat the diluted alcohol to boiling, and plot as the first temperature that obtained when the liquid begins to con- dense in the delivery tube of the flask. Read the tem- perature from this point on as soon as each successive 3 cm. 3 of the distillate is collected. Plot the readings as soon as made. Paste the cross-section paper by an edge in the note-book. MELTING POINTS AND BOILING POINTS 219 OBSERVATIONS Melting points, Stearic acid O. Naphthalene ' . <7. Boiling point, Carbon tetrachloride .... C. Make drawings showing both the melting-point and the boiling-point apparatus. Describe the experimental methods with reference to these drawings. Discussion : The boiling point of ordinary alcohol is 78.4 C. . What effect does the water in the 50 per cent alcohol have on the boiling point of the alcohol ? Between what tempera- tures does most of the alcohol distill ? (Examine the curve.) How many cubic centimeters of distillate were collected between these two temperatures ? What liquid is present in the larger amount during the latter part of the distillation ? What makes you think so ? Is the boil- ing point of water raised when it contains a little alcohol ? Conclusion : What difference do you notice between the boiling point of a pure substance and the boiling point of a solu- tion ? How does a liquid dissolved in a second liquid affect the boiling point of the second liquid ? 220 LABORATORY EXERCISES EXPERIMENT 61 Heat Changes during Solution and Evaporation OBJECT. To observe the heat changes which accompany solu- tion and evaporation. APPARATUS. Centigrade thermometer ; 50 cm. 3 beaker ; wooden block; bicycle pump or foot bellows; two 100 cm. 3 Erlenmeyer flasks ; battery jar or other receptacle for hypo solu- tion ; test tube. MATERIAL. Strips of cheesecloth one inch wide ; alcohol ; ether ; " hypo " crystals ; supersaturated solution of hypo, made by dissolving 100 g. of hypo in 20 cm. 3 of water for each 100 cm. 3 flask. Introductory : Photographers notice that a freshly made " hypo " solu- tion feels much colder than the water used in making it. Is there an actual fall of temperature during solution ? Camphor is rubbed on the head for headache ; alcohol baths are given to fever patients. On a hot day we feel cooler in a breeze. In each of these cases rapid evapora- tion takes place on the skin. Is or is not the body actually cooled by this evaporation ? CAUTION. No flame is to be allowed in the laboratory during this experiment, and at the close the windows should be opened wide. Experimental : (a) A thermometer bulb is wrapped with a strip of cheesecloth, which is then tied with a raveling from the cloth. The thermometer is held by the upper part of the stem and a reading taken. Continue to hold the ther- mometer by the stem; then dip the bulb into a test tube HEAT CHANGES DURING SOLUTION 221 of alcohol and remove it when the cloth is thoroughly wet. The cloth is allowed to dry, in a draft if possible, the temperature being constantly watched. Record the tem- perature (1) immediately before dipping into the alcohol, (2) immediately after withdrawing the bulb from the alcohol, (3) at the reading showing the greatest change from the temperature taken in (2). Is the change in temperature that you noticed due to the temperature of the alcohol, or is it the result of the evaporation of the alcohol? (6) A few drops of water are placed on a wooden block and a beaker is set down in the 'water, so that there will be a film of water between the beaker and the block. Enough ether is poured in the beaker to cover the bottom. Cork the ether bottle tightly and do not inhale the fumes during the experiment. 1 With a bicycle pump or a foot bellows having a piece of rubber tubing connected to it, blow gently on the sur- face of the ether until it is evaporated. What has hap- pened to the water ? If there is no marked change of state in the water, repeat, using a little larger amount of ether. Has the ether, while evaporating, absorbed heat from the water or lost heat to it ? Explain. (<;) Into a small, clean flask are placed enough crystals of hypo to fill the flask a third full. Water, whose tem- perature has been observed and recorded, is added till the crystals are just covered. The flask is then shaken vigor- ously with a rotary motion until as much as possible of the hypo has dissolved. The bottom of the flask is then felt with the hand. Result ? The thermometer is in- 1 This part of the experiment must be carried on where there is a good draft to remove the ether vapor. If this condition cannot be met, or if the class is large, it is advisable to call the class together and perform this test as a demonstration. 222 LABORATORY EXERCISES serted in the solution and the temperature taken and recorded. Has the water taken heat from the hypo or given heat to it during the process of solution? The result ob- tained with hypo is typical of the heat change in solution, when no chemical action takes place between the dissolved substance and the solvent. After the temperature of the solution has been observed, it should be placed in a receptacle indicated by the in- structor, so that the hypo may be recovered by the evapo- ration of the water. (c?) At each laboratory 1 table is placed one or more flasks with the necks plugged with cotton, each contain- ing a supersaturated solution of hypo, which has stood in the room long enough to reach room temperature. When the students at a table have completed and recorded the results of the preceding parts of the experiment, they should make this final test together. Each student should touch the flask with his finger, without moving the flask or disturbing the liquid. The cotton should then be removed and a crystal of hypo dropped in. Result? When the change is complete, each student should feel of the flask and record his observation. What heat change takes place when the hypo is dissolved? When the hypo comes out of solution, what heat change occurs ? The results of Parts (a) and (c) should be recorded in tabular form near the top of the left-hand page. Other observed results should be recorded in the description of the part of the experiment to which they belong. OBSERVATIONS Part (a) : Temperature of room (1) Q. Temperature of alcohol (2) ...... G. Extreme temperature noticed (3) .... 0. HEAT OF FUSION OF ICE 223 Part 0): Temperature of water before dissolving hypo . 0. Temperature of hypo solution C. Drawings should be made of the apparatus used in parts (a) and (6). A brief description of the tests and of all results not noted in the table should follow the table. Discussion : Answer, under this heading, the italicized questions occurring in the experimental directions. Conclusion : Is sensible heat absorbed or given out when a liquid changes to a gas ? When a solid dissolves ? EXPERIMENT 62 Heat of Fusion of Ice OBJECT. To find the number of calories of heat required to change one gram of ice to water without warming the ice water above the melting point of the ice. APPARATUS. Calorimeter ; thermometer ; graduate, or balance and weights ; 150 cm. 3 beaker. MATERIAL. Supply of ice cracked into pieces about the sizo of a hickory nut ; supply of hot water at about 50 C. Introductory : When water at boiling temperature is thrown upon ice that is just ready to melt, some ice will melt and the boiling water will be cooled down to the freezing point. If just enough boiling water to melt the ice is used, it will 224 LABORATORY EXERCISES be found that there will be one and a quarter times as much ice melted as there was boiling water, and the whole mass will be ice cold. What becomes of the heat that was in the boiling water ? When heat is continuously applied to a solid body, as when pieces of ice are stirred about quickly in a pan on a hot stove, the solid is heated only up to the melting temperature. If stirred vigorously, the melted part and the part not yet melted do not get warmer than the melting temperature until the last bit is melted. After this the liquid will get warmer. We wish to find how much heat must be applied and must disappear as heat energy, when we change a definite amount of a solid to its liquid state. This number of calories is called the heat of fusion of the substance. Experimental : (a) In the calorimeter are to be placed 300 cm. 8 of hot water. 1 Since the calorimeter is being heated or cooled at the same time as the water in it, this fact must be taken into account in the calculations. The number of grams of water which require the same amount of heat to raise them one degree as is required to raise the temperature Qf the calorimeter one degree, will be furnished by the in- structor. This number of grams, called the water equiva- lent of the calorimeter, is always to be added to the number of grams of water actually placed in the calo- rimeter. (6) Insert the thermometer into the water, and when the temperature becomes about 50 C., begin to add dry 1 If the instructor prefers, the masses of water and ice may be found by direct weighing. The method of measurement used here is much simpler, and the results are accurate within the limits of error which may be expected in the experiment. HEAT OF FUSION OF ICE 225 ice, and continue until enough dry ice to fill a 150 cm. 8 beaker has been added. Stir constantly. As soon as the last particle of ice has been melted, give one final stir and take the temperature at once. Record this temperature as well as the first temperature, in a table near the top of the left-hand page. (_*<^^ll the known and through the Fig. 97. Reversing Key. unknown resistances. (6) Determine in a similar way the value of a second unknown resistance. OBSERVATIONS PART A PART B Deflection with unknown resistance . Total known resistance in ohms . . . Deflection* with known resistance . . Make a drawing showing the arrangement of the appa- ratus, and describe with reference to it the experimental method. State also the precautions to be observed with regard to the galvanometer and its readings. Discussion : Why is the circuit kept open, except when readings are being taken ? When the resistance box is in circuit, should the first resistance inserted be a large one or a small one? Explain. State why a repeated comparison is made of the readings of the galvanometer through the known and through the unknown resistance. Conclusion : The resistance of is ohms ; that of .. .. is . .. ohms. 272 LABORATORY EXERCISES EXPERIMENT 79 Heating Effect of an Electric Current OBJECT. To measure the number of calories of heat furnished by an incandescent lamp and to calculate the cost. APPARATUS. Calorimeter ; thermometer ; 1 6 candle power incandescent lamp ; porcelain keyless socket ; voltmeter ; amme- ter ; source of 1 10-volt current ; graduate, or balance and weights ; flexible insulated wire for connections ; watch or clock with sec- ond hand. Introductory : Electrical heating devices are widely advertised and many of them extensively used on account of their con- venience. The common feature of them all is a well- insulated conductor of comparatively high resistance, made of a material capable of being heated to a high temperature with- out melting. The incandescent lamp has these properties and is sometimes used for heating purposes in " lumi- nous radiators." By allowing a lamp to heat a known weight of water for a measured time, we may find the calories per second furnished by the 1 1 j lamp. If we know the current and ^* voltage of the lamp, we may estimate ^) the heat liberated per kilowatt hour. Although all the heat liberated by the lamp will not be measured in this experiment, yet the efficiency of the lamp as a heater, as used here, compares favorably with regular electrical heating apparatus. Fig. 98. HEATING EFFECT OF AN ELECTRIC CURRENT 273 Experimental : A porcelain keyless socket is connected to a 110-volt line, with an ammeter between the socket and the 110-volt terminals (Fig. 98). A voltmeter is connected across the terminals of the socket. A lamp is then screwed into the socket and the switch closed in the circuit to make sure that the connections are correct and that the in- struments read in the proper direction. The lamp is then turned off till needed. Into a nickel-plated brass calorimeter is placed 250 grams (cm. 3 ) of water at a temperature six or seven degrees below room temperature. 1 This is stirred thoroughly with a thermometer and the temperature noted ; immediately the cur- rent is turned on through the lamp which is inserted in the calorimeter, the exact time in minutes and seconds being noted. The time and the temperature of the water are recorded in the tabular form near the top of the left-hand page, the voltmeter and ammeter also being read and their readings recorded. The lamp should be immersed until the tip rests on the bottom of the calorimeter, and the thermometer should stand in the calorimeter beside the lamp (Fig. 99). For the next five minutes the lamp burns inverted in the water. By moving the lamp up and down in the water, never raising it more than a quarter of an inch from the bottom, the water can be kept stirred and so of equal temperature 1 This is the correct amount of water for the ordinary size calorimeter. The water should reach to within a quarter of an inch of the metal base of the bulb, when the latter is completely immersed. If the calorimeter is large enough to permit the use of a larger lamp, it should be used and the amount of water adjusted as just stated. Fig. 99. 274 LABORATORY EXERCISES throughout. The calorimeter should not be handled dur- ing the experiment. The voltmeter and ammeter should be frequently observed, aijd if there is any variation, the average reading for the whole time .should be the one recorded and used. When the lamp has been in the water exactly five min- utes, take it out promptly, stir the water vigorously with the thermometer, and read and record the temperature. Using fresh quantities of water, repeat the test twice. The water equivalent of the calorimeter should be obtained from the instructor. OBSERVATIONS TRIAL TIME TEMPEBATI:RE VOLTS A.MPEKE8 . Begin End Begin End Begin End Begin End 1 o 3 Weight of water Water equivalent of calorimeter Make a sectional drawing of the calorimeter with lamp and thermometer in place and with the connections of the instrument shown. A brief description of the method of the experiment should accompany the drawing. From the weight of the water, with the water equiva- lent of the calorimeter added, and the change of tempera- ture, the number of calories furnished in five minutes can be calculated. The number of watt-seconds is found by multiplying volts, amperes, and seconds together. From these two results calculate the calories per watt-second HEATING EFFECT OF AN ELECTRIC CURRENT 275 and per kilowatt hour. As the time and the weight of water are the same in all three tests, the averages of tem- perature changes, volts, and amperes will be used in the calculation. The problem called for in the conclusion should be worked out in the note-book, using the local rate for electricity. CALCULATED RESULTS Corrected weight of water (water -\- water equivalent of calorimeter) g. Average temperature change in five minutes . C. Calories furnished in five minutes .... cal. Calories furnished per second cal. Watt-seconds of energy used in five minutes . w.s. Calories per watt-second Calories per kilowatt hour Cost of current per kilowatt hour .... cts. Discussion : Explain any way in which heat generated by the lamp may escape without being measured in this experiment. Conclusion : At the price of cents per kilowatt hour, the cost of raising 4 liters of water from 15 C. to 100 C. will be cents, if an electric heater of the same efficiency as the lamp is employed. 276 LABORATORY EXERCISES EXPERIMENT 80 Study of an Incandescent Lamp OBJECT. To measure the current, voltage, resistance, and power consumption of an incandescent lamp. APPARATUS. Lamp socket, mounted on block with two bind- ing posts connected to the socket ; 1 6 and 32 candle power in- candescent lamps ; low-range ammeter ; 120-volt voltmeter ; one or more lamps with the metal cap removed ; at least one tung- sten lamp, of known candle power; $ 18 wire for connections to source of 1 10-volt current. Introductory : When we pay for electric light, we desire to get as much as possible for our money. We need to know the pressure required and the current consumed by our lamps. From these we can calculate the resistance of the lamp anr j the power in watts required to light it. By the use of a voltmeter and an ammeter properly connected to the lamp, we can observe the pressure and current directly. The resistance may be calculated by applying Ohm's Law. The watts are equal to the volts multiplied by the amperes. Experimental : Connect the ammeter in series with the lamp and the source of current. Connect the voltmeter to the terminals of the lamp socket, so that it will measure the fall of potential through the lamp only. Readings are to be made with 16 and 32 candle power lamps, and the results worked STUDY OF AN INCANDESCENT LAMP 277 out in each case. Readings with a tungsten lamp should be made by some members of the class. The results may be entered by the other members of the class for purposes of comparison. Assuming the candle power to be cor- rectly stated for the lamp, the number of watts required for each unit of candle power of the lamp should be cal- culated. This is known as the efficiency of the lamp, and, since power is what we pay for, it is used in comparing the economy of different kinds of lamps. The readings obtained should be recorded in tabular form near the top of the left-hand page. OBSERVATIONS CUBRENT VOLTAGE 16 candle power lamp .... amp. volts 32 candle power lamp .... amp. volts __ candle power tungsten lamp . amp. volts A careful outline drawing, showing a vertical section of the lamp, with the parts labeled, should be made, in addition to the diagram showing the connections. At the top of the right-hand page place the results obtained by calculation. RESISTANCE POWER EFFICIENCY watts CALCULATED RESULTS RESISTANCE Po 16 candle power lamp . ohms watts 32 candle power lamp . ohms watts c.p. Conclusion : The average efficiency of a carbon incandescent lamp is wat . t f ; of a tungsten lamp is-. - watts .. caudle candle 278 LABORATORY EXERCISES EXPERIMENT 81 Lines of Force around a Conductor OBJECT. To investigate the magnetic field surrounding a con- ductor. APPARATUS. No. 10 copper wire, bent at right angles and pro- vided with binding posts or double connectors at the ends ; dry cell or other source of current ; reversing switch ; $ 1 8 insulated copper wire for connections ; 4 small exploring compasses ; 2.5 cm. compass; support which will permit the exploring compasses to be placed around the vertical portion of the wire, while the larger compass may be placed either above or beneath the hori- zontal portion. Introductory : When a current passes through a wire, magnetic effects may be observed in the vicinity of the wire. As such effects are always associated with the presence of lines of force, we wish. to explore the field around the conductor to find the direction of these lines. This may easily be done by using compass needles, if we remember that a magnetic compass will set itself tangent to a line of force, and that a north pole will point in the direction of a line of force. Experimental : The direction of the current is from the + terminal of the cell, or dynamo, to the apparatus. Trace the current through the apparatus and back to the terminal. 1 Note to Instructor. The apparatus may be assembled permanently in the form shown in Fig. 101. The small compasses are set in holes bored in the block with a bit and cemented in place by rubbing them with a little shellac just before they are set in place. LINES OF FORCE AROUND A CONDUCTOR 279 (a) We may determine the direction of the magnetic field around a conductor passing vertically through a block by placing small compasses on the block around the wire and observing their position, (1) when there is no current flowing ; (2) when the current flows up; (3) when the current flows down. The observations are to be recorded in three diagrams at the top of the left-hand page. In each diagram the position taken by the small needles is to be shown by arrows in the four larger circles. The small circle in the cen- ter represents the wire. A current flowing up (toward the observer) is represented by a dot in a circle, thus O ; a current flowing down (away from the observer) by . These signs represent respectively the point of an arrow coming toward the observer and the feathers of an arrow going away from him. A sample diagram, showing the ^ -^ position of the needles in one case, is given in Fig. 102. (J) Place your apparatus so that the horizontal wire is parallel to one needle when no current is flowing. Place the compass under the wire and turn on the current. Observe the direction of deflection of the needle and record in diagrams, simi- lar to that shown in Fig. 103, placed in the upper part of the rightrhand page. Note beside each diagram the posi- 280 LABORATORY EXERCISES tion of the wire with respect to the needle (wire above or wire below}. The dotted arrow indicates the original position of the needle before the current passes and the solid arrow the position of the needle during the passage of the current. In all representations of the compass needle, the arrowhead indicates the north pole. Observe and record in the manner just described the four following cases : (1) Current S to N, wire over needle ; (2) Current N to S, wire over needle ; (3) Current S to N, wire under needle ; (4) Current N to S, wire under needle. Fig. 103. A simple outline drawing of the apparatus should be made on the left-hand page immediately below the diagrams of results, and a brief description of opera- tions written, referring to the drawings and diagrams. On the lower part of the right-hand page state the conclusions. Conclusion : (1) What is the shape of the lines of force around a straight conductor ? (2) Imagine the current as flowing in your right hand toward the fingers. If the palm faces the needle, toward what part of the hand is the needle deflected ? Make a full statement of this relation. (3) Suppose the wire to be grasped in the right hand, with the current flowing in the direction in which the thumb points. In what direction do the lines of force extend ? Make a full statement of this relation. THE ELECTROMAGNET 281 EXPERIMENT 82 The Electromagnet OBJECT. To study the construction of the electromagnet, and to determine the conditions of its operation. APPARATUS. 1 Three electromagnet coils; 2 a good dry cell; single contact key; small box of half-inch brads; ft 18 wire for connections ; compass. Introductory : Doorbells, telegraph instruments, dynamos, motors, and many other kinds of electrical apparatus depend for their operation on electromagnets. These electromagnets con- sist of coils of wire, or solenoids, usually containing an iron core. We wish to locate the poles of such a magnet, to find the effect of the iron core on the strength of the magnet, and to find the effect of the number of turns of wire. Later experiments will take up applications of the electromagnet. Experimental : (a) Connect the terminals of the coil wound on the wooden core (Fig. 104, (7) to the dry cell through the con- tact key. By means of a compass needle, determine which 1 The authors are indebted to Mr. W. R. Pyle, Morris High School, N. Y. City, for the plan of this experiment. 2 Two of the coils are wound on ^" soft iron cores and the third on \" dowel rod. The ends of the iron cores should be rounded off, as shown in Fig. 104, to increase the effect. On one of the iron cores (B) wind 100 turns of # 22 insulated wire ; the ends of the coil are held in place by rubber rings, cut from a piece of tubing, with a slightly smaller internal diameter than the rod. After winding, the magnet is dipped in shellac, to hold the windings and rings in place. On the wooden core an exactly similar winding is placed and shellacked. The other iron core (.4) is simi- larly wound, but with 60 turns only. 282 LABORATORY EXERCISES end of the coil acts like a north pole and which end like a south pole. The key should be closed only when readings are being made, as otherwise the cell will rapidly polarize. Trace the direction of the current from the positive (carbon) pole of the cell through the coil, noting particu- larly the direction in which it flowed around the coil. Record this in the form of a simple diagram, showing only a very few turns of wire wound on the core, with an arrowhead on each to show the direction of the current, and with the poles marked. Grasp the coil in the right hand, with the fingers pointing around it in the direction of the current and the thumb extended. Does the thumb point in the direction of the north pole or in the direction of the south pole of the coil? State the relation in full in the Discussion. (5) Using the coil (Fig. 104, A) having the smaller number of turns wound on an iron core, test for polarity as in (a). Does the presence of an iron core change the relation between the direction of the current around the mag- net and the location of the poles? Test the strength of the electromagnet by pushing one end into a box of brads, and then closing the circuit and removing the magnet with the brads which stick to it. Observe the behavior of the brads when the circuit is opened. What does this behavior indicate ? The brads picked up by the electromagnet should be counted and the number recorded. Fig. 104. THE ELECTROMAGNET 283 (c) Determine the number of brads which can be picked up by the coil with the larger number of turns and the iron core (Fig. 104, .5), and record. Count the number of turns on each of the three coils. How is the strength of an electromagnet affected by the number of turns of wire it has ? (rf) Try to pick up brads with the coil on the wooden core, and record the result. What effect has the use of an iron core on the strength of an electromagnet ? Record the numerical results obtained in tabular form near the top of the left-hand page. OBSERVATIONS MATERIAL OP COBB NUMBER OF TURNS NUMBER OF BRADS PICKED UP A brief description of the tests made should follow the table of observations and should include such observed results as are not stated in the table. A simple drawing should be made, showing one of the coils connected with the cell and key. Discussion : The questions in italics in the experimental directions should be answered under this heading. Conclusion : State the conditions necessary for a strong electro- magnet. 284 LABORATORY EXERCISES The Electric Bell OBJECT. To study the construction and operation of the elec- tric bell. APPARATUS. Electric bell with cover removed ; dry cell ; push button; $ 18 wire for connections ; magnetic compass. It is de- sirable to bend the hammer rod so that the hammer does not actually strike the bell. Introductory : The electric bell is one of the most familiar applications of the electromagnet. A clear understanding of its con- struction, therefore, is of value to enable us to know what may be expected of the bell and what adjustments are necessary when it fails to operate properly. Experimental : (a) Connect the bell, the cell, and the push button in series, so that the bell will ring when the circuit is closed by the push button. (6) Trace the path of the current through the bell, starting at one of the binding posts. What draws the hammer toward the bell ? What draws the hammer away from the bell ? (c) Place a compass needle near the ends of the mag- net coils. Hold the armature against the contact screw. Close the circuit and observe the result. Repeat with the armature held against the magnet poles. Is the mag- net stronger when the armature is pressed against the contact, or when it is against the poles ? (cT) Detach the wire from the binding post on the THE ELECTRIC BELL 285 armature side of the bell, and press the end of the wire against the contact screw. Close the circuit. Note and explain the difference in operation. (js) On the right-hand page, make a full-size diagram of the instrument and its connections. Indicate by arrows the direction of the current at each im- portant point. Label the following parts : electromagnet cores contact screw spring electromagnet yoke vibrating armature push button. Battery (/) Examine a push button and determine how the contact is made. Below the diagram of the bell, make a sketch of a vertical section of the push button and show the proper connections of battery, push button, and bell. Discussion : Explain the results of the tests in part (