LABORATORY EXERCISES IN ELEMENTARY PHYSICS BY i/ CHARLES R. ALLEN, S.B.'" L Instructor in the New Bedford, Mass., High School NEW YORK HENRY HOLT AND COMPANY 1895 COPYRIGHT, 1893, BY HENRY HOLT & CO. ROBERT DRUMMOND, ELECTROTYPER AND PRINTER, NEW YORK. Add to Lib. PREFACE. MOST of the experiments in this collection exact of the pupil measurements of some sort, that is, are quantitive. A few, included for the training in accurate work they afford or for their suggestiveness, demand the investigations of the conditions under which certain phenomena develop. They require, however, the use of some physical instrument. Those purely illustrative are given because they demand more careful observation than the pupil can give to a lec- ture experiment. In the course will be found, I think, illustrations of many of the more common methods of physical research. The exercises are planned for young pupils with no previous training in physics, employ no un- duly expensive apparatus, and require no more than forty- five minutes each in the laboratory. The subjects selected are among those bearing on the commoner applications of physical science. Pains have been taken to so frame the instructions that the pupil can prepare himself beforehand to make the most of his laboratory time with the least help from his instructor. This I regard of prime importance. Unless the instructor assures himself before each exercise that the pupils understand what they are to do and how to do it, they will pretty surely exceed the time-limit, and may even make wreck of the whole exercise. Five unprepared pupils require more attention than fifteen who have thor- oughly mastered the preliminary work. When entirely new or especially complicated apparatus is to be used, I iii iv PREFACE. find it advisable to place a " dummy" set before the class, and spend part or the whole of one period in requiring individual pupils to go through the motions with it, to answer questions on the general method and the special manipulations, and, in case of a complicated calculation, to work out results from imaginary data. The arrangement and even the phrasing of the ma- terial is the outgrowth of much searching for a general form which would be most effective in stimulating clear and independent thinking. Each exercise is introduced by some preliminary explanation and a distinct statement of its object. This puts before the pupil the precise thing he is after, and the general course of his investigation. The manipulation is then described with what some may deem unnecessary minuteness, but I find this minuteness part of the secret of speed and success. I have added ques- tions where I have found them convenient in guiding the pupils' thought, but in no instance, I believe, do they con- tain their own answer. In a few cases I have given alter- native exercises on the same topic, for the purpose of suiting the varying experimental aptitude of pupils. In the order of subjects, the exercises form a somewhat roughly graded course, from magnetic phenomena, where work is simplest and most stimulative to attention, through experiments involving the measurement of a single value by means of some single instrument, to the more compli- cated quantitive determinations of Dynamics. This order places the most difficult part of Physics last, where the pupil can bring to his aid, in grasping abstract ideas and performing intricate experiments, the training acquired in the previous parts of the course. But since the instruc- tions in one subject do not assume a previous knowledge of any other, there is nothing to prevent the subjects being taken up in any order desired, though of course practice in mensuration should precede the quantitive exercises. PREFACE. V The book is made up mainly of the author's instructions to his own pupils for their laboratory work. The course of which this forms a part includes also the performance of all necessary descriptive experiments before the class, and the use of a text-book. Before the pupil goes to work in the laboratory at all, he should be given a general idea of how knowledge is acquired experimentally, and the steps involved in carrying on an experimental investigation. The instruction on these points should be illustrated by some simple typical experiments by the teacher. After- wards the relative order of text-book and laboratory work will naturally depend upon the nature of the laboratory exercises. In exercises involving the study of conditions, as in those on Magnetism, and some of those on Electricity and Heat, the author prefers that the laboratory work pre- cede the text-book work; but in exercises involving definite measurement, as in Specific Gravity and Specific Heat, this order may well be reversed. Certainly, in the investiga- tion of a physical law by measurements of two values, as in the exercises on Elasticity or on the Pendulum, the labora- tory work should come first. In order to reduce the volume to a convenient size for the laboratory table, all matter meant chiefly for the in- structor is appended to the Teachers' Edition and omitted from the Pupils' Edition, the two being identical in other respects. Appendix A offers general suggestions for ar- ranging the pupil's work and economizing his and the in- structor's time, together with directions for applying the ordinary 110-volt Edison electric current to laboratory work, and for the care of mercury. Appendix B gives complete lists of all the apparatus needed for each exercise, hints as to substitutes and duplicates, and itemized esti- mates of cost with references to dealers' catalogues. Ap- pendix C contains full instructions for making the more important pieces of apparatus. Appendix D furnishes vi PREFACE. topical references to Avery's "First Principles of Natural Philosophy" and "Elements of Natural Philosophy/' to Gage's "Elements of Physics" and "Introduction to Physi- cal Science," and to Hall and Bergen's "Text-Book of Physics," supplemented by hints on conducting the vari- ous exercises, the educational purpose each is meant to serve, the degree of accuracy to be expected, etc. While, so far as I know, none of the experiments will be found elsewhere in exactly their form here, many have been modified from other manuals. No attempt is made to credit each exercise to the source of the original idea. The chief books laid under contribution are Worthington's "Laboratory's Practice," Stewart and Gee's "Physics," Pickering's "Physical Manipulations," the Harvard College Course of Experiments, and Maxwell's " Matter and Mo- tion." The metric system has been employed because it is the language of quantity in physical laboratories, scientific text-books and journals, and the higher scientific manu- facturing processes the world over. Pupils learn with such ease to use so much of it as this book requires, that it forms no bar to their progress. C. R. A. NEW BEDFORD, MASS., February 1, 1892. CONTENTS. MAGNETISM. PAGB Exercise 1. General Study of a Magnet, . . . . . 1 " 2. The Action of the Attracted Body on the Magnet, . 4 " 3. Mutual Action of two Magnets 6 " 4. Induced Magnetism. Breaking Magnets, . . 8 " 5. Law of Induced Magnets, 10 " 6. Lines of Magnetic Force, 12 CURRENT ELECTRICITY. Exercise 1. Voltaic Electricity, . . . - ; : . . .17 " 2. Conditions for Producing Current, . . . .20 " 3. Action of Currents on Magnets, . . v . 25 ' 4. Conditions Affecting Electrical Resistance, . . 29 " 5. Electrical Resistance, 33 " 6. Methods of Connecting Galvanic Cells, . . . 36 " 7. Relative Resistance, 40 " 8. A. Measurement of Resistance, . . . .42 B. Measurement of Resistance, . . . .45 " 9. Electro-motive Force, 48 " 10. Electro-magnetism, . ... . . . .50 ' 11. Induced Currents, * . 52 MENSURATION. Notes on Measurement, . . . . . , .56 Determination of Length, . . ; . r . .59 Exercise 1. Practice in the Use of Linear Scales, . . .62 " 2. The Relation of Circumference to Diameter, . . 64 vii VU1 CONTENTS. PAGE Determination of Volumes, . 67 Exercise 3. Practice in Determining Volumes, . . . .74 " 4. Cross-section and Internal Diameter of a Tube, . 76 Determination of Weight, . . 78 Exercise 5. Practice in Weighing, 83 6. Estimation of Metric Values, 84 Notes on Errors, . . . 85 Exercise 7. Physical and Chemical Change, . . . .86 DENSITY AND SPECIFIC GRAVITY. Exercise 1. Density and its Determination, . . . .89 " 2. Determination of Specific Gravity, . . . .92 " 3. Weight Lost by a Body when Immersed in a Liquid, 93 " 4. Specific Gravity by Immersion, . . . .96 " 5. Liquid Pressure Due to Weight, . . . .99 " 6. Specific Gravity of Liquids by Balancing, , . 103 " 7. Weight of Liquid Displaced by a Floating Body, . 106 " 8. Atmospheric Pressure and the Barometer, . . 107 " 9. Specific Gravity of Two Liquids by Balancing against Atmospheric Pressure, . . . .109 HEAT. Introductory, ... . 112 Exercise 1. How Heat Travels, . 113 " 2. Testing Thermometers 117 " 3. Temperature and Physical Form, . . . .119 " 4. Laws of Cooling, 124 5. Melting and Boiling Points, 125 6. Heat Capacity, 127 7. Determination of Specific Heat, . . . .128 " 8. Latent Heat, . 133 " 9. Coefficient of Linear Expansion, . . . .138 " 10. Cubical Coefficient of a Liquid, . . . .145 " 11. Coefficient of Expansion of a Gas at Constant Press- ure, . . . , . . .V . . . 146 " 12. Absorption and Radiation, 150 " 13. Solution, . .'. . . . . . . 152 CONTENTS. x PAGE DYNAMICS. Exercise 1. Action of a Force upon a Body, . . . .153 2. The Force of Friction, . . . ; . .156 " 3. Composition of Forces, 160 4. Parallel Forces, 166 " 5. The Inclined Plane, 169 6. The Wedge and the Screw, . . . . 173 " 7. Laws of the Pendulum, 174 " 8. Action and Reaction, ...... 177 " 9. The Force of Tenacity, .181 " 10. The Force of Elasticity, . . . . . ' - . 188 " 11. Boyle's Law, 185 " 12. Specific Gravity without Scales or Weights, . . 189 LIGHT. Exercise 1. Foci of Lenses, . 191 2. Distance and Intensity of Light, . . . .194 3. Radiation of Light, 197 " 4. Candle-power by the Rumford Photometer, . .199 SOUND. Exercise 1. Conditions Affecting Pitch, . ... . .201 2. Velocity of Sound, 20d LABORATORY PHYSICS. MAGNETISM. EXERCISE 1. GENERAL STUDY OF A MAGNET. EXPERIMENT 1. Apparatus. Bar magnet, a piece of steel (knife-blade or knitting- needle), some carpet-tacks; pieces of paper, glass, wood, etc.; cop per tacks; a piece of window-glass two or three inches square; iron- filings; larger tack or nail; bottle which may contain the iron-filings or block of wood. OBJECT. To compare the results of bringing first a piece of steel and then the magnet near a piece of iron or another piece of steel. MANIPULATION. Bring one end of the magnet near a few tacks scattered on a piece of paper. Observe carefully what happens. Repeat two or three times until you are sure that you have noticed all thatoccurs. Repeat with an ordinary piece of steel. Compare results. Try other bodies in place of the iron. Do you get the same result ? Definitions. If whenever a body is brought near a piece of iron or steel we obtain the results observed above, that body is called a magnet. This name is given it not because it is made of any particular substance or made in any par- ticular shape, but only because when placed under certain conditions, for instance those in Experiment 1, certain 2 MAGNETISM. things happen that do not happen when other substances are placed under the same conditions. Anything that happens among physical things (things that have weight or take up room) is called a physical phenomenon ; for example, the behavior of the tack when the magnet was brought near it would be a phenomenon. Placing a body under certain conditions and observing the resultant phenomena is called an experiment. A magnet in the form of a straight bar is usually called a bar magnet. EXPERIMENT 2. OBJECT. To see (a) if contact is necessary to get the results of Experiment 1, and (b) the effect of interposing various bodies between the magnet and the iron. MANIPULATION. Stand a tack on its head and bring the magnet slowly up to it. Note particularly whether or not the tack moves before the magnet touches it. Repeat the experiment, holding successively a piece of paper, a piece of glass, and a thin piece of wood between the end of the magnet and the tack. EXPERIMENT 3. OBJECT. To see if the magnetism is of the same strength all along the bar; and if not, how it varies at different points. MANIPULATION. Lay the magnet on a sheet of paper and dust iron-filings over it all along the bar. Now raise the bar. By the number of filings that adhere to the various parts of the magnet you can form some idea of the distribution of the magnetism. EXPERIMENT 4. OBJECT. To see if the distance between the magnet and the iron produces any effects. MANIPULATION. S^nd a large tack on its head, slowly bring one end of the magnet up to it, and observe the GENERAL STUDY OF A MAGNET. distance between the end of the tack and the end of the magnet when the tack begins to mo\ 7 e. Repeat with a small tack. EXPERIMENT 5. OBJECT. To see what happens when iron is brought be- tween the magnet and another piece of iron. MANIPULATION Lay the magnet so that one end pro- jects over the edge of the table. Attach a tack to it and then bring a second tack up to the first. Try other sub- stances in place of the second tack. EXPERIMENT 6. OBJECT. To measure the magnetic pulls at different points of the bar. MANIPULATION". Rest the centre of the magnet on top of a bottle or block of wood, as in Fig. 1, and suspend a tack from one end, then carefully at- tach a second tack to the first, and so proceed until you have as long a chain of tacks as the magnet will hold. Count and record the number of tacks. Remove the chain and repeat from a point about one-half inch nearer the centre of the magnet. Continue these measurements at points about one-half inch apart through the length of the magnet. Make a table of your results as follows: Distance from right-hand end of magnet. Number of tacks. Holding the magnet vertically, measure in the same way its power at the ends. 4 MAGNETISM. Definitions. The points in the magnet where the mag- netism is the strongest are called the Poles. When one body moves towards another, as the tack moved towards the magnet in Exercise 1, it is said to be attracted; thus, instead of saying that the tack moved towards the magnet, we would say that the tack was " at- tracted " by the magnet. Under the same circumstances, if the body moved away, it would be said that it was A qualitative experiment is one in which whatever hap- pens is simply observed; a quantitative experiment is one in which measurements are made. For example, Experiment 6 in Exercise 1 was quantitative, while all the other experi- ments were qualitative. When a body acts as if it were pushed or pulled, as for example the tack in Experiment 1, it is said to be acted on by & force. EXERCISE 2. THE ACTION OF THE ATTRACTED BODY ON THE MAGNET. Preliminary. How the iron behaves toward a magnet was shown in Exercise 1; now it is desired to find out whether the magnet is also affected. When the magnet was brought up to the tack, the tack moved; but the magnet, if it tended to move, could not do so because it was held firmly. In studying the action of the attracted body on the magnet, the conditions of Ex. 1 would natu- rally be reversed. The magnet would be placed on the table and the tack held near it. This could be done if the mag- net were very small, but the magnets ordinarily used are so heavy that, if the experiment were tried in that way, the attraction would have to be very strong in order to move them. If, however, the magnet be suspended, it will not ACTION OF THE ATTRACTED BODY. 5 rub against anything if it tends to move, and even a very slight pull will cause it to swing; therefore in the follow- ing Exercise the magnet is suspended and a body brought up to it. EXPERIMENT 1. Apparatus. Bar magnet; a new nail or tack; stirrup and thread for suspending the magnet.* OBJECT. To see if the attracted body also attracts the magnet. MANIPULATION. Make a small stirrup of wire (copper is the best), as in Fig. 2, and by means of it suspend the magnet so that it swings freely and hangs hori- zontally. When it has come to rest, bring a large nail near one end, but not touching it. Ob- serve carefully what happens, and - record. Now repeat with the other end of the magnet. Notice particularly whether the results are the same for both ends. EXPERIMENT 2. OBJECT. To see what happens when a magnet is free to move in a horizontal plane. MANIPULATION. Set the suspended magnet to swinging gently. Note if it tends to come to rest in any particular direction, and if so in what direction. If there is any doubt, after the magnet has come to rest displace it slightly and see if it shows any tendency to return to that position. Does any particular end of the magnet tend to point in any particular direction? * If a compass is available, it may be conveniently substituted for the suspended magnet. 6 MAGNETISM. Definitions. If something happens to one substance when another substance is brought near it, the second is said to act on the first. If the action is mutual, either body may be said to act and the other would then be said to react. Does a magnet act on a piece of iron ? Is there any reaction ? If so, where ? The pole of a magnet that tends to point north is called the North-seeking or North pole. In the same way the other is called the South pole. When new properties are developed in one body by bring- ing another body near it, the new properties of the first body are said to be induced by the second. Any contrivance for getting desired conditions is called a piece of apparatus; for instance, a compass is a contrivance or piece of apparatus for arranging a magnet so that it can swing freely. When the same experiment has beeniried a great many times, with the same results wherever or whenever it was tried, such results are said to be a law. For example, whenever a magnet has been brought near a piece of iron that could move, the iron has moved towards the magnet; and whenever the magnet has been placed under such con- tions that it could move, it has moved toward the iron. Whenever this has not happened, it has always been found that some other conditions had been introduced into the experiment, and when these were removed the usual results have taken place; hence it is said to be a law that a magnet attracts a piece of iron and the piece of iron at- tracts the magnet. EXERCISE 3. MUTUAL ACTION OF TWO MAGNETS. Preliminary. So far, magnets have been studied; but in the following Exercise the subjects are not magnets, but magnetic poles, and it is desired to study the action of one MUTUAL ACTION OF TWO MAGNETS. 7 magnetic pole on another. In order to do this, one pole must be free to move and the other must be brought near it. As there are two kinds of poles, both like and unlike poles must be tried. It is impossible to get the poles alone, so whole magnets must be used; and in order to have the poles free to move, one magnet must be suspended. The same device could be used as in Exercise 2, but a more convenient apparatus is a compass, which consists of a magnet supported on a sharp point and contained in a circular box, usually provided with a glass cover. EXPERIMENT 1. Apparatus. Bar magnet; compass; wood; glass; paper; etc. (as in Ex. 1). OBJECT. To study what takes place when two magnetic poles are brought near each other, one pole being free to move. MANIPULATION. Take a compass and find the north pole (Ex. 2, Exp. 2). Lay the bar magnet on the table and bring the north pole of the compass-needle up to the north pole of the magnet. In the same way try bringing the north pole of the compass-needle up to the south pole of the magnet. Try also the south pole of the compass and the south pole of the magnet, and the south pole of the compass and the north pole of the magnet. Tabulate your results as follows : Pole of Compass. Pole of Magnet. Results. From the study of the table, write in your note-book the " law" of the action of magnetic poles. EXPERIMENT 2.. OBJECT. To see if the results of Experiment 1 still hold when various bodies are placed between the poles, 8 MAGNETISM. MANIPULATION. Repeat Experiment 1 with pieces of wood, glass, paper, etc., held between the poles. Tabulate results as follows : 1st Pole. 2d Pole. Body Used. Results. EXERCISE 4. INDUCED MAGNETISM. BREAKING MAGNETS. EXPERIMENT 1. Apparatus. Bar magnet; compass; large darning- or knitting, needle of quite hard steel; piece of iron wire; copper wire (say No. 16); large horse-shoe nail ; iron-filings; piece of paper on which to put the filings; pieces of wood, and glass rod or tubing. OBJECT. To observe the effect of bringing a piece of steel in contact with a magnet. MANIPULATION. Take a large darning-needle and stroke one end, always in the same direction, several times on one pole of a bar magnet, is shown in Fig. 3. Note the nature of the pole used. Bring the end of Hie needle that you stroked on the mag- net up to a compass-needle. Note what change has been produced in the darning-needle. Test the other end in the same way EXPERIMENT 2. OBJECT. To find out how the nature of the inducing pole affects the nature of the induced pole. MANIPULATION. Compare the nature of the pole in- duced in the end of the needle that was rubbed on the magnet with the nature of the pole on which it was rubbed. Test the nature of the poles by the knowledge gained in Ex. 3. Test also the other end of the needle. State in your note-book the law for the induction of magnetic poles, FIG. 3. INDUCED MAGNETISM. BREAKING MAGNETS. 9 EXPERIMENT 3. OBJECT. To see if all substances can be magnetized. MANIPULATION. Repeat Exp. I with the following: Soft iron wire which you are sure is not magnetized, wood, glass, and copper. Tabulate your results. EXPERIMENT 4. OBJECT. To observe the results of breaking a magnet. MANIPULATION. Break your magnetized needle in the centre and, with the compass, examine both ends of each part. Record results, and draw figures illustrating them. EXPERIMENT 5. OBJECT. To find what happens when the broken parts of the magnet are put together again. MANIPULATION. Bring the broken parts of Exp. 4 together, opposite poles in contact, and with the compass examine it all along its length for magnetism. From these results suggest, if you can, why the centre of a magnet shows no magnetism. Break one half of your needle and test each half as before. As the magnet is broken into smaller and smaller pieces, what will apparently be true of each part ? EXPERIMENT 6. OBJECT. To see if a change is produced in a piece of iron when brought near a pole. (Compare this with Exercises 1 and 2.) MANIPULATION. Take a wrought-iron horseshoe-nail, test it to make sure that it is free from magnetism, and then hold it vertically with the lower end in some iron-fillings; bring the magnet over the upper end of the nail, but not in contact 1 [ with it. (See Fig. 4.) Lift the magnet and nail together, still holding them a little distance FIG. 4. apart. Observe results, Take away the magnet and again 10 MAGNETISM. observe results. Repeat the experiment with the other pole of the magnet. Try putting a piece of paper between the magnet and the nail. Put the bar magnet entirely out of the way and test the nail for magnetism by means of the compass. After a lapse of five or ten minutes test the nail again. State in your notes anything that you have observed regarding the different behavior of iron and steel when brought near or in contact with a magnet. If needed, Exp. 6 may be repeated roughly, with the nail and the magnet in contact. QuESTiONSo What tests could you apply to distinguish a magnet from a piece of steel ? Why are magnets made of steel instead of iron ? EXERCISE 5. LAW OF INDUCED MAGNETS. Preliminary. When a piece of iron or steel is mag- netized by being brought near or in contact with a magnet, it is said to be an induced magnet, and the original magnet is said to be an inducing magnet. The different behavior of iron and steel is expressed by saying that the steel has a greater retentivity than iron. The magnetism remaining in a piece of soft iron after the inducing magnet has been removed is called residual magnetism. In the following exercise, we wish to find out how the poles of the inducing magnet affect the poles of the in- duced magnet. EXPERIMENT 1. Apparatus. Bar magnet; compass; 2 horseshoe-nails, or 2 pieces of soft iron wire, 3 or 4 inches long. If nails are used, they will prob- ably have to be new ones, as the nail used in Exercise 4 will probably retain some magnetism. OBJECT, To study the nature of the pole of the induced LAW OF INDUCED MAGNETS. 11 magnet, furthest from the inducing pole. MANIPULATION". Arrange apparatus as in Fig. 5, where AB represents the bar magnet, CD represents a soft iron FIG. 5. nail (free from all magnetism), and N8 represents the compass. Be sure that the direction in which the nail and magnet lie is an east and west one, i.e., at right angles to the normal position of the compass-needle. Starting with the magnet three or four inches from the end of the nail, slowly bring it up to the end 0. Note how the end D affects the north pole of the compass-needle. Eepeat, using the south pole of the magnet. State in your notes how you find the pole of the induced magnet at the end furthest from the pole of the inducing magnet to compare with the inducing pole of the inducing magnet. Illustrate by a diagram. EXPERIMENT 2. OBJECT. To discover the nature of the induced pole nearest to the inducing pole. FIG. 6. MANIPULATION. Arrange apparatus as in Fig. 6. The distance from the pole of the magnet to the pole of 12 MAGNETISM. the compass-needle should be about an inch. When the nail is brought close to the pole, it becomes an induced magnet and, if suddenly removed from the pole, retains its magnetism for an instant. (See Ex. 4, Exp. 6.) When the compass-needle is at rest, suddenly move the end of the nail which is in front of the magnetic pole up to the compass. The induced pole in the nail, remaining for an instant, is brought so much nearer to the pole of the compass that its action is noticeable, in spite of the greater action of the pole of the bar magnet.* EXERCISE 6. LINES OF MAGNETIC FORCE. Preliminary. We know from previous experiments that the space around the poles of a magnet is in such a condition that a body which can be magnetized is acted upon when brought into that space. This space is called the field of a magnet. If the body moves towards the magnet, it moves in the direction of the force, that is, in the direction in which the magnetic push or pull is exerted. Suppose a small piece of iron placed near a magnetic pole, as in Fig. 7. It is magnetized by induction and becomes a magnet. The end nearest the inducing magnet will be, as shown in the figure, a pole opposite to the FIG. 7. nearest pole of the inducing magnet. The pole farthest from the inducing pole will be like it. The bit of iron will be attracted at one end and repelled at the other end with practically equal force, hence it will not tend to move toward the magnet, but will swing around until its length lies in the line of the push and pull. To illustrate this, imagine a stick lying on the floor, * SUGGESTION. Prepare an essay on Induced Magnetism. LINES OF MAGNETIC FORCE. 13 with a string attached to each end, as in Fig. 8. On pulling both strings the stick will not move in either FIG. 8. direction, but will twist around on its centre until it lies in the line in which the strings were pulled, as in the second diagram. The lines marking the direction of the magnetic push or pull are called lines of magnetic force. In the follow- ing exercise we wish to observe these lines for various cases. EXPERIMENT. Apparatus. A piece of sized writing-paper; fine iron-filings; two bar magnets; shellac; glass tube; blocks of wood. OBJECT. To study the lines of magnetic force. MANIPULATION. Take a piece of glazed paper, and pour fine iron-filings on it. Pour off the iron-filings and you will find that a layer of iron-dust remains on the paper. Lay a bar magnet on the table, hold the paper horizontally over it and then bring it straight down until it rests upon the magnet. If the magnet can be placed between two blocks of wood whose thickness is the same as the depth of the bar, so that the paper lies on a level surface, better results can be obtained. Tap the paper very gently with a lead-pencil and the little particles of iron will swing around on their centres until they everywhere lie in the line of the magnetic force. There will also be a number of 14 MAGNETISM. lines on the paper which surround the outline of the mag- net. These lines are called lines of force, and each line represents the line of the magnetic force in its part of the field. If a good set of lines is not obtained with one or two gentle taps, remove the paper and try again, as continual tapping will only cause the iron particles to bunch. The positions taken by the iron-filings now give the diagram of the lines of force, and in order to study them they must be preserved in some way. Method 1. Lift the paper vertically off the magnet to a height of about 6 inches, then gently place it on the table and carefully copy on another piece of paper the diagram obtained. Method 2. With a lead-pencil trace out the different lines one after another on the paper itself. On wiping off the iron- dust you will have a fairly good reproduction of the lines. Method 3. If it is desired to preserve in place the parti- cles of iron themselves, there will be needed, in addition to the other apparatus, some thin shellac and a glass tube, open at both ends, about in. internal diameter and 3 in. long. Holding this tube as in Fig. 9, insert one end into the shellac and remove the finger from the top for an instant. Keplace the finger and lift the tube from the liquid. So long as the finger is pressed on the top of the tube some shellac will remain inside and may be allowed to run out by raising the finger. With the paper lying upon the magnet, rest the tube very gently on the paper just inside the outline of the magnet (at the point marked x in Fig. 9), inclining it at an angle of about 45. After it is on the paper, but not before, remove the Fl - 9 - finger, thus allowing the shellac to run out. The rate at which the shellac flows LINES OF MAGNETIC FORCfl. 1 may be regulated by the degree to which the finger is removed. Care must be used to prevent the shellac from running out with sufficient force to move the iron parti- cles. If the operation is properly conducted,, the particles will not be disturbed and the shellac will soak in among them. If the first application of shellac does not en- tirely cover the figure, more may be added, with the same precaution, at other parts of the paper. The greatest care must be used not to allow any of the liquid to drop on the paper, as it will displace the iron-dust where it strikes. When the operation is completed, it is best to leave the paper until the alcohol has evaporated, which may be in five or ten minutes. During this time be careful that the paper is not disturbed. If in a hurry, the paper may be lifted vertically from the magnet and placed upon a hori- zontal surface until dry. When the shellac has become hard the iron is permanently fixed and the figure may be pasted in the note-book. Method 4. For this the shellac should be somewhat thicker than in the preceding method. Place the paper over the magnet and pour the shellac on the paper, allow- ing it to spread out in a thin layer. Then carefully scatter the iron-dust over it and the iron particles will spread in the shellac, on which they will float. Tap gently until the lines appear, and allow the paper to remain undisturbed until dry. By one of these methods obtain the lines of force in the following cases: 1. A north pole. 2. A south pole. 3. Two like poles. (Use two bar magnets end to end, the ends being about half an inch apart.) 4. Two unlike poles, arranged in the same way as in 3. QUESTIONS. 1. What is the form of the lines of force around a single magnetic pole ? 2. What is the shape of the lines of force around two like poles situated near each other? 3. What is the shape of the lines of force 16 MAMETI8M. around two uulike poles situated near each other? 4. How does the form of the lines of force around two like poles compare with the form of the lines of force around two unlike poles ? 5. In what case are the lines continu- ous from pole to pole, and in what case are they not ? 6. How do the lines of force compare around a north or south pole when no other poles are near ? CURBENT ELECTRICITY. EXERCISE 1. VOLTAIC ELECTRICITY. Introductory. The word Electricity is the name given to the cause of certain phenomena, just as Magnetism is the name given to the cause of certain other phenomena, such as the attraction of iron and steel by a magnet or the attraction and repulsion of magnetic poles; When chemical, as well as some other changes are pro- duced under certain conditions, the resulting phenomena are said to be caused by electricity. When these phenom- ena are produced by chemical change, they are said to be due to current or voltaic electricity. In the following exercises some of these phenomena are observed, the con- ditions under which they can be brought about in- vestigated, and some points connected with the useful applications of electricity examined. EXPERIMENT 1. Apparatus. 5 test-tubes ; a bit of zinc ; a copper tack ; an iron nail ; a piece of carbon (electric-light carbon or piece of old battery carbon); a piece of amalgamated sheet zinc; copper and zinc strips; diluted sulphuric acid ; compass ; tumbler ; some means of sup- porting the tubes in an upright position; bar magnet. OBJECT. To observe the action of dilute sulphuric acid on a number of substances.* MANIPULATION". Take 5 test-tubes and in each place 5 cc. 10$ f sulphuric acid. Place in each tube one of * Much time can be saved by working this experiment simul- taneously with Experiment 2. f One part of strong acid to nine parts of water. 17 18 tiVRRENT BLECTRlGITY. the following substances: zinc, copper, iron, carbon, and a bit of zinc which has first been wet with acid and then rubbed with mercury.* From, time to time during 15 or 20 minutes, watch carefully what goes on and record your observations. Watch particularly for answers to the fol- lowing questions, but make in addition a complete record of all that takes place. QUESTIONS. 1. Does any change go on ? 2. If so, is it the same in all the tubes ? 3. Has there been any change in the size of the bodies ? 4. Arrange the names of the bodies in the order of the energy of the action, beginning with the body acted on the least and ending with that acted on the most.f 5. In any of the tubes is there any change in the nature of the action after it has gone on for a while ? If such a case is noted, make a careful record of all that is observed in connection with it. 6. Summarize what has been learned regarding the action of cold dilute sulphuric acid on various substances. EXPERIMENT 2. Apparatus. Strip of copper, strip of zinc (unamalgamated), with wires; a tumbler; dilute sulphuric acid ; compass. OBJECT. To observe how electric phenomena may be brought about by chemical action. MANIPULATION'. You are provided with two strips, one of copper and one of zinc, a copper wire being attached to each. Place these strips in the tumbler and pour in 10$ sulphuric acid until the plates are covered to a depth of about two inches. The acid must not be deep enough to cover the points where the wires are attached to the plates. * Zinc so treated is said to be amalgamated. f The bubbles of air which may slowly come out of some of the bodies, particularly the carbon, are not to be confounded with the bubbles of hydrogen gas given by the chemical action. The air has no smell, the hydrogen has. On thrusting a lighted match into hydrogen the gas will usually burn. VOLTAIC ELECTRICITY. 19 FIG. 10. During this operation, do not allow the strips to come in contact. To prevent this, before pouring in the acid arrange as in Fig. 10, bending the wires back so as to spring against the sides, thus holding the two plates on opposite sides of the tumbler. Note carefully what happens on each plate, then bring the wires in contact, watching each plate carefully while you do so. Lay the compass on the table and arrange ap- paratus as in Fig. 11, so that when the compass-needle is at rest, one of the wires lies directly beneath and parallel to it. While arranging this, the wires must not be in contact. Now connect the ends of the wires.* What goes on in the tumbler? What goes on in the com- FIG - "' pass ? Disconnect the wires and, when the compass-needle has come to rest, hold a bar magnet about six inches above it. Bring the magnet slowly down to the compass, watching the needle as you do so. Find in what direction the magnet must be held, and how it must be moved to produce the same effect on the compass- needle that was produced by (1) connecting the wires, (2) discon- necting them. How could a number of magnets be arranged so as to produce the same * Should any marked phenomena fail to appear on bringing the wires in contact, remove plates, clean carefully, and repeat. ^ 3- FIG. 12. 20 CURRENT ELECTRICITY. effect on the compass as was produced by the wires ? Il- lustrate by a sketch in your note-book. EXERCISE 2. CONDITIONS FOR PRODUCING CURRENT. Preliminary. When, on bringing a wire near a compass- needle, or any magnet free to deflect, a phenomenon like that in the preceding exercise is observed, the wire is said to have a current of electricity flowing through it. We do not know exactly what goes on in the wire, or why the needle acts as it does; and when we say that a wire is carrying a "current "we only mean that, if the wire were brought near a compass-needle, the needle would be affected as we have observed in the preceding exercise. The wire is the same wire whether it "carries a current" or not. When, for example, one plate is lifted from the liquid, the power of the wire to twist the needle dis- appears. This also happens if the wire is not complete from one plate to another. But while we do not change the wire, we do change the conditions under which the wire is placed. Hence when we speak of a wire carrying a current we imply a special condition of the wire. The steps necessary to develop in a wire the power indicated by the compass-needle are called the conditions needed for the pro- duction of an electric current. As will be seen later, there are other ways in which this condition of the wire may be brought about besides that of the galvanic cell ; but no matter what has been done to a wire, if it can do what the Wire in the preceding exercise could do, it is said to carry a current while in that condition, and at no other time. QUESTIONS. Define electricity; an electric current. How could you determine whether a telegraph-wire was carrying a current or not > Name any method for generating elec- CONDITIONS FOR PRODUCING CURRENT. 21 tricity besides the chemical one. Must anything be de- stroyed in order that the current may be generated ? Diagrams. Figs. 11 and 12 1fl5th represent the set of apparatus used in this exercise. On examining them, however, you will see that Fig. 11 is a picture of the ap- paratus, showing it as it actually looks, while Fig. 12 bears no resemblance to it at all. In Fig. 12 the tumbler and plates are represented by a circle with two lines inside, the compass by a circle with a long diamond inside, and the wires by lines. It is not necessary to show what the tumbler looks like, or what the compass looks like, or what sort of wires are used; the essential thing is to make clear that the wire connecting the plates is carried under the compass in a north and south line, and this is done just as well in Fig. 12 as in Fig. 11. Such a figure as Fig. 12, which only shows the way in which the parts of the appa- ratus are arranged to bring about the conditions under which the experiment is worked, is called a diagram; and as diagrams are much easier to draw, in scientific work they are often used in place of pictures. In making diagrams, each instrument has its own sign. Where a picture of an instrument is given in this book, the sign by which it is to be represented in diagrams is also given (for example, see Figs. 13 and 14). Unless otherwise instructed, always represent apparatus by dia- grams in your note-book, and the instruments by the regular signs. Use a ruler whenever you can, and be care- ful to make the diagram large enough. A space at least 3x3 inches, and often even half a page or a whole page of your note-book should be used. A space reserved for a diagram should never have notes written in it. In a dia- gram the different parts are usually indicated by letters, generally the initials of the names of those parts ; thus a compass is marked C, a wire W, etc. Where the same letters have to be used more than once, one or more accents 22 CURRENT ELECTRICITY. are added. For example, if two wires were to be marked, they would be lettered W and W (W prime), respectively, and a third wire would be marked W" (W second). Or capitals and small letters might be used. EXPERIMENT 1. Apparatus. Copper strip ; zinc of "tumbler cell" (amalga- mated); tumbler ; compass ; dilute acid ; iron plate ; carbon plate of cell; water; nail; wood; glass; etc. OBJECT. (a) To observe the effects, in the tumbler and on the compass-needle, of amalgamating the zinc, (b) To study the conditions under which this effect on the com- pass-needle can be produced. MANIPULATION. Part 1. Proceed as in the preceding exercise, noting carefully what goes on in the tumbler with amalgamated zinc, the wires first in contact, then not in contact. Eepeat the test with the' wire and compass. QUESTIONS. What effect has the amalgamation of the zinc on (1) the action in the tumbler when the wires are not in contact ? (2) the action in the tumbler when the wires are in contact? (3) the action of the wire on the compass-needle ? Part II. (a) Bring the wires in contact and, holding one wire over the compass, cause the needle to deflect. Still holding the wire over the compass, separate the ends (it is well to tap the compass gently, as the needle is liable to stick). Having again caused the needle to deflect, raise one plate from the liquid. Note what happens in the compass and in the tumbler. Replace the plate, watch- ing carefully for any changes. Try the other plate, (b) As regards the nature of the liquid: replace the acid in the tumbler by water, trying the compass test and watch- ing the tumbler carefully, (c) As regards the relation of the plates to the liquid : place in the acid two strips of CONDITIONS FOR PRODUCING CURRENT. 23 zinc, also try two strips of copper.* Repeat the compass- test. Try other metals zinc and iron, zinc and carbon, iron and carbon. In each case try the compass-test and watch carefully what goes on in the tumbler. QUESTIONS. 1. Can the compass-needle effect be pro- duced with any two plates ? 2. Do the plates all produce the same effect ? If not, name them in the order of the amount of deflection they produce. 3. Is any change notice- able in. the plates as the action goes on? If so, where? 4. Can the plates be connected by any substance ? Lay a nail over the compass and touch the ends of the wires one to each end. Try in the same way wood, glass, wire, etc. Note the behavior of the compass in each case. (5) What conditions, then, must be fulfilled in order that the mag- netic needle shall be deflected by the wire as regards (a) the wire, (b) the plates, (c) the liquid, (d) the magnetic needle ? Supplementary. An arrangement of plates, liquid, etc., fulfilling the conditions found in the this exercise, is called FIG. 13. a galvanic cell. The plates are called the elements or plates. The fluid is called the exciting fluid. The * Exchange strips with your neighbor. CURRENT ELECTRICITY. wires leading from the plates are called the conductors, or the leading wires. One form of cell is shown in Fig. 13. The plates of carbon (C) and zinc (Z) are separated by pieces of wood ( WW) and held in place by a rubber band (RR). The plates are set in a glass vessel to contain the exciting liquid, and to each plate is attached a wire, as shown in the figure. In diagrams a cell is usually indi- cated by two parallel lines of unequal length, as B in Fig. -j- FIG. 14. 14, which would represent one cell. The connecting wires are indicated by straight lines, as shown, while arrows near the lines indicate the direction of the current. When the cell is so arranged that the current is passing through the conductors, as in Fig. 14, the cell is sometimes said to be running. Although we only know that the wires possess certain properties when the cell is running that they do not possess when the cell is not running, it has been customary to imagine that electricity flows through the wire, and to speak of a current of electricity We have no means of finding out which way this current flows, but it is generally considered as flowing in the wire con- necting the plates from the metal least acted upon to that most acted upon, and through the liquid in the cell in the reverse direction. The plate from which the current is sup- posed to flow in the wires is called the positive plate, and is indicated by the -\- sign. The plate to which the current flows is called the negative or minus plate, and is indicated by the sign. The whole path of the current, plates, liquid, and conductors is called the circuit. ACTION OF CURRENTS ON MAGNETS. EXERCISE 3. ACTION OF CURRENTS ON MAGNETS. EXPERIMENT 1. Apparatus. About 100 cm. of No. 18 insulated copper wire ; com- pass ; electric current. Tumbler-cell. Supports for compass. OBJECT. To study the conditions affecting the behavior of a magnetic needle free to move, when near an electric current. MANIPULATION. 1. Place the wire over the needle in a north and south line, arranging the wire so that the cur- Fio. 15. rent flow r s from north to south. Complete the circuit and note the direction of the swing of the needle. 2. Repeat with the wire directly under the needle. 3. Repeat 1 with the current reversed, that is, flowing from south to north over the needle. 4. Repeat 2 with the current flowing from south to north. 5. Place the compass on a tumbler 26 CURRENT ELECTRICITY. or block of wood as shown in Fig. 15. Hold the wire vertically, due north from the compass, with the current flowing down, and bring it slowly up to the north pole. 6. Eepeat 5, holding the wire due south of the compass and bring it up to the south pole. 7. Invert the wire so that the current flows up, and repeat 5. 8. Repeat 6, the current flowing up. 9. Wind the wire tightly around the compass so as to form a rectangle. Hold this rectangle vertically in a north and south line ; place the compass in the centre of the rectangle. 10. Repeat 9 with a loop instead of a rectangle. 11. Observe the effect of using more than one loop, by winding the wire around the com- pass once, then 5 or 6 times. 12. Observe the effect of the size of the loops. Try a large loop and a small one, keep- ing the compass in the centre of each, 13. Observe the effect of the distance of the wire from the needle. QUESTIONS. 1. Illustrate each case by means of a dia- gram. 2. What conditions affect the direction of the swing of the needle ? 3. If a man were swimming in the current so that it enters his feet and leaves his head, he always facing the needle, to which hand, right or left, would a north-seeking pole be urged ? * A south-seeking pole ? If you cannot tell, put yourself in the place of the imaginary man by holding the wire in front of you, or make a little paper man, marking the right and left hands, and, holding it in the position described, move it around the loop, observing towards which of his hands the north pole of the needle is deflected. In marking the hands of the paper man, do not forget that if he faces you his hands would be the opposite of yours, that is, his left hand would be opposite your right. 4. What conditions affect the amount of the swing? 5. Remembering that * Notice that we are dealing here wilh poles, not with entire magnets. ACTION Off CURRENTS ON MAGNETS. 27 the needle always tends to place itself in the line of mag- netic force, from a study of the diagrams make a diagram of the field of force around a wire carrying a current. The Galvanometer. The law connecting the direction of the swing of the needle with the direction of the cur- rent is called Ampere's law. Advantage of this law is taken in constructing an instrument for observing the direction and strengths of electric currents. The in- strument is called a galvanometer, and consists of a magnetic needle placed in the centre of a coil of wire and arranged so as to move freely. When this coil is placed in a north and south line and a current is passed through it, the needle is deflected. The direction of the deflection indicates the direction of the current, while the degree of the deflection indicates the relative strength of the cur- rent. In a general way, the stronger the current, the greater the deflection. We found that with a given current the amount of deflec- tion could be changed by varying the number of turns of wire. In most galvanometers this is done by changing the connections. With a very heavy current, but few turns would be needed; with a weak current, more turns would be required to give readable changes in the position of the needle for small differences in current. Of course, in comparing various currents, the same number of turns must be used. Fig. 16 is a representation of a galvanometer. The coil of wire Wis wound upon -a wooden hoop, H, which is sup- ported in an upright position by the base-boards E and D. This coil is connected with the three binding-posts B, B', B". Starting from B, the wire passes once around the hoop and is led out to B'. It then is wound around the hoop nine times more, so that if B and B' be connected, the current passes around the hoop once ; if B' and B" , the current passes through nine turns; while if B and B" 28 CURRENT ELECTRICITY. be connected, ten turns are in circuit. A compass C placed in the centre of the hoop furnishes the magnetic needle whose indications are observed, the scale on the compass providing a means or; measuring the amount of the FIG. 16. swing. A galvanometer is represented in diagram by the small figure on the left. This sign does not represent simply this form of galvanometer, but any form. PRECAUTIONS. 1. The compass must be in the centre of the hoop. 2. The coil must be in a north and south line. 3. There must be no iron. or magnets near. 4. All contacts must be good. 5. Before reading tap the hoop gently, as the needle may stick. 6. In reading hold the eye as nearly as possible vertically over the needle. 7. The end of the needle when at rest should be directly over the zero of the scale. 8. When using the galvanometer con- nect it for ten turns, unless the instructions state other- wise. ELECTRICAL RESISTANCE. 29 To READ BY "REVEBSAL." As getting the zero of the scale just under the end of the needle requires quite nice adjustment and takes time, it is better to read the instru- ment by what is known as the "reversal method." Adjust the instrument, having the coil nearly north and south and the zero of the scale within five degrees or so of the posi- tion taken by the end of the needle when at rest. Close the circuit, read; reverse, and read again.* The average of the two readings will be the true deflection. This method saves time and is more accurate. It should be used whenever current strengths are to be compared. EXERCISE 4. CONDITIONS AFFECTING ELECTRICAL RESISTANCE. Preliminary. When a circuit is so arranged that the current can pass entirely through it, it is said to be "-closed," and a circuit so arranged is called a closed cir- cuit. When the current cannot pass at any point, the cir- cuit is said to be "open," or "broken," and such a circuit is called a broken or open circuit. Connecting two points on a circuit so as to close it (e.g. bringing the ends of the wires together) is called dosing the circuit or making the circuit; separating two parts of a closed circuit, so as to open it (separating the ends of the wires, lifting one plate from the liquid, etc.), is called breaking the circuit or breaking contact. Sep- arating two parts of a circuit and attaching the ends to a conductor (as a wire or a piece of apparatus), so as to include it in the circuit, is called introducing that bochj into the circuit. When several cells are arranged so as to give a current * If no reverser is used, this may be done by changing the con- nections at the binding-posts. 30 CURRENT ELECTRICITY. they are called a galvanic battery, or simply a battery. That part of the circuit which connects the plates out- side of the vessel is called the external circuit, and the part inside of the vessel is called the internal circuit. We have already observed that when various bodies were inserted in the external circuit of the same cell, and the wires were laid over the compass at the same dis- tance from the needle, the deflections of the needle were not the same. We have also learned that the amount of this deflection is, under similar conditions, taken as indi- cating the strength of the current. We naturally infer that all bodies do not possess to the same degree the property of allowing the current to pass. This idea is expressed by saying that the relative conductivity, or, more commonly, the resistance, of all bodies is not the same. A body that will transmit but little current is said to have a high resistance; one that will transmit considerable current is said to have a low resistance.* Resistance, then, may be taken to indicate the degree to which a body possesses the property of not transmitting the current. In the fol- lowing exercise we wish to find out 1. What sort of bodies have high, and what sort low, resistance. 2. What effect length, material, and cross-section have on the resistance of bodies. EXPERIMENT 1. Apparatus. For Part I : Cell; galvanometer ; connecting wires ; coil of copper wire ; iron nail ; pieces of zinc ; carbon ; wood ; glass rod ; dilute sulphuric acid and water ; tumbler. For Part II : In addition, mercury cups ; reverser ; wire coils. OBJECT. To study (1) the power of various bodies to transmit the current, and (2) the conditions effecting this power. * Of course, under the same conditions regarding cell, distance of wire from magnetic needle, etc, ELECTH1CAL RESISTANCE. 31 MANIPULATION'. In Fig. 17, B represents a cell and a galvanometer. One wire from the cell connects with the binding-post on the galvan- ometer. A wire leads from the galvanometer connected FIG. 17. so that 10 galvanometer-turns are in circuit. If, now, the ends of wires xx f are pressed on any substance, the circuit is completed. The ends of the wires should be scraped bright and free from insulation, and all contacts made per- fect. The screws in the binding-posts should press firmly on the wires. These precautions are important. Set up the ap- paratus and show it to the instructor before beginning the experiment. The galvanometer must be carefully read according to the instructions already given. Part /. Tabulate the results of inserting the following bodies, in turn, into the circuit: iron, copper, zinc, carbon, wood, glass, paper, water,* dilute sulphuric acid, etc., re- cording results as follows: TABLE I. Substance. Galvanometer Reading. Part II. Introduce the mercury-cup, M. C., into the circuit by attaching the ends to the binding-posts, one end to one post, as in Fig. 18. To introduce coils of wire into the circuit, dip one end well down into the mercury in. one cup, and the other end into that in the other cup. Lay the card on which the coil is mounted flat on the table, and bend the ends of the wires so that they will not spring out of the mercury while the galvanometer is read. When * To test the water, place the naked ends of the wires in a tumbler of water. Note and record anything going on in the tumbler, as well as the reading of the galvanometer. Then add to the water 10 or 12 drops of sulphuric acid, and repeat your observations. CURRENT ELECTRICITY. two single ends, a a, Fig. 19, are placed in the cups, there are 10 meters of wire in circuit. When one single end, a, and one twisted end, b, are in the cups, there are 5 meters in the circuit. The coils are labelled, and cou- M.C. FIG. 18. sist of, 1, 5 and 10 yards No. 28 copper wire ; 2, 20 yards No. 28 copper wire; 3, 5 yards No. 24 (larger cross-section) copper wire ; 4, 5 yards German-silver wire, No. 24 or No. 28, as labelled, same cross-section as one of the coils of copper wire of 5-meter length. Insert in turn 5, 10, 20 FIG 19. yards No. 28 copper wire, 5 yards No. 24 copper wire, 5 yards German-silver wire. Record results in : TABLE II. Material. Length. Cross-section. (By number.) Galv. Read. ELECTRICAL RESISTANCE. 33 QUESTIONS. Write in your note-books what has been learned as regards: 1. The equal resistance of bodies. 2. The sort of bodies that seem to have the highest resistance, and the sort that seem to have the lowest. 3. The resist- ance of water and the effect of adding acid. 4. The condi- tions affecting the resistance of a body. 5. The reason why the wires are of copper. 6. The reason why they are covered with cotton, etc. t 7. The reason why the covering must be removed where connections are made. 8. Give a definition of resistance. 9. What part of the circuit has been used in this experiment ? 10. Has anything been observed at the ends of the wires on making and breaking circuit ? If so, what? 11. What goes on, so far as you have observed, when the current is passed through water ? Or through water and acid ? 12. Arrange the names of all the bodies that you have examined in a list, commencing with those of the highest and ending with those of the lowest resist- ance. Include air in this list. EXERCISE 5. ELECTRICAL RESISTANCE. Preliminary. If we wish to insert more than one con- ductor into the external circuit, connection can be made in two ways; either end to end, or side by side, as in Fig. 20. C7rsrr'~=~ **&*- FIG. 20. The first arrangement is called connecting in series, and the second connecting in parallel, or in multiple arc. The 34 CURRENT ELECTRICITY. question is naturally suggested whether, with the same bodies, it makes any difference to the total resistance of the circuit which method is used. Write out the general method * of an experiment to answer this question, outline a special method, using the apparatus of the preceding exercise, and give the reasons for the use of each part of the apparatus. Prepare a diagram showing the relation of the parts, connections, etc. EXPERIMENT 1. Apparatus. The same as in Ex. 4 (reverser) shown in Fig. 21, the mercury -cups being used to insert the various conductors in the cir- cuit. M.C. FIG. 21. * The general method is a brief statement of the bodies experi- mented upon and of the conditions under which they must be placed in order to fulfil the object of the experiment. As different forms of the bodies may be used, and as the required conditions may be brought about by various means, the special method is a statement of just what forms of the bodies are used and just how these forms are placed under the conditions required by the experiment. The general method might be taken as the plan and the special method as the particular way in which the plan is carried out. ELECTRICAL RESISTANCE. 35 OBJECT. To see if the manner in which conductors are placed in the external circuit affects the resistance of the circuit. MANIPULATION. Part I. Place in the circuit 20 meters No. 28 copper wire. Observe the deflection. Remove one end, attach to it, by twisting, one end of the 10-meter coil of No. 28 copper wire, and place the free end of the IO- meter coil in the mercury-cup. There are now in all 30 meters No. 28 wire in the circuit. Observe the deflection. Add to the other two coils the coil of No. 24 copper wire. Insert also the coil of German-silver wire. Record results as follows: TABLE I. No. of Trial. Lengths and Substances Used. Galvanometer Reading. Right. Left. Average Part II. Place the coil of German-silver wire in the circuit and read the galvanometer. Without removing the first coil, also put in the circuit the 20 meters of copper wire. The current can now pass through both coils at the same time. Read the galvanometer. Also place in the circuit 5 meters No. 24 copper wire, in addition to the others. Record the results as above. Great care must be used in securing the contacts in the mercury- cups, and all precautions should be taken to get as accu- rate galvanometer-readings as possible. QUESTIONS. 1. What effect is produced on the resist- ance of the external circuit by introducing conductors (a) in parallel ? (b) In series ? 2. Explain this result from the knowledge obtained in the preceding exercise. 3. Can the external circuit be composed of more than one sort of material ? 36 CURRENT ELECTRICITY. EXERCISE 6. METHODS OF CONNECTING GALVANIC CELLS. Preliminary. When more than one cell is to be used, there are two ways of connecting them ; as in Fig. 22, where the positive plate of one is connected with the negative plate of the next; or, as in Fig. 23, where all the posi- tives are connected by one wire and all the negatives by the other. The former method is called connecting in series; the latter, con- necting in parallel, or multiple. Now, the external resistance may be either com- paratively high or low. For instance, the con- ductor may be a short, thick piece of copper wire, or a considerable length of fine German-silver wire. Hence it is a matter of some consequence to know which method of connection gives the most current, (a) when the external resistance is high, and (b) when it is low. EXPERIMENT I. Apparatus. Two cells; galvanometer; reverser; mercury-cups; short piece of thick copper wire; connecting wires (connecter, if available); wire-coil for high resistance. OBJECT. To determine which method of connecting cells gives the most current, (a) when the external resistance is high, and (b) when it is low. METHODS OF CONNECTING GALVANIC CELLS. 37 MANIPULATION. Insert a galvanometer (one turn) and mercury-cups into the circuit of a single cell, as in Fig. 24. Connect the two mercury-cups with a short piece of copper wire and read the galvanometer. Disconnect the wire leading from the cell to the binding-post of the mercury- cup (marked a in Fig. 24), and by means of the connecter, or by twisting the ends of the wires together, connect it with the wire leading from the opposite element of the second cell. Attach the other wire of the second cell to the empty binding-post of the mercury-cup. There are now two cells in circuit, the carbon of one connected with the zinc of the other that is, the cells are in "series," as in Fig. 25. Connect the mercury-cups with the short piece of wire and read the galvanometer. The resistance of the external cir- cuit is that of the connecting wires, the galvanometer con- nection, the mercury in the mercury-cup, and the short piece of wire connecting them; and as these are all good conductors, large and short, the total resistance of the ex- ternal circuit is very small. Take out the short piece of copper wire connecting the mercury-cups, and put in its place a coil of Ger- 38 CURRENT ELECTRICITY. man-silver wire or 20 meters of No. 28 copper wire. This makes the resistance of the external circuit quite high. Change the galvanometer connections so as to have ten turns, and read the instrument. Leaving the coil of FIG. 25. wire in the circuit, disconnect cell No. 2 (B,) and con- nect cell No. 1 (B 2 ) alone with the mercury-cups. Read the galvanometer. Connect the carbon plates of both cells with a wire lead- ing to the galvanometer, as in Fig. 26. In the same way connect both zinc plates with the same binding-post on the G.S. Wire FIG. 26. mercury-cup. The two cells are now connected in "paral- lel." Read the galvanometer. Replace the coil of wire in the mercury-cup by the short copper wire. Connect the galvanometer for one turn and read it. Arrange results as follows : METHODS OF CONNECTING GALVANIC CELLS. 39 TABLE. No. of Cells. How Connected. External Resist. Galv-read. 1 High R. L. Av. 2 Series 44 2 Parallel 1 Low 2 Series 2 Parallel < The cases in the table are not arranged as they are tried in the experiment. The table arrangement, however, makes it much easier to compare results. The table, made out in this way, should be placed in the note-book, and as the different cases are tried the galvanometer readings obtained can be placed where they belong in the last col- umn. From the study of the table, which arrangement of cells seems to give the most current when the external re- sistance is high and which when the external resistance is low ? Unit of Resistance. If resistances are to be compared accurately, a standard of resistance is needed. As we have found that resistance depends on length, cross-section, and material, we can get a standard of resistance by taking a specified length of a specified body of a specified cross-sec- tion. When the body used is mercury, cooled to the freez- ing-point of water, the length about 1 meter, and the cross-section 1 sq. millimeter, the resistance is said to be 1 ohm. Any body having a resistance equal to that of the standard mercury column is said to have a resistance of 1 ohm. Resistance-box. The instrument commonly used in measuring resistance is called a resistance-box or rheostat. It is an arrangement by which different coils of wire of known resistance may be placed in the circuit. A com- mon form, together with a sign for a diagram, is shown 40 CURRENT ELECTRICITY. in Fig. 27. It consists of a wooden box provided with three switches. A number of metallic heads are placed in semicircles about the pivots of the switches. Each head is furnished with a number which indicates the resistance FIG. 27. in the circuit when the end of the switch rests on that head. One switch (the one at the right in Fig. 27) places from to 1 ohm in the circuit, the second from 1 to 10 ohms, and the third from 10 to 100 ohms. By using all three switches, any resistance from to 111 ohms may be placed in the circuit, The sum of the readings of the three switches is taken as the measure of the resistance ; for example, in the figure the box reads 55.9 ohms. The box has two binding-posts for making connections. EXERCISE 7. RELATIVE RESISTANCE. Preliminary. In the following experiment we wish to find the lengths of iron and copper wire equivalent in re- sistance to 1 centimeter of German-silver wire. We must place a known length of German-silver wire in the cjr- RELATIVE RESISTANCE. 41 cuit, observe the deflection of the galvanometer, and then find the lengths of the wires of other materials required to produce the same deflection of the galvanometer. We will use the apparatus indicated in Fig. 28. The board A carries two uprights, BB, which support a meter-stick, M. Stretched between these upright, is a piece of uncovered German-silver wire, on which slides a hook made of the end of one connecting-wire. Above the Ger- man-silver wire the iron and copper wires are stretched between the uprights, passing back and forth several times. A binding-post, a, is connected with one end of all three FIG. 28. sets of wires. When the circuit is completed from the binding-post a, through the wire and the hook that slides on it, the length of wire in the circuit will be determined by the length of wire between a and the hook, as read on the meter-stick, and can be varied by sliding the hook along the wire, so varying the resistance. (Experiment 4, Part II.) More than one meter of the wire may be placed in circuit by attaching the hook to the wire running back to the right-hand upright. The total length of wire in the circuit in each case will be the whole length which the current passes through in going from the binding-post to the hook, CURRENT ELECTRICITY. EXPERIMENT. Apparatus. Cell; rack with wires (Fig. 28); reverser; galvanome- ter ; connecting-wires.* OBJECT. To find what length of iron and copper wires give a resistance equivalent to that of one centimeter of German-silver wire. MANIPULATION. Having set up the cell and connected the galvanometer for ten turns, introduce the German- silver wire into the circuit, by attaching one connecting wire to the binding-post a and connecting the wire leading from the hook with the other element of the cell. The distance from the hook to the binding post, as read on the meter-stick, gives the length of German-silver wire in the circuit. Observe the galvanometer-reading with 50 cm. of wire in the circuit, then remove the hook from the German- silver wire, place it on the iron wire, and find by trial the position which gives the same galvanometer-reading. Re- peat the operation with the copper wire, recording the total lengths in circuit in each case. Now, starting with 40 cm. of German-silver wire, again find corresponding lengths of iron and copper wire. Try some other lengths if time allows. Tabulate results as follows : G.S. wire. Galv.-read. Iron wire. Copper wire. Iron wire equal to 1 cm. G.-S. Copper wire equal to 1 cm. G.-S. R. L. Av. EXERCISE 8, A. MEASUREMENT OF RESISTANCE. Preliminary. The purpose of the following exercise is to determine the resistance of a body by what is called the " method of substitution." This method is based upon * Que witU book, or a.u "English" binding post, MEASUREMENT OF HR8I8TAN08, 4B the fact that bodies of equal resistance introduced into the same circuit will transmit the same amount of current. We find the resistance in ohms of a body which will transmit the same amount of current transmitted by a body of unknown resistance.* The apparatus used is as shown in Fig. 29. A galvanometer, G, a resistance-box,. 72, and mercury-cups, mm, are connected in the circuits of a FIG. 29. cell, B. The mercury-cups afford a means of easily insert- ing a body into the circuit. On replacing the body by a piece of thick copper wire the resistance of the mercury cups is practically reduced to 0, which is equivalent to taking them out of the circuit. By setting the switches of the resistance-box at 0, that also is practically taken out of the circuit, so that it is not necessary to disconnect it when the current is passed through the body. EXPERIMENT. Apparatus. Cell; resistance-box; galvanometer; connecting- wire; conductor whose resistances are to be measured; mercury-cups; reverser. OBJECT. To determine the resistance of a body in ohms by the method of substitution. * Let the pupil prepare a statement of the conditions necessary for carrying out such an experiment. 44 CURRENT ELECTRICITY. MANIPULATION. Having all three switches of the re- sistance-box on the zero-point (that is, having no resist- ance in the box), connect the mercury-cups by each, in turn, of the coils of wire whose resistance is required, and read the galvanometer.* Replace the coil by the short piece of copper wire (so that the mercury-cups offer practically no resistance), bring your eye directly over the galvanometer- needle, and, without looking at the box, turn the 10-ohm switch until the galvanometer reads as close to the former reading as you can get, that is, until the addition of an- other 10 ohms makes it too low. Adjust now the ohm switch in the same manner, and lastly the 0. 10-ohm switch. The adjustment of the switches should be done with the right hand, the eye being kept constantly on the needle. Read the resistance in the box. This is equal to the re- quired resistance of the coil of wire. Repeat with the same coil, being careful not to look at the box so that your second trial may not be biased by the results of the first. Determine in this way the resistance of several coils of wire. Record as follows : Length. Material. Galv. -reading. Resistance. No. of Wire. R. L. Av. * As all that is needed is to get the same galvanometer-reading, it is not necessary to reverse the galvanometer. In this case, however, all deflections must be on the same side. The first and second read- ings should be taken in as rapid succession as possible, in order to decrease the effect of any possible change in the current. MEASUREMENT Off RESISTANCE. 45 EXERCISE 8, B. MEASUREMENT OF RESISTANCE. Preliminary. When, in such an apparatus as Fig. 30 rep- resents, the current of the battery B comes to the point a, it divides, part going down the side abd and part down the side acd. If the resistances of the two sides are alike, the same amount of current will flow through each ; but if they are not alike, more current will follow the side having the less resistance. If we attach wires at the points b and c and connect them with the galvanometer, so long as the same amount of current passes on each side the galvanome- ter will not be affected ; but if the resistance of one side FIG. 30. be made greater than that of the other, then the current will flow through the galvanometer from the side carrying the greater current. Suppose we insert in cd a resistance- box, and in bd the body whose resistance we wish to meas- ure, x. If the resistance-box is at 0, the resistance of x will hold back the current in bd, and a portion of it will flow from b to c through the galvanometer, which will be deflected. Suppose now we increase the resistance in the box until the galvanometer reads 0, then we know that the resistance of acd equals the resistance of abd (since the wires of which the instrument are constructed have practi- 46 CURRENT ELECTRICITY. cally no resistance), and that the required resistance of x equals the known resistance in the box. Wheatstone's Bridge. On a board is placed a square of wire, abed, Fig. 31, with a binding-post at each corner. The sides Id and dc are cut, and two binding-posts inserted in each. From the binding-posts b and c wires (dotted lines) are led to the galvanometer 6r, and the battery-wires are attached to the binding-posts a and d. In the battery- I I FIG. 3-2. circuit is placed a key, K, which closes the circuit when depressed. A similar key, K' , is placed in the galvanom- eter-circuit. The substance to be tested, x 9 is attached MEASUREMENT OF &ESISTANCE. 47 to the binding-posts gh, and the resistance-box, R, is con- nected at ef. Fig. 32 is a picture of the same apparatus when ready for use. EXPERIMENT. Apparatus. Wheatstone's Bridge; cell; galvanometer; two con- tact-keys; resistance-box; bodies whose resistances are to be meas- ured; bar-magnet; connecting-wires. OBJECT. To determine the resistance of a body by the use of Wheatstone's Bridge. MANIPULATION*. Connect the binding-posts gli, Fig. 31, by the substance whose resistance is required. Close the battery-circuit. Then close the galvanometer-circuit for an instant only, and observe the direction of the " throw" of the galvanometer-needle. Add resistances, observing the throw of the galvanometer-needle after each addition, until it begins to move the other way. Then work down with the resistance-box until, on closing both circuits, no tremble of the needle is observed. The resistance in the box is then equal to the unknown resistance. PRECAUTIONS. 1. Avoid throwing the galvanometer- needle violently. This may be avoided by closing the gal- vanometer-circuit only for an instant until there are such resistances in the box that the galvanometer-needle scarcely moves. A longer contact is then safe. 2. Always close the battery-circuit before closing the galvanometer-circuit. 3. Be sure that all contacts are good. During the first part of the experiment the motion of the needle may be very much deadened by placing a bar- magnet due north of the needle, in a north and south line, with its south pole near the north pole of the needle. During the latter part of the experiment the magnet may be removed. The presence of the magnet also tends to prevent the needle from oscillating, and saves time lost in waiting for the needle to come to rest after each trial. 48 CURRENT ELECTRICITY. EXERCISE 9. ELECTRO-MOTIVE FORCE. Preliminary. We have observed that bodies differ from one another in resistance to an electric current, and have also noted the conditions upon which this resistance de- pends. Suppose, now, we place the same body in various circuits, will it always transmit the same amount of cur- rent ? That is, have all currents the same power of over- coming a given resistance? Let us see if the conditions under which the current is generated make any difference. For this purpose try plates of various materials in the cell, being careful that they are the same size and distance apart, and that the external circuit is the same. With a galvanometer connected, we can see if the currents gener- ated all have the same power of overcoming resistance. EXPERIMENT. Apparatus. Tumbler-cell; plates of iron, lead, copper, with leadiug-wires; galvanometer; reverser. OBJECT. (1) To see if all currents have the same power of overcoming resistance. (2) To study the conditions af- fecting this power. MANIPULATION. Lay one of the plates on the table, put on it two little pieces of wood, lay the other plate on them, slip a rubber band around the whole, and place in the liquid in the tumbler. Connect the galvanometer, ad- justed for ten turns, close the circuit, and resul the galva- nometer. If a reverser is available, use it; if not, reverse by changing connections. Try the cases given in the fol- lowing table, and any others that you can. The plates in each case being the same size and distance apart, and the external circuit the same, the resistance is practically alike in each trinl. From the study of the re- FORCE. 49 Positive Plate. Negative Plate. Galv.-reading. R. L. Av. Copper Carbon Carbon Zinc Iron Iron Lead Carbon M Lead Zinc Carbon Carbon Zinc Zinc Copper .< Iron Lead Copper suits obtained, what do you infer regarding (1) the power of different currents to overcome resistance, and (2) the conditions affecting this power? QUESTIONS. Why are zinc and carbon usually used in galvanic cells ? Would zinc and copper do as well ? Why not use iron ? What conditions seem to affect the results observed? Supplementary. The power possessed by a current of overcoming, or the power that pushes the current through the resistance, is said to be due to the Electro-motive Force (often written, for brevity, E. M. F.). The higher the E. M. F., the more current will pass through a given re- sistance, and the lower the E. M. F., the less current will pass through the same resistance. In a general way, the idea of electro-motive force corresponds to the "head" of water in a pipe; that is, to the pressure which pushes the water through the pipe. The higher the pressure, the more water will pass through the pipe; and the lower the pressure, the less will pass through the same pipe. In the measurement of E. M. F., the standard is very nearly that given by a gravity-cell (zinc and copper in solutions of blue and white vitriol). The amount of cur 60 CVRRBNT ELECTRICITY. rent generated by the cell under test that will pass through a resistance is measured and compared with the amount that passes when a standard cell is used. QUESTIONS. 1. Which gives the greater E. M. F., car- bon and zinc, or iron and zinc ? 2. What E. M. E. is pro- duced by two like plates ? 3. What seems to determine the E. M. F. in a galvanic cell ? EXERCISE 10. ELECTRO-MAGNETISM. EXPERIMENT 1. Apparatus. Carriage-bolt ; 100 cm. No. 18 wire ; cell ; compass ; iron-filings ; paper and pencil ; current; some means of varying resistance of the circuit and of reversing the current. OBJECT. To study the magnetic effects of an electric current and the conditions affecting the strength of an electro-magnet-. MANIPULATION. Part L Hold the carriage-bolt in front of you with the nut away from you and wind around it 15 or 20 turns of insulated wire from left to right (if a watch were facing you, the turns would be with the direc- tion of the motion of the hands). Arrange as in Fig. 33. FIG. 33. Complete the circuit. Note what happens. Test the other end at the compass. Move the compass along from one end of the bolt to the other. Note what happens to a piece of soft iron when a wire carrying a current is coiled around it. Part 1L Repeat Part I with the current reversed. ELECTRO- MA GNETISM. 51 Part IH. Rewind the wire in the opposite direction, repeat Part I, and observe the result. Part IV. Reverse the current, and again repeat. QUESTIONS. 1. What is the effect of reversing the cur- rent ? 2. What effect has the direction of the current ? 3. What happens when the circuit is broken? Does the effect produced by the direction of the current entirely disappear when the circuit is broken ? EXPERIMENT 2. OBJECT. To see if an electro- magnet* resembles an ordinary magnet. MANIPULATION. Bring the electro-magnet up to some iron-filings, and see if it attracts them. EXPERIMENT 3. OBJECT. To investigate the conditions affecting the power of an electro-magnet. MANIPULATION. Lay a sheet of paper on the table, place the electro-magnet on it, and draw a pencil-line around the magnet so as to mark its position on the paper, f Place the compass about east of one pole of the electro-magnet, and at such a distance that when the cur- rent is turned on the magnet pulls the compass-needle around 15 or 20 degrees. Mark this position also. Change the current by varying the resistance in the circuit. Has the strength of the current any effect on the strength of the magnet? Put as many more turns on the magnet as yon have already. Observe the results.]; What effect has the number of turns ? Give diagrams. * A piece of iron magnetized as in Exp. 1, by au electric current, is called an electro-magnet. f This precaution is taken in order that the distance from the magnet to the compass may be kept the same Of course, for each test, both magnet, and compass must be on the marks. | In comparing the effects of different numbers of turns, the same current should be used. CURRENT ELECTRICITY. QUESTIONS. 1. What must be done in order to obtain an electro-magnet ? 2. What determines the nature of the poles ? 3. What determines the strength of the mag- net? EXERCISE 11. INDUCED CURRENTS. Preliminary. Arrange the apparatus as in Fig. 34, f - FIG. 34. where the electro-magnet, A, is placed in the circuit, into which is also introduced the reverser, It. The ends of the coil of a second electro-magnet, B, are connected by flexible wires with the sensitive galvanometer, G. When the current passes around A it becomes a magnet } and, if B is placed upon it, B becomes an induced mag- net. Hence when the current is sent into A the result is equivalent to thrusting a magnet suddenly into the coil 7>, whose ends are connected with the galvanometer. By means of the reverser, the poles of A may be suddenly changed, and the same effect produced as if the magnet in B were suddenly withdrawn, turned end for end, and replaced in the coil. Slowly separate A and B and the effect is equivalent to slowly withdrawing the magnet from the coil B. Bring them slowly together, and the opposite effect is produced, INDUCED CURRENTS. . 53 EXPERIMENT 1. Apparatus. Two electro-magnets; a strong current; connecting- wires; galvanometer; reverser; means of making and breaking the circuit, and, if possible, some means of varying current strength; clamp to suspend one coil. OBJECT. To observe the results of suddenly thrusting a magnet into a coil of wire. MANIPULATION. Place B upon A. When the galva- nometer-needle is at rest, suddenly close the circuit of A (that is, suddenly introduce a magnet into B). Observe and record carefully the behavior of the needle. EXPERIMENT 2. OBJECT. To observe the effect of withdrawing the mag- net from the coil. MANIPULATION. While the current is passing through A and the galvanometer-needle is at rest, break the circuit of A. Observe and record as above, EXPERIMENT 3. OBJECT. To investigate the effect of the nature of the pole used. MANIPULATION. Change the reverser and turn on the current in A. The poles of A, and hence those of the induced magnet in B, will be reversed. Observe results. EXPERIMENT 4. OBJECT. To observe the effect of moving a coil of wire with an iron core in the field of a magnet. MANIPULATION. Remove the coil B from A. Close the circuit of A, and then move B up to and away from A, in various directions and with various speeds. Observe the galvanometer indications carefully in each case, with a view to stating the conditions affecting the amount of cur- rent, its direction, etc. If practicable, change the strength of the current through A to see if the strength of the 54: CURRENT ELECTRICITY. magnetic field makes any difference. Tabulate results as follows : How B was moved. Direction of Galvanometer-reading:. Amount of Galv.- reading. In the first column insert the words "towards A" "away from A" "in a horizontal circle above A" as the case may be. In the second column insert the words "right" or "left/' as the case may be. In the third column, the words " more," " less," etc. QUESTIONS. 1. Is it possible to obtain electricity by the use of magnets ? 2. What conditions have you found to be necessary ? 3. What conditions have you observed to affect the amount of the current,* and its direction? 4. Would it be possible to construct a machine on this principle which could be used to produce a current of electricity? 5. What would be the essential parts of such a machine? A mechanical contrivance for fulfilling these conditions, and thus generating electricity from motion, is called a Dynamo-electric Machine, or simply a Dynamo. EXPERIMENT 5. OBJECT. To see if, reversing the last process, motion can be obtained from a current. MANIPULATION. Set up the apparatus as in Fig. 35. Having a arranged as in Exp. 4, suspend b above it, and disconnecting the wires from the galvanometer, connect * Notice that as the resistance of the galvanometer coil B and the connecting-wires is always the same, any changes in the amount of current observed must be due to changes in the E. M. F. of the induced current ; hence the conditions that seem to determine the amount of the current are really those which determine the E, M, F, INDUCED CURRENTS. 55 them with the circuit as shown, the reverser being in circuit with the lower magnet and b being suspended a little to one side of a.* Close the circuit through b and then through a, and notice the results. Suddenly reverse FIG. 35. the current through a, and see if by reversing at the right time you can keep b swinging. A bar-magnet arranged as in Exp. 8 may be useful. QUESTIONS. 1. Is it possible to obtain motion from an electric current? 2. Would it be possible to construct a machine on this principle which could be used to produce motion from an electric current ? 3. What would be the essential parts of such a machine ? A mechanical device for fulfilling these conditions and thus obtaining motion from electricity is called an Electric Motor. * Two cells may be used, or the two coils may be placed in paral- lel on one circuit. MENSUEATION. NOTES ON MEASUREMENT. Units of Measure. If we wish to know just how many times one body is larger than another, that is, if we wish to make an exact comparison between the two bodies, we must ascertain the value of each one in terms of some fixed standard of measurement. Thus, to compare exactly the lengths of two boards, as a preliminary we refer both lengths to a fixed standard of length, and find out how many times this standard is contained in each of the lengths. Or, again, suppose we wish to compare the lengths of the two lines AB and CD, Fig. 36. Let us FIG. 36. call the short line cd the standard. We find that AB is equal to 10 times cd and CD 7 cd. Then we know that the lengths of AB and CD are as 10 to 7. In case cd is not contained an integral number of times in AB and CD, it must be divided into known fractional parts, and the lengths expressed as so many cd's plus so many fractions of cd. In the same way, if we wish to compare volumes, a standard volume must be employed. Thus we can find 56 NOTE8 ON MEASUREMENT. how many times the little cube, aficdef, Fig. 37, is con- tained in the two larger cubes. If it is contained 36 times in one and 8 times in another, we say the volumes of the larger cubes are as 8 to 36. As a standard in comparing FIG. 37. values we refer to dollars; in lengths, we refer to feet, meters, or miles; in volumes, we refer to quarts, gallons, or cubic inches, etc. Such a standard is called a Unit. English and French Systems. Of course any length or volume could be used as a unit, but in practice those adopted by the government or by custom are employed. Measurements of length, breadth, or thickness are called Linear Measurements. The common standard of length is the yard, which was originally adopted by the English Government as the length of a certain metal rod in their possession, and has been accepted by our own Government. The smaller units are the foot (one third of a yard), and the inch (one thirty-sixth of a yard, or one twelfth of a foot). These are called the English units, and in using them we are said to use English Measure. The inch is commonly divided into halves, fourths, eighths, sixteenths, etc. In scientific work, however, fractions of an inch are expressed as decimals. We also use the French or Metric System. Its standard is the length of a certain rod, called a Meter, 58 MENSURATION. which is in the possession of the French Government. This is divided into 100 equal parts, called centimeters, and into 1000 parts, called millimeters. Thus a centi- meter equals 10 millimeters. These prefixes, cent and mill, and their meanings, are familiar in our money. Dollar. Meter. 1. Cent. ^ Centimeter. Mill. Millimeter. This system has the advantage of being divided decimally, so that a change from one unit to another can be effected by moving the decimal-point. As a unit of Surface, we use a surface equal to that of a square measuring a unit of length on each side. Thus we have a square yard, square meter, etc. Such measure is called Surface or Square Measure. The surface expressed in square measure is the Area. For comparing volumes, we use a volume equal to that of a cube, measuring a unit of length on each edge. Thus we have a cubic foot, cubic meter, etc. The unit used in our experimental work is generally the cubic centimeter, and sometimes 1000 cu. cm. or a liter. We have also quarts, gallons, etc., these quantities being the volumes of certain vessels belonging to the Government. Change from one System to the Other. If we know the value of one unit in terms of another, we can change from one system to another. The meter is 39.37Ciwches long. Suppose we wish to express 26 meters in yards. If one meter = 39.3*&i0., 26 meters = 26 X 39.37, or 1023.62 in., 1023.62 and as one yard = 36 in., = number of yards oo 4l 28.85. Again, let us -change 15 yards to meters. 15 yds. = 15 X 36 in. = 540 in. If one meter = 39.37 in., there will be as many meters in 540 in. as 39.37 is con- tained in 540, or 13.7 meters. Another method is as fol- DETERMINATION Of LENGTH. 59 lows: One yard = 36 in., one meter = 39.37; then a yard 36 39.37 ^7-^ of a meter, and a meter - of a yard. If we change these fractions to decimals, we get 1 yard nr Oft OfV = .-Trimeters, = 0.9144meter; 1 meter = -^-- = 1.0936 39. o7 oo yds. Then if 1 meter = 1.0936 yards, 26 meters will equal 26 X 1.0936 yds., or 28.85. Similarly, if 1 yd. = 0.9144 meter, 15 yds. = 15 X 0.9144 = 13.7 meters. Abbreviations. Meter, m. ; centimeter, cm. ; millimeter, mm. ; liter, 1. ; cubic centimeter, cu. cm. It must be remembered that in surface measurement the units go by the square of 10, and in cubic measure by the cube of 10. Thus there are 100' or 10,000 sq. cm. in 1 sq. m., and 100 3 or 1,000,000 cu. cm. in a cu. m. DETERMINATION OF LENGTH. Scales. The English Scale gives results in inches, and is shown as commonly arranged in Fig. 38. The long numbered lines mark inches; the shorter lines, half- inches ; the still shorter, quarter- inches ; and the shortest, eighths. FIG. 38. The results are here expressed in inches and decimals of an inch, not in vulgar fractions; as 0.125, instead of , or 2.375 in. for 2| in. Yard-sticks are used in laboratories.* The usual form of the Metric Scale is shown in Fig. 39. The long lines, as aa, mark decimeters; the shorter num- bered lines, as bb, centimeters; the still shorter, cc, 0.5 cm., or 5 millimeters; the shortest lines, millimeters. Readings * In some forms of meter-sticks there is an inch-scale on one side. Do not use these for yard-sticks. { 60 MENSURATION. are usually expressed in centimeters arid decimals of a cen- timeter. For example, the scale to the line AB reads, in Fig. 39 (from right to left), 59 cm. plus 3 mm. ; this would be recorded 59.30 cm. Meters are used for distances of over 100 cm. When the figures on scales are right side up, the scale reads from right to left. This must be remembered or mistakes will happen, as it is natural to try to read from left to right. Tenths of millimeters should be esti- mated by the eye. Reading Scales. The scales are car- ried out to the edge of the rod (Figs. 40 and 41), and when possible this os edge should be placed against the dis- cs tance to be measured, as in Fig. 40, ta where it is desired to measure the dis- tance between the lines aa. Where the scale cannot be applied directly to the object, be sure that the line of sight is always perpendicular to the scale. A metric scale should be read to T V mm., the fraction of a millimeter di- vision being estimated by the eye. In general, an attempt should be made to read a scale to a fraction of the smallest division. When determining shorter distances than the length of the measuring rod, where the body is loose and can be brought directly against the scale, it is not best to start at one end of the rod, but rather to bring the body to be measured near the middle of the rod, place one point on a numbered line (in a metric scale one of the decimeter lines), and ^-z DETERMINATION OF LENGTH. 61 read the position of each point on the scale. Suppose, for example, it is desired to measure the length of the box A BCD in Fig. 41. Lay the scale down on top as in the the diagram, and read the positions of A and B. Say A = 26.14 cm., B 42.81 cm., then B A = 42.81 26.14, or 16.67 cm. FIG. 40. Suppose, again, the diameter of a sphere is needed. Obtain two rectangular blocks, aa in Fig. 42, and place the sphere between them, the whole resting on a level surface. Bring the blocks up against the sphere with their faces parallel. Then the distance between the blocks is the diameter of the sphere. Measure from edge to edge di- FIG. 41. rectly over the centre of the sphere. The ball should be turned and the work repeated a few times. Both blocks should be set against a smooth vertical surface. In all these cases the same precaution is necessary, to have the line of sight at right angles to the surface on which the scale is marked. 62 MENSURATION. When the scale cannot be brought up to the body, special methods are resorted to. One is called The Compass Method. A pair of compasses or dividers are adjusted until the distance between their points is just that to be measured. The compasses are then applied to the scale, with one point on a num- bered line, and the position of the other point is read. Sometimes a pointer is to be read against a scale, as in getting the Coefficient of Expansion. Always have the pointer as near the scale as possible, but not touching it, and arranged so that in moving it along the scale it is the same distance from it. Always read from the same side of the pointer. Best of all, end the pointer with a fine needle, and have the point of the needle read on the scale. A magnifying-glass is often of assistance. FIG. 42. EXERCISE 1. PRACTICE IN THE USE OF LINEAR SCALES. EXPERIMENT. Apparatus. A sheet of paper on which two crosses have been ruled with a sharp pencil, 30 or 40 cm. apart; a meter-stick with English scale on one side (or a meter-stick and a yard-stick). OBJECT. To determine: (a) The distance between the centres of the two crosses in inches, (b) The same distance in centimeters, (c) From these data,* the number of inches in a meter. MANIPULATION. Lay the sheet of paper smoothly upon the table, place the metric scale upon it, bring the centres of both crosses to the edge of the scale, and record their *This word means the numerical results of the experiment, which are afterwards used in the calculation. PRACTICE IN THE TTSE OF LINEAR SCALES. 63 readings. Read the scale to 0.1 mm., observing all the pre- cautions given in the " Notes on Measurement." Try five times, using different parts of the scale each time. Record results as in the following example, which gives the actual data of one set of determinations with this apparatus : TABLE I. METRIC MEASURE. No. of Trial. Reading L. H. Point. Reading R. H. Point. Length in Cm. 1 72.81 cm. 50.00 cm. 22.81 2 82.80 " 60.00 " 22.80 3 51.79 " 29.00 " 22.79 4 61.30 " 38.50 " 22.80 5 30.79 " 8.00 " 22.79 Average length in cm., 22.79 cm. With the same precations, measure the distance between the centres of the crosses in the English system, reading to one-sixteenth (0.0625) inch, mentally changing the fractions of an inch to decimals. Arrange the results as follows : TABLE II. ENGLISH MEASURE. No. of Trials. Reading L. H. Point. Reading R. H. Point. Length in Inches. 1 1 inch. 9.937 inches. 8.937 2 5 inches. 13.975 " 8.975 3 7 " 15.959 " 8.959 4 10 " 18.968 " 8.968 5 13 " 21.975 " 8.975 Average length in inches, 8.963 inches. CALCULATION. Having now the values of the same dis- tance in centimeters and in inches, the number of centi- meters to the inch can be found by the following calcula- tion: Number of cms. : 100 cms. : : number of inches : x. x = number of inches in 100 cms. (1 meter). 64 MENSURATION. Taking the data given above : 22.79 cms. : 100 cms. :: 8.963 inches : x _100 X 8.963 ~ 39 ' 31 which would be the value given by these data for the num- ber of inches in the meter.* EXERCISE 2. THE RELATION OF CIRCUMFERENCE TO DIAMETER. EXPERIMENT. Apparatus. Meter-stick (English and French scales), card-board circles, 10 cm., 20 cm., and 30 cm. in diameter; pencil; strip of paper or card-board about 1 m. long. OBJECT. To obtain answers to the following questions : (1) Is there any definite relation between the diameter of a circle and its circumference ? (2) Do these results hold true for more than one method of measurement ? (3) Is this relation the same for circles of different diameters? (4) Given the diameter of a circle, can the circumference be found ? If so, how ? (5) Given the circumference of a circle, can the diameter be found ? If so, how ? f MANIPULATION". Method A. Make a pencil-mark on the edge of the circular disk of paper (Fig. 43). Roll the disk along a straight line ruled on a piece of paper tacked to the table, starting with the Fia 4a pencil-mark just on the line, and rolling until the mark just touches the line again. * These data give a value a little below the true one, viz., 39.37. f As iu all experimental work, first lay out a general method. In this case the general method is, to answer question 1, measure the RELATION Off CIRCUMFERENCE TO DIAMETER. 65 Carefully measure the distance on the line between the two points touched by the pencil-mark. This gives you the circumference. Method B. Lay the measuring-rod on the table and roll the disk along it, as in Fig. 44. This gives the required n FIG. 44. length directly on the rod. To measure the diameter, lay the disk flat on the table and measure the distance across it at its widest part. Make each measurement both in centimetres and inches; repeat three times, and record the results each time. The three numbers obtained for the circumference will not be just the same, owing to errors in manipulation, reading, etc. Add them, and divide the sum by the number of measurements. This gives the average measurement of the circumference.* Do the same for the diameter measurements. Then divide the average circumference by the average diameter. This gives a num- ber which, except for errors, is that by which the diameter must be multiplied to obtain the circumference. It should be a little over three, and should be carried out to four decimal places. Do the same for the measurements in inches, and compare the numbers obtained in the two circumference and diameter of a circle and find if any relation exists between them ; to answer questions 4 and 5, use the knowl- edge obtained in answering question 1 ; to answer question 2, com- pare results obtained by using different methods of measurement ; to answer question 3, use circles of different sizes. * Of course this is to be done separately for the measurements in inches and in centimeters. 66 MENSURATION. cases. Arrange in the note-book a table of results as follows : CIRCLE I. Measured in centimeters. Method * A. ' Circum. Diana. Av. Circum. Av. Diana. Av. Circum. Av. Diam. CIRCLE I. Measured in inches. Method " B.' Circum. Diam. Av. Circum. Av. Diam. Av. Circum. Av. Diam. Kepeat in exactly the same way with Circle II. Answer in order the questions given above, and also state which method in your opinion yields the best results, and why ? CALCULATION. There have now been obtained at least four values for the number which stands for the numerical relation between diameter and circumference. Average them, and the result should be nearly correct. Using this number, solve the following: PROBLEMS. 1. A circle has a diameter of 6 cm.; find the circumference. 2. If the circumference is 25 cm., find the diameter. 3. If the diameter is 6 inches, find the circumference. 4. If the circumference is 25 inches, find the diameter. The number is represented in geometry by the sign it (pronounced " pi "). Then, with this sign, using D as the symbol for the diameter and C for the circumfer- ence, express as an algebraic equation the rule for solving such problems as the above. DETERMINATION OF VOLUMES. 67 -50 DETERMINATION OF VOLUMES. The Graduate Cylinder. There are two kinds of meas- uring vessels in use for fluids those measuring only a fixed quantity and those meas- uring varying quantities. Of the latter kind, the two commonly used in laboratory work are grad- uated cylinders and bu- rettes. The graduated cylinder, often called simply a graduate, is a glass cylinder furnished with a foot so as to stand upright, and with a scale 20- for reading volumes, usu- ally in cubic centimeters. The scale is engraved on the glass, and arranged as in Fig. 45. There is a long numbered line for every 10 cu. cm., as a a. Between these are shorter lines, marking cubic centi- meters, as c c; and between these, in turn, still shorter ones, marking half cu. cm. Such a scale is said to read to 0.5 c.c. There are usu- ally two scales, one having the at the top and the FIG. 45. other at the bottom, the former used in measuring the volumes of liquids poured out of the cylinder, the latter in measuring the volumes of liquids poured in. -10 68 MENSURATION. On looking horizontally at a graduate containing a liquid, the surface of the liquid appears as a dark band, FIG. 46. FIG. 47. usually curving down in the centre, as in Fig. 46. This curve is called the meniscus, and the line correspond- ing to the loivest point of the meniscus is taken as the level of the liquid. The cylinder must be placed on a firm horizontal surface, and the eye brought to the level of the meniscus and directly opposite the scale. In Fig. 47 a represents the correct method of reading, b and c the incorrect, b would give a reading greater and c less than the true one. Errors caused by failure to read a scale with the line of sight in the proper position are said to be due to Parallax. The following method will avoid such errors: Take a piece of stiff paper about 1J X 4 inches, being sure that the upper edge is clean and straight. Wrap it around the cylinder, and allow a portion to project, as shown in Fig. 48. Grasp the projecting portion with the finger and thumb, taking care that the upper and lower DETERMINATION OF VOLUMES. 69 edges are even with each other. Draw the paper tightly around the cylinder, and move it until, on sighting across the top edge from one side to the other, the meniscus just FIG. 48. FIG. 49. touches it; Fig. 49. In this position the "sight " is horizontal. If the upper edge of the paper is just on a line of the scale, this gives the reading ; but if not, the fraction must be estimated by the eye and expressed as a decimal. Sup- pose it comes, as in Fig. 50, between the 17 and 18 line. If half-way between, read 17.5 ; if one third the way, 17.33 ; if two thirds, 17.66 ; if three fourths, 17.75; etc. On the graduates commonly used remember that the space between two lines is half a cubic centimeter. Hence, if half-way, read 0.25 ; if one fourth above, 0.12 cu. cm.; etc. As a 70 MENSURATION. rule, any scale can be read to one tenth of its smallest division. When there is occasion to read mercury in a FIG. 50. tube or graduate, it will be found that the meniscus is re- versed (Fig. 51), curving up in the centre instead of down. In this case always read the level of the top of the menis- cus, which can be done by the method just described. When measuring out from a cylinder, it is generally best to fill it first to the mark; though of course the level of the liquid can be read anywhere on the scale, and then read again after pouring off; the difference in the readings giving the volume poured off. In pouring from a cylinder, spilling can be avoided by holding one end of a glass rod against the lip of the jar, and the other end DETERMINATION OF VOLUMES. 71 against the inside of the receiving vessel, as in Fig. 52. The liquid will follow the rod. On righting the cylinder FIG. 51. FIG. 52. always wait a moment before reading the volume, so that the water which has collected on the sides may run back again. The Burette. This is a long narrow tube having a scale on one side. (See Fig. 53.) A rubber tube is drawn over the lower end, which is narrowed, and the tube is provided with a spring clamp, a, which pinches the sides together. On pressing the ends of the clarnp the rubber tube is allowed to expand and the liquid runs out at C at a rate proportioned to the pressure on the clamp. A burette is filled from the top and usually supported in a vertical posi- tion by a clamp. Burettes are usually graduated as in Fig. 54, which shows a portion of the scale. The long lines mark cu. cm. Each space between the cu. cm. lines is divided into five parts. Thus the scale reads to one fifth (0.2) cu. cm. The lines are numbered at every two cubic centimeters. In estimating fractions, one half a space = 0.1 cu. cm., one third = 0.06, two thirds = 0.12 cu. cm., etc. The scale may be read with a piece of paper like a graduated cylinder. 72 MENSURATION. Many burettes are provided with a float, consisting of a bulb of glass shaped as in Fig. 55, with a little mercury in the lower end so that it will float upright. A line is ruled around it (a in Fig. 55). When the float is placed in the burette it floats in the liquid, rising and falling with it, and the line is observed on the scale through the glass. The position of the line is read as the level of the liquid. As the float is of nearly the same diameter as the inside of the burette (thus bringing the line very near the scale), with ordinary care there is little danger of error due to parallax. It is well to tap the burette gently before read- ing, as the float is apt to stick a little to its sides. When filling the burette, pour the liquid in until the line mark- ing its level is above the mark, which is near the top of the scale, and carefully draw out the excess until the read- ing is 0, allowing the waste liquid to run into a vessel pro- vided for the purpose. To make sure that no air remains in the rubber tube, fill the burette part full, place the upper end in the mouth, and, holding the clamp open, blow the liquid nearly out. This repeated several times will generally drive out the air. Instead of a clamp, burettes are sometimes provided with the arrangement shown in Fig. 56. A piece of glass rod about a fourth of an inch long, whose diameter is such that it will fit tightly in the rubber tube, is cut off, and the ends are rounded by heating. The little plug thus formed is thrust about half-way up the tube. By pinching with the forefinger and thumb on one side of the tube at the point where the plug is situated, a channel is formed through which the liquid can pass. The rate at which the liquid flows depends upon the amount of the pressure. Graduated Flask. This is a vessel having a mark en- graved upon its neck. When filled so that the lower end of the meniscus just touches the mark, the flask holds a fixed quantity of liquid. Those commonly used hold 1 DETERMINATION OF VOLUMES. 73 c c FIG, 53, FIG. 54. A 74 MENSURATION. liter (1000 cu. cm.), one-half liter (500 cu. cm.), and one-fourth liter (250 cu. cm.), their capacity being marked upon them. For accurate measurements, fill the flask nearly to the mark, and placing the eye so that the mark appears as a straight line, drop in the liquid with a piece of glass tube * until the correct level is reached. If you fill above the mark, use the tube to withdraw some of the liquid. The flask should rest on a firm horizontal surface. It is well to mark the position of the line by a piece of paper, as described in the directions for using graduates. EXERCISE 3. PRACTICE IN DETERMINING VOLUMES. EXPERIMENT. Apparatus. Method A: Graduated cylinder; body whose volume is to be measured; water. Method B: Piece of fine wire; cylinder; rubber band; paper for markers; body; water. Method C: Burette or equivalent; ungraduated jar or equivalent; rubber band; paper for markers ; body; water. OBJECT, To determine the volume of an irregular body by displacement. MANIPULATION. Method A. Fill the graduated cylin- der part full of water, read the volume (as a in Fig. 57), observing all the precautions given in the preliminary notes on determination of volume, and record the reading. Drop the body whose volume is to be determined (as e) into the cylinder, and again read the volume (as C). The dif- ference in the readings on the scale (a to C) is the volume of the body. Method B. Attach a fine thread or wire to the body whose volume is to be determined, and drop the body into the glass cylinder. Partially fill the cylinder with water. * As in using the sliejl^c in tke exercise oij the lines of magnetic forge, PRACTtC!fi IN DETERMINING VOLUMES. FIG. 57. Mark the level of the water by means of a piece of paper about 4 cm. wide and long enough to be wrapped several times around the cylinder. Fasten this marker in position by a rubber band. Be sure that the upper edge of the paper is at the same level all around the cylinder, and that, when looked at horizontally, the line of the paper just touches the lowest point of the meniscus. By means of the thread remove the object, allowing as much of the water as possible to drain back into the cylinder. Run in water with a burette until the level in the cylin- der is the same as before. The volume of water run in, as measured on the burette, is the volume of the body. Method C. From a burette, run into a dry, empty cylinder any known volume of water, say 50 cu. cm. and mark its meniscus by a strip of paper as in B. Empty the cylinder, wipe it dry and put in the object whose volume is to be determined. Run in water from the burette until the level is the same as it was before; note the reading of the burette. The difference between the two volumes of water drawn from the burette is the volume of the object. For an object that floats, a sinker must be used. First get the volume of the sinker alone, attach the object to it, and get the volume of both ; then by subtracting the volume of the sinker from the volume of the two, the volume of the body alone can be obtained. Determine by each of these methods the volume of the same body. Compare the results, and state which is the best process in your opinion, and why. As many deter- 76 MENSURATION minations should be made as time allows, and the results averaged. Arrange as follows : METHOD A. 1st Trial. 2d Trial. Vol. water plus body = cu. cm. cu. cm. " alone = " " " " " of body " " " " Average vol. by A = cu. cm. METHOD B. 1st Trial. 2d Trial. Burette-reading after running in, cu. cm. cu. cm. before " " " " " Difference in burette-reading, or volume, " " " " Average vol. by B = cu. cm. METHOD C. 1st Trial : Body out. 2d Trial. Burette reading after running in, cu. cm. cu. cm. " " before " " " " " Volume run in, " " " " Body in. Burette-reading after running in, cu. cm. cu. cm. before " " " " " " Vol. run in. Vol. run into empty cyl., cu. cm. cu. cm. " " " cyl. +body, " " * " " of body, Av. vol. of body = cu. cm. EXERCISE 4. CROSS-SECTION AND INTERNAL DIAMETER OF A TUBE. EXPERIMENT. Apparatus. Glass tube; burette or equivalent; markers; rubber band; cork; water; meter-stick. OBJECT. To find the cross-section and internal diameter of a tube by determining its length and volume. CROSS-SECTION AND DIAMETER OF A TtTBE. T? MANIPULATION. Method A. Cork one end of the tube, and pour in water enough to cover the cork to a depth of about 1 cm. Carefully mark the level of the water by means of a piece of paper and rubber band, as in the preceding experiment. Run in a known volume of water, say 40 or 50 cu. cm. Place on your tube a second measuring-paper, and move the paper until it just marks the level of the liquid when the tube is held vertically. The distance between the two water-levels, as indicated by the markers, is the height to which the known volume has filled the tube. Pour out the water and place the tube close against the meter-rod, taking care not to disturb the mark- ers. Record the distance corresponding to ab in Fig. 58. Then Volume Cross-section = Height* Repeat several times with varying volumes. Fro. 58. This will re- duce the errors due to the uneven bore of the tube. Ar- range the results as follows : No. Trial. Vol. run in. Height in Tube. Cross-section. Average cross-section = Method B. Place the two paper markers so that they are a certain distance apart * from upper edge to upper edge, as measured on the scale. Set the tube upright and run in water until the level of the liquid is just at the lower mark. Read the burette. Run in more water to * The distance between the markers should be an integral number on the scale. 78 MENSURATION. the level of the upper mark, and read the burette again. The difference of the readings is the volume run in be- tween the markers. Repeat several times with the markers at various heights. Arrange results on the plan indicated in the preceding exercise. In Method A, the volume being measured to an integral number, the chief liability to error is in the determination of the height. In Method B, the height being measured to an integral number, the chief liability to error is in the determination of the volume. Therefore the values obtained by averaging the results of the two methods should be very nearly correct. To find the diameter, take the average value for the cross- Z> 2 section and substitute it for A in the formula, A n . 4 Determine the cross-section of a glass tube by both meth- ods, and, if so instructed, compute its diameter, calculating the internal diameter by this formula; carefully measure it according to notes on Measurement, and compare the cal- culated and the measured results. For comparison, take the average of the diameters of the two ends of the tube. All measurements of length should be made to 0.1 mm., and burette-readings to 0.1 cu. cm. All values of cross- sections to be expressed in sq. cm., and carried out to fourth decimal place. Express the values of diameters in mm. to first decimal place. DETERMINATION OF WEIGHT. Introductory. For exact comparisons of weights, units are required, as in comparisons of lengths or volumes. The ordinary English units are the pound (lb.), and the ounce (oz.), one sixteenth of a pound. The pound is a weight equal to that of a piece of metal in the posses- sion of the government. The metric unit of weight is the gram (g. or grm.), and is the weight of a cubic centi- DETERMINATION Off WElGBT. 79 meter of water at a specified temperature. A larger unit, the kilogram (k.), is the weight of 1000 grams. The gram is divided into decigrams (d. or dg.), .1 gram ; centi- grams (eg.), .01 gram ; milligrams (mg.), .001 gram. Large weights are expressed in kilograms and decimals of a kilo- gram ; small weights in grams and decimals of a gram. In a general way, the kilogram, is used in place of the pound in English measure, and the gram in place of the ounce. The Balance. This instrument is represented in Fig. 59. S is the support, BB the beam, and PP the pans. Before use the beam should be level, and the bottoms of the pans about half an inch from some surface underneath. The body to be weighed should be placed in the left-hand pan, and FIG. 59. weights in the right-hand pan, one by one, until the beam again hangs level. Then the sum of the weights used is the weight of the body. The weights used in laboratories are generally metric. The larger ones down to one gram are made of brass (Fig. 60), and their values are stamped on the top. Weights of less than one gram are made of platinum or aluminium. These have values stamped on them in decimals of a gram.* For example, a weight marked 0.1 would be 0.1 (one tenth) of a gram, or a deci- * Sometimes the smaller weights are made of wire. The number of parts represented is indicated by bending the wire into a polygon of a corresponding number of sides. BO MENSURATION. gram; 0.02 means two centigrams, etc. The larger weights are kept in holes bored in a bloc'k of wood; the smaller are either in one hole provided with a cover, or in shallow holes covered by a glass plate. In case the smaller weights FIG. are in one hole, they should be taken out and placed upon a piece of paper, marked as follows : .5 .2 .2 .1 .05 .02 .02 .01 Each weight should be laid so as to cover the mark cor- responding to it, and, except when in the scale-pan, should be kept there until the operation is completed. A glance at the uncovered numbers on the card then tells which weights are in the scale pan. Unless very heavy (say above 500 grams), weights should be handled with the pincers provided for this purpose, and not with the fingers. All weights should be placed at once in the proper receptacle when removed from the scale-pan, and never allowed to lie on the table. The large brass weights are handled by the knob on top. Never allow the scales or weights to come in contact with anything that might corrode or injure them. Weights are of the following numbers and denominations: one five, two twos, and a one. Thus, the weights under one gram would be one-half gram (0.5 grm.), two one-fifth gram (0.2 grm.), and one one-tenth gram (0.1 grm.). Or there are one 100-grm., one 50-grm., two 20-grm., and one 10-grm., etc. Time is saved by weighing in a methodical manner, and not taking weights at random. Usually the weight of a bodv can be estimated in round numbers, and the first ^TERMINATION Of WEIGHT. 81 Weight tried should be about that estimated. For example, the body is estimated to weigh about 20 grm. Placing it in the left-hand pan, put a 20-grm. weight in the other. The weight-pan remains in the air, hence 20 grm. is not enough. Add 10 grm. more: this is too much. Replace by 5 grm. : also too much. Replace by 2 grm. : now it is too little. Add 2 grm.: too little still. The weight must be between 24 and 25 grm. Add 0.5 grm. : too little. Add 0.2 grm. more: too much. Replace by 0.1 grm. : still too little. Add 0.05 grm., and the correct weight is found. On add- ing up the weights in the scale-pan they amount to 24.00 g 6 dc. or .60 g. 5 eg. or .05 g. 24.65 g. Weights are usually expressed in.grams and decimals of a gram. We would not say that a weight was 24 grams, 6 decigrams, and 5 centigrams, but 24.65 grams; just as we do not say that a thing cost 2 dollars, 4 dimes, and 7 cents, but $2.47. In getting the weight of a liquid, one method is to first weigh the empty vessel, and then the liquid and vessel to- gether. For example, suppose 10 grams of a liquid are wanted. Weigh a vessel and then add 10 grm. to the weights on the pan and pour the liquid into the vessel until the beam balances. Arrange notes as follows, always plac- ing the weight of the dish alone on the lower line, since it is to be subtracted from the larger weight of the dish and liquid : Dish and liquid = 26.249 Dish alone, = 16.249 Liquid = 10.000 Another method, called counterpoising, is to place the vessel in one pan, and balance it by some substance, such as sand or shot, in the other. The weight of the liquid alone need not then be determined by actual weighing. It is generally easier to counterpoise a flask or dish than to weigh it accurately. The Spring-balance. In this, the weight attached pulls out the spring and registers itself by a pointer on a scale engraved on the brass. The scale is generally graduated up to twenty-five pounds and reads down to one-half pound, A every four pounds being numbered. In Fig. 61 the long lines are pound marks, and the shorter lines between them, half-pound marks. In read- ing, be sure that the eye is directly over the pointer. Always read from the same side of the pointer, which is usually wide enough to cover half a pound on the scale. The scale is quite fine, and a magiiifying-glass is often useful. As the pointer is liable to stick, it is well to shake the balance a little before reading. Be careful to hold it so that the rod to which the hook is attached can slide freely. This is especially needful when using the balance to measure force. FIG. 61. rp} ie b a ] ance niust be held just in the line of the pull; otherwise it will bind and give incorrect readings. There are some balances which read to 48 pounds. In these the scale only reads to pounds. After being used to reading on a 24-pound balance, one is almost certain to make mistakes in reading on one of the 48-pound bal- ances. Balances reading up to 8 oz. are also used. The scale reads to oz. In using one of these balances, fractions of less than one scale-division should be estimated by the eye. With practice one should be able to read to 3*5- of an ounce (.037 oz.). Never leave a balance stretched out any longer than necessary, as it injures the spring. If PRACTICE IN WEIGHING. 83 the pointer does not stand at when there is no pull on the spring, read the position of the index before beginning to weigh, and subtract (if over 0) from subsequent read- ings. Thus, if the pointer read one-half pound, all read- ings are half a pound too high, and half a pound must be subtracted.* A spring-balance is generally used to measure forces; it is then often called a Dynamometer, i.e., "force- measurer." When a spring-balance is used for weighing, it should never be held in the hand, but suspended from some solid object. EXERCISE 5. PRACTICE IN WEIGHING. EXPERIMENT. Apparatus, Scales; weights; avoirdupois weights or 8-oz. bal- ances (if the latter, one to three students is enough). Several bodies weighing one to two ounces. OBJECT. To determine the value of the ounce in grams. MANIPULATION. Weigh some body to 0.01 grm. on the scales.f Determine the weight of the same body in ounces by means of a spring-balance or by the scales and English weights. From the following proportion calculate the number of grams to the ounce: wt. in oz. : wt. 1 oz. ::wt. in grins. : x. x = no. of grms. to the oz. Repeat with as many different substances as time allows, average the values so obtained, and tabulate the results as follows : Body. Wt. in oz. Wt. in grm. Grm. per oz. * This is often called the zero error. f Select some body weighing 100 to 200 grin. In a general way, the heavier the body, the more accurate the results. 84 MENSURATION. EXERCISE 6. EXPERIMENT. Apparatus. Part I. Meter-stick; blocks of wood; lead-pencils; books; etc. Part I. Tumbler; measuring-cylinder; water. Part III. Scales and weights; bodies weighing from 10 g. to 50 g. OBJECT. To practise estimating values in the Metric system. MANIPULATION. Length. Estimate carefully, by the eye alone, the dimensions of one of the blocks, the meter-stick being out of sight. Record the estimate. Carefully meas- ure the same distance and record. Try this a number of times, varying the distances measured each time until esti- mates on several different lengths in succession come quite near to measured values. Record as follows: Estimated. Found. Difference. The figures in the third column are got by finding the difference between the measured and the estimated dis- tances. If the estimate is less than the true distance, the difference has the minus sign; if greater, the plus sign. It is best to select lengths ending in sharp corners, distances between points marked by a pencil, etc. Volume. Put some water into the tumbler, estimate the volume in cu. cm. Measure the volume, repeat with vari- ous volumes, and record as above. If possible, change the vessel used to hold the water. Weight. Estimate the weight of a few bodies in grams. Weigh the bodies, NOTES ON ERRORS. 85 Measure as accurately as possible, but do not try to esti- mate too closely. It is enough to get within 0.5 cm. of correctness in length, one centimeter in volume, and one gram in weight. NOTES ON ERRORS. The results of measurements are never absolutely correct. This is because of imperfections in the apparatus and mis- takes of the experimenter. In physical experiments, any- thing due to these causes, which tends to make results incorrect, is called an error. Errors of the experimenter are called Personal Errors. For example, in Experiment 1, any mistake in estimating the fraction of a mm., in not reading the scale correctly, or not placing it properly on the table, would be a personal error. Personal errors may be often avoided by using care, and their effect on the result may be still further reduced by averaging. In esti- mating the fraction of a millimeter, a person is just as liable to over-estimate as to under-estimate ; if he makes a number of determinations, and averages his results, the over-estimates and the under-esti mates will tend to neutral- ize each other, and the average will.be nearer the truth. For this reason, in conducting an experiment calling for measurement, the more careful the work, and the greater the number of determinations, the closer to the truth will be the average result. Errors due to the apparatus are called apparatus errors. An error which produces a con- stant effect, always tending to make the result too high or too low, is called a constant error. For example, in Method B, Ex. 3 (Volume of an Irregular Body), when the body was removed from the water it took some water with it. The volume obtained included this water, and was always higher than the truth. Sometimes the value of a constant error can be determined and eliminated. Suppose a spring-balance with no weight attached reads 86 MENSURATION. 1 Ib., then every reading on the balance will be 1 Ib. high, and the true weights can be obtained by subtracting 1 Ib. from each weight as given by the balance. QUESTIONS. 1. Why were a number of determinations made in Ex. 1, and the results averaged ? 2. What were some of the personal errors in Ex. 1 ? What was an appa- ratus error in Ex. 2? Were there any constant errors in this Exercise ? Prepare a list of the personal and appara- tus errors in each experiment in this chapter, with sug- gestions for their avoidance. EXERCISE 7. PHYSICAL AND CHEMICAL CHANGE. Preliminary. Are physical and chemical changes accom- panied by change in weight? As good examples of physi- cal change we may take, first, the solidifying of a liquid (that is, the changing of it from a liquid to a solid when cooled), and, second, the dissolving of a solid, in both cases observing the weight before and after the change. In selecting an example of chemical change, we must take two substances whose union will give a new substance, mix known weights of each, and weigh the products. We can then compare the weight of the new substance formed, with the sum of the weights of the original substance. EXPERIMENT 1. Apparatus. Scales and weights; test-tube and fine wire to sus- pend it; shavings of wax or paraffiue; means of heating; bits of solid caustic potash; water; solutions "No. 1" and "No. 2" ; two small vessels in which liquids may be weighed. OBJECT. To see if the weight of substances is the same before and after a physical change. MANIPULATION. (a) Place some scraps of wax or paraf- fine in a test-tube. Suspend the tube from one end of a balance and gently warm it until the solid melts, Counter* NOTES ON ERRORS. 87 poise and watch while the contents of the tube cool again. What sort of a change have you here ? How do the weights of the solid and liquid compare ? (b) Suspend a test-tube half full of water from one arm of your balance, by means of a thread, and place a small piece of caustic potash on a scrap of paper in the pan. Counterpoise. Drop the solid into the water, leaving the paper on the pan. Watch for any change in weight while the solid dissolves in the liquid. What sort of a change is this ? What is your inference ? If these experiments illustrate a general law as regards change of weight during a physical change, what do you infer the law to be ? EXPERIMENT 2. OBJECT. To see if the weight of substance is the same before and after a chemical change. MANIPULATION". Put a small glass vessel on the left- hand scale-pan and record the weight. Add a 10-gram weight to the right-hand scale-pan. Pour some of solu- tion No. 1 slowly into the vessel until it nearly balances (in all probability you cannot get it to exactly balance) ; change the weight on the scale-pan until you have the exact weight of the vessel + the liquid. Record and find the weight of the solution alone. Weigh in the same man- ner a part of solution No. 2. The quantity must be exactly determined, but need not be exactly equal to that used of No. 1. Pour the contents of one vessel into the other ; note what occurs, and weigh the whole. From this weight subtract the weight of the vessel, and you have the weight of the contents. Compare this weight with the sums of the weights of the two liquids. Have we changed our forms of matter ? Is this change chemical or physi- cal ? During a chemical change, what is true as regards the weight of matter? This experiment illustrates a gen- 88 MENSURATION. eral law. From your work, can you state the law ? Ar- range the results as follows : Weight of solution No. 1 -f- vessel = grm. " " vessel = " " " solution alone = " " " solution No. 2 + vessel = " " " vessel = " " " solution alone = " " " two solutions -f- vessel = (i 11 " vessel = " " two solutions alone = " " " No. 1 = " " " No. 2 " both solutions weighed separately = DENSITY AND SPECIFIC GEAYITY. EXERCISE 1. DENSITY AND ITS DETERMINATION. Preliminary. The same weight of matter may take up a great deal of room or only a little. We express this quality of bodies by the words "heavy" and "light." When we say that a body is " light/' we mean that the space it occupies, its volume, is great compared with its weight, and by the use of the word "heavy" we mean the reverse. In using these words we always refer to some other bodies. Thus, when we say that gas is light, we mean that the relation of its volume to its weight is smaller than that of most bodies. Suppose, now, we com- pare a stone and a piece of lead. By very rough tests we can determine which is the heavier ; but if any exact com- parison is desired, the relation of volume and weight must be expressed as a number. To get this number, we must measure the volume and weight of each body, and divide the weight by the volume. The quotient shows how many times the volume number is contained in the weight num- ber. A number which, like this, expresses the number of times one quantity is contained in another is called a ratio. The ratio of the weight of a body to its volume is called the density of the body. By comparing the density num- ber for lead with the density number for stone, we can determine just how many times the lead is denser than the stone. Density is sometimes represented by the sign A ; * * Called delta. 90 DENSITY AND SPECIFIC GRAVITY. and so we can write* A = , or density is the weight of the unit of volume. Would these numbers be the same for different systems of measurement ? EXPERIMENT. Apparatus. Scales and weights ; 8-oz. balance or English weights ; measuring-cylinder ; bodies whose densities are to be determined ; measuring-sticks (English and French). OBJECT. To determine (1) the density of the given substances (a) in the Metric system, (b) in the English system, ounces to the cubic inch and pounds to the cubic foot ; and (2) the order in which the substances should be arranged as regards density. MANIPULATION. (a) Determine the weight of each body in grams, weighing to 0.1 grm. and its volume in cu. cm. If the body is a geometrical figure, measure the dimensions of the figure and calculate the volume. If the body is irregular, get its volume by one of the methods given in the exercises on mensuration. Find the density by dividing the weight by the volume. Carry this number out to the second decimal place. (b) Determine the weight of each body in ounces by a spring-balance,! expressing fractions of an ounce as deci- mals. If possible measure the volume in cu. in.; if it is not possible, calculate the volume in cu. in. from the vol- ume in cu. cm., as already found. 1 cu. cm. = 0.061 cu. in.; hence, Vol. in cu. cm. X 0.061 vol. in cu. in. Cal- culate the density in English measure, (1) ounces per cu. in., (2) pounds per cu. foot. Arrange the results in two tables, heading the first table, " Table I, French," and the second, "Table II, English, as follows:" * Such an algebraic arrangement of symbols, as a short way of giving a rule, is called a formula. f An 8-oz. balance is the best. DENSITY AND ITS DETERMINATION. TABLE I, FRENCH. Body. Weight. Volume. Density. (2) Arrange the bodies in the order of their densities, that having the greatest density heading the list. Weigh the liquid in a small vessel in the usual way. In case the vessel is too large for the scale-pan, make a bale of string or wire, like the handle of a pail, and suspend the vessel below the scale-pan, as in Fig. 62. Be careful that the string or wire by which it is suspended does not break, and allow it to drop. Unit of Density. We need some standard with which to compare densities. Some density must be taken as the unit, and all densities expressed in terms of that unit. The density of water at a specified temperature is used as the unit for solids and liquids, and that of air under fixed conditions of temperture and pressure, for gases. In com- paring the densities of solids or liquids, we take the num- bers obtained by dividing each density by that of water. Specific Gravity. The number which shows how many times the density of water is contained in the density of any solid or liquid is called the Specific Gravity of that body. If the destiny of iron were 437.5 Ibs. per cu. ft., its specific gravity would be found by dividing its density, 437.5 Ibs. by 62.5 Ibs., which is the density of water ex- pressed in the same system. We find that the density of iron is seven times that of water, hence the specific gravity of iron is 7. Calculate the specific gravities of the bodies whose densities you determined in Exercise 1. Are the specific-gravity numbers the same for all the systems of measurement used ? 92 DENSITY AND SPECIFIC GRAVITY. EXERCISE 2. DETERMINATION OF SPECIFIC GRAVITY. Preliminary. In order to determine the specific gravity of a body we could get its density, as in Ex. 1, by dividing its weight by its volume. The density so obtained would be divided by the density of water (if not known, this would have to be found) ; the quotient would be the spe- cific gravity of the body. Or, again, to simplify the pro- cess, we could take equal volumes of water and the body under examination. Thus, if any volume of a body weighs 50 grm., and an equal volume of water weighs 10 grm., then the density of the body is five times that of the water, and the specific gravity is five. Suppose we take a bottle, weigh it, then fill it completely full of water and weigh it again. The weight of the bottle subtracted from the combined weight of the bottle and water gives the weight of the water. Suppose, now, we empty the water completely out, and fill the bottle with the liquid whose specific gravity we wish to determine. Then, since we have the same bottle, and have filled it completely full, we have the same volume of liquid that we took of water. If we weigh the bottle and liquid together, and subtract the weight of the bottle, we get the weight of the liquid. Having the weights of equal bulks of water and the liquid, we can get the specific gravity of the liquid by dividing the weight of the liquid by the weight of the water. EXPERIMENT. Apparatus. Scales ; weights ; specific-gravity bottle ; liquid whose specific gravity is to be determined; water. OBJECT. To determine the specific gravity of a liquid by the method of the " Specific-gravity Bottle." DETERMINATION OF SPECIFIC GRAVITY. 93 MANIPULATION. Weigh the bottle with the stopper in. Be sure that it is perfectly dry. Fill it | | to the top with the liquid, and, holding it over some vessel to catch the overflow, slowly insert the stopper squarely, as in Fig. 61. During this operation the liquid should run over the rim of the bottle all around. With care, the bottle will be completely filled. To test this, turn the bottle upside down and see if any air bubbles appear. If they do, the bottle is not entirely full, and the operation of fill- ing must be repeated. Wipe the outside of the bottle dry and weigh it. Pour the liquid back into the " stock-bottle," rinse the gravity-bottle, fill it com- pletely with water with the same precautions as before, and weigh it. Arrange results as follows : Wt. bottle + liquid = " " alone = FIG. 61. Wt. bottle + water = " alone = " water " = _ Wt. of liquid _ " liquid " QUESTIONS. 1. What is the principle of this experi- ment? 2. Why must you be sure that the bottle is com- pletely full each time ? 3. What do you consider the most important error that is likely to be made? 4. Why must the same bottle be used each time ? 5. Why should the bottle be rinsed out before filling it with water ? EXERCISE 3. THE WEIGHT LOST BY A BODY WHEN IMMERSED IN A LIQUID. Preliminary. We know that a body does not weigh as much under water as it does above, and that when it is 94 DENSITY AND SPECIFIC GRAVITY. completely immersed it displaces a volume of water equal to its own volume.* The object of the following exercise is to see if there is any connection between -this loss of weight and the weight of the water displaced. On what principle must we work in order to be able to make this compari- son? In order to get the loss of weight, we can weigh the body in air and then in water. The difference is the body's loss of weight. To weigh the water displaced, we can fill the specific-gravity bottle completely full of water, and weigh it and the body together. Then if we put the body into the bottle it will crowd out a volume of water equal to its own volume. If, after inserting the stopper, we weigh the bottle with the remaining water and the body, the weight will be less than before by the weight of the water crowded out. This difference is the weight of the displaced water. Having found the body's loss of weight and the weight of the displaced water, we can see if there is any connection between the two facts. EXPERIMENT. Apparatus. Specific-gravity bottle; water; scales and weights; solid body; fine wire for suspension; tumbler. OBJECT. To compare the weight lost by a body when immersed in a liquid, with the weight of a volume of the liquid equal to the volume of the body. MANIPULATION". Fill the specific-gravity bottle full of water and place it in the scale-pan. Place the body in the same pan and weigh both. Take the stopper out of the bottle, put in the body, replace the stopper, wipe the bottle dry and weigh again. The difference in the weights is the weight of the water crowded out of the bottle when the body was put in, and hence the weight of a volume of water equal to the volume of the body. * Provided, of course, the liquid does affect on tbe solid. BODT IMMERSED IN A LIQUID WEIGHT LOST- 95 To get the body's loss of weight in a liquid, suspend it by a thread, or, better, a fine wire, which, as shown in Fig. 62, passes through holes in the scale-pan and box, and is attached to the scale arm-hook. Weigh. Put a tumbler of water under the box and adjust it so that the body is FIG. 62. completely immersed in the liquid and touches neither the sides nor the bottom. Weigh the body, being careful to keep it entirely under water. If time allows, repeat with some other liquid. Record results as follows : Bottle + water -f- body outside = " + " + " inside = Weight of water displaced = Weight of body in air = " " " " water = Loss of weight = 96 DENSITY AND SPECIFIC GRAVITY. EXERCISE 4. THE DETERMINATION OF SPECIFIC GRAVITY BY IMMERSION. Preliminary. It is evident that the method of the spe- cific-gravity bottle cannot be used for solids, and so the principle of the preceding exercise is employed in deter- mining the weight of the water equal in bulk to the solid whose specific gravity is required. By weighing the solid in air and then in water we can get its loss of weight, which last, we have found, is also the weight of an equal volume of water. We then have the weight of the body and the weight of an equal volume of water, and can calculate the specific gravity. The same principle can be used in getting the specific gravity of liquids. By ascertaining the loss of weight of a solid in water, we get the weight of a volume of water equal to the volume of the solid. By finding the loss of weight of the same solid in the liquid whose specific gravity is to be determined, we get the weight of a volume of the liquid equal to the volume of the solid. The body being the same, we have the weights of equal volumes of the liquids, and can compute the required specific gravity. EXPERIMENT 1. Apparatus. Scales and weights; body and wire for suspension; tumbler; liquid whose specific gravity is to be determined; water. OBJECT. To determine the specific gravity of a solid not affected by water, and of a liquid, by the method of " Double Weighing." MANIPULATION. Part I. Suspend the solid by a thread or fine wire, as in the preceding exercise (Fig. 62). Care must be taken not to let the solid touch the glass at any point.* Weigh the solid as closely as can be done on the * With an irregular body, a glass stopper for instance, some judg- ment must be exercised regarding the manner in whicb the bodj- is suspended. SPECIFIC GRAVITY DETERMINED BY IMMERSION. 97 scales. Record the weight. Fill the tumbler with water and weigh again, taking care that the body is entirely im- mersed and touches neither the sides nor the bottom of the glass, and that the suspending thread does not touch the sides of the hole in the box. Record as follows : Wt. in air = " " water = Loss of " " " = Wt. in air rn , -. op. err. = r ; : ; = Carry out to 3d dec. pi. Loss of wt. in water Part II. After weighing the body first in air and then in water, and recording the weights, empty the water out from the tumbler, fill the tumbler with the given liquid, and weigh the body again, using in all cases the same pre- cautions as in Part I. Record results as follows : Wt. in air = Wt. in air = " " water = " " liquid = Loss of " " " = Loss of " " " Loss wt. in liquid Sp. grav. = f T-. - = Loss wt. in water How does this experiment compare in principle with the method of the specific-gravity bottle ? If Part II is pel-formed immediately after Part I., the solid's loss of weight in water is already known, and we have only to weigh the solid in the liquid whose specific gravity is required. The record would then take the fol- lowing form : [From Part I.] Wt. in air = " " liquid = Loss of " " " = [From Part L] " " water = 98 DENSITY AND SPECIFIC GRAVITY. Loss of wt. in liquid Sp. grav. = T 5 . - = Loss of wt. in water EXPERIMENT 2. Apparatus. Scales and weights; water; tumbler; body lighter than water; sinker; thread or fine wire. OBJECT. To determine the specific gravity of a body that will float in water. MANIPULATION". Weigh the body in air. Attach the sinker close to the body with thread or wire; suspend the two, as in the previous experiment, and with the same precautions determine the weight of the two in air. De- termine the weight of the two when immersed in water, in the same way as in the previous experiment. Remove the body and determine the weight of the sinker alone when immersed in water.* Arrange results as follows: Sinker -j- body in air '' alone in air = Body in air = Sinker in water CALCULATION. Arrange calculations as follows: Sinker -J- body in air = Sinker in air = " " " water = " " water = Loss of wt. of both in water = Loss of wt. of sinker = Loss of wt. of body -f sinker = " u " " sinker alone = " " " " body " o f Wt. of body in air ~~ Loss of wt. of body in water ~~ * The number of operations involved in this experiment may be reduced by taking the data obtained in Experiment 1, which may be done by using for a sinker the body whose specific gravity was there determined. It is then only necessary to ascertain the weight of the sinker plus the body in air and the loss of weight of both in water. LIQUID PRESSURE DUE TO WEIGHT. 99 Questions. 1. In these experiments, is the weight of the equal volume of water actually measured at all ? 2. Why are you justified in taking the loss of weight as the weight of a bulk of water whose volume equals that of the body? 3. State the principles of this experiment. 4. How does it differ from that used in getting the specific gravity of a liquid ? EXERCISE 5. LIQUID PRESSURE DUE TO WEIGHT. Preliminary. For investigating the conditions affecting liquid pressure, we use the apparatus shown in Fig. 63. A pressure-gauge is made of a glass funnel, , whose end is FIG. 63. covered with thin rubber, k. From the other end, a rubber tube, I, connects the funnel with the glass tube, cd, which 100 DENSITY AND SPECIFIC GRAVITY. is attached to the scale, w, and contains a drop of water, d, to act as an index. Changes of pressure will cause the rubber, k, to bulge more or less, and this will cause a motion of the index which can be read upon the scale. This gauge is hung from the block, e, by a wire on which it turns, so that it may be made to face in any direction and the centre of k remain at the same depth. To this block is attached a meter-stick, /, which indicates the depth. The apparatus is held by a clamp, g, and is placed in a pail of water, h. The scale m lies flat upon the table. EXPERIMENT. Apparatus. As shown in Fig. 63. Water and pail (or equivalent); measuring-cylinder (or something that can be used to produce changes in depth directly over the gauge-face.) OBJECT. To investigate the conditions affecting the pressure of a liquid upon a surface immersed in it. MANIPULATION. Before commencing the experiment it is necessary to know how the movements of the index correspond with changes in pressure. The gauge being in the water, press on its face gently with the finger and note the direction of the movement of the index. Remove the pressure and note again. Record the direction of move- ment for increased and decreased pressure, as follows : Increased pressure-index moves Decreased " Part I. Effect of depth. The gauge-face being 1 or 2 cm. below the level of the liquid, note the position of one end of the index, and the depth of the gauge. Increase, the depth 4 or 5 cm. (most easily done by setting the clamp lower down on the rod), read the depth and the position of the index. Be careful to always read from the same end of the index, to clamp the apparatus firmly at each depth, and to wait for the liquid to come to rest before reading. In this way take readings at various depths, working first down to as near the bottom of the LIQUID PRESSURE DUE TO WEIGHT. 101 vessel as is possible, and then up again to near the surface. Tabulate results as follows : Depth. Index-reading. From the study of these figuures, place in the note-book an inference regarding the effect of depth on pressure. Part II. Effect of direction. Adjust the apparatus so that the gauge-face is 6 or 7 cm. below the surface. Put- ting the hand into the water, take the rubber tube gently between the thumb and finger at a point just below where it joins the glass, and slowly turn the gauge-face in various directions, reading the index for each direction. Take care that there is plenty of slack rubber tube, and that it does not " kink" anywhere. Make three or four trials at this depth, and then repeat at some other. Kecord results as follows: Depth. Direction of gauge-face. Index-reading. "What inference ? Part III. Effect of distance from sides of vessel at same depth. Gently set the gauge at various points at the same level by moving either the arm of the clamp horizontally or the pail under the apparatus. In each case wait for the liquid to come to rest, read, and record as follows : Depth. Position relative to vessel sides. Index-reading. What inference ? 102 DENSITY AND SPECIFIC GRAVITY. Part IV. Effect of depth of liquid directly over the immersed body. Tip the apparatus sideways as shown in Fig. 64, and clamp it there. Bring the bottom of a glass FIG. 64. cylinder down over the gauge-face, as in the figure. This reduces very much the depth and amount of the liquid directly over the gauge-face, but does not change the gen- eral level of the liquid to a noticeable degree.* Immerse the bottom of the cylinder to various distances above the gauge-face. Read the index each time. At each point hold the cylinder steady and wait until the water in the pail has come to rest before reading the index. To in- crease the depth of liquid directly over the gauge-face, submerge the cylinder completely and invert it. Holding the inverted cylinder by the bottom, raise it until the lower end is only one or two cm. below the level of the liquid. So long as no air enters, the water will remain in the cylin- der, and by bringing it over the gauge-face, as in Part IV, the depth of water there may be made considerably greater * Of course, the larger the pail, the less this error amounts to. SPECIFIC ORA VITY OF LIQ UIDS BY BALANCING. 103 than elsewhere in the pail. The admission of air into the cylinder, by raising one edge for an instant above the level of the liquid, will enable you to change the depth of water in it. In this way try various depths. Eecord results as follows : Depth of Gauge-face below General Surface. Depth Liquid directly above Gauge-face. Index- reading. What inference ? Write out a summary of what you have learned about all the conditions affecting the pressure that the weight of a liquid causes it to exert on an immersed surface. EXERCISE 6. SPECIFIC GRAVITY OF LIQUIDS BY THE METHOD OF BALANCING. Preliminary. In the following exercise we wish to de- termine the specific gravity of a liquid by the method of balancing. This method is based on the laws of liquid pressure. Suppose we have two tubes, con- nected as at a in Fig. 65. Pour some, liquid into one tube, and a liquid that will not mix with it into the other. Then, when the liquids have come to rest, we shall have two columns balancing each other. Where the two liquids join, a, there are two pressures a down- ward pressure due to the weight of the liquid above, and an upward pressure due to the liquid in the other tube, When the Fia. 65. 104 DENSITY AND SPECIFIC GRAVITY. liquids have come to rest, we know that these pressures are equal. Call the upward pressure P, and the downward pressure P'; then P = P'. But we know that P =. a X D X A, and P' = a' X D' X 4', calling a', D', and A' the values for the second liquid. So a X D X A = a' X D' X A'. But as the pressures come together in the same tube at the same point, a = a', so when two liquids come to rest in communicating vessels, D X4 = D' X4' or, the depth times the density of one equals the depth times the density of the other. Hence, to determine the required density, we have only to put into one tube a liquid of known density, into the other the liquid under examina- tion, measure the depths of the two liquids, and divide the product of the density and depth of the former by the depth of the latter, or A' = - TV""" EXPERIMENT. Apparatus. As shown in Fig. 66. Funnel; water and oil with vessels to contain them; meter-stick; solution of copper sulphate or equivalent. OBJECT. To determine the specific gravity of a liquid by the method of balancing.* * Observe that this special method can only be used for liquids that do not mix, SPECIFIC GRA VITT OF LIQUIDS BY BALANCING. 105 -F -B I c MANIPULATION. By the aid of the funnel, pour water into the tube until it stands about half-way up in both branches. Make sure that no air remains in the rub- ber tube by drawing the tube through the fingers pressed together. Slowly pour the oil into the larger tube, at first letting it run down the sides so as to ac- cumulate quietly on top of the water, and continu- ing until the column is 50 cm. or so long. Care must be taken that the junction of the liquids does not get below the glass into the rubber tube. In case this happens, it can some- times be remedied by pour- ing more water into the water tube. Avoid getting the oil into the water tube. When the liquids have come to rest, starting from some horizontal line below the tubes, as D, Fig. 60 (the floor, the base-board, or the table will do), measure the distance: (a) from the reference-line to the top of the water col- umn, or DA; (b) from the reference-line to the top of the other col- umn, DB\ (c) from the reference-line to the junction of the liquids, marked DC. CALCULATION. BD CD = Height of the column of the liquid whose specific gravity is to be determined, ancj i a s r 3 a B %m^ i I J3 FIG. 66. 106 DENSITY AND SPECIFIC GRAVITY. AD CD = Height of the water column producing the same pressure on the same area. Therefore A- C Sp. grav. = B- C Make three or four determinations with various heights, changing the heights by pouring in either water or oil. Tabulate results as follows: TABLE I. BD AD CD BD - CD AD -CD Sp. Grav. If time allows, repeat, using solution of copper sulphate as the liquid whose specific gravity is to be determined, and the oil as the liquid of known density, taking for its specific gravity the. average of three trials with water. EXERCISE 7. EXPERIMENT 1. Apparat us. Loaded test-tube with cork and weights; measuring- cylinder; water; other liquids of known density. OBJECT. To compare the weight of a body that will float with the weight of the liquid displaced by the body when floating. MANIPULATION. Weigh the test-tube; pour about 30 cu. cm. of some liquid into the measuring-cylinder, care- fully rend the volume, and holding the test-tube by the cork, let it slip gently into the liquid until it floats. Be careful that the measuring-cylinder is dry above the level of the liquid after the test-tube is inserted. In order that the body may float freely, tap the measuring-cylinder sev- eral times with a lead-pencil. Again read the volume of ATMOSPHERIC PRESSURE AND THE BA&O METER. 107 the liquid. The difference in the readings gives the vol- ume of liquid displaced by the body, and this volume multiplied by its density gives the weight. Repeat the determination with two other liquids. Record results as follows: Vol. before. Vol. after. Vol. displaced. Weight displaced. Liq. used. Wt. of Body. EXPERIMENT 2. OBJECT. To determine the specific gravity of a liquid by the use of a floating body. MANIPULATION. With the apparatus above, determine the specific gravity of another liquid, writing out in the note-book a complete statement of the special method, etc. QUESTIONS. 1. State the principle of these experiments. 2. How does it differ from that on which the preceding exercises were based ? 3. How does the loss of weight of the body compare with its weight in air? 4. Do you think this fact had any connection with the floating of the body ? EXERCISE 8. ATMOSPHERIC PRESSURE AND THE BAROMETER. EXPERIMENT. Apparatus. Barometer tube; clamp; handkerchief or cloth; mer- cury (about 1 k.) funnel ; feather on wire for removing air-bubbles ; dish to hold mercury; meter-stick; scales and weights; beaker glass for weighing mercury. OBJECT. To measure the pressure of the atmosphere. MANIPULATION. Clamp the barometer-tube in an up- right position, closed end down, placing under it some soft substance, as a handkerchief or towel. By the aid of the funnel fill the tube about half full of mercury, then gently 10& DENSITY AND SPECIFIC insert the feather, and, by turning the wire, remove the bubbles of air which adhere to the side. Add 10 or 15 cm. more of mercury and repeat the removal of the air-bubbles. Proceed in this way until the tube is filled with mercury and contains no air. Have ready the dish containing the mercury filled to a depth of 3 or 4 cm.; grasp the tube near the top with the right hand, placing the thumb firmly over the opening. With the left hand unclamp the tube, grasp it near the bottom, and (keeping the thumb firmly on the open end) inverting the tube, place the end in the vessel below the level of the mercury. Kemove the thumb and again clamp the tube vertically, being sure that the clamp takes the weight of the tube, which must not rest on the bottom of the vessel. Observe and record what happens. When the mercury column has come to rest, carefully measure its height above the level of the mercury in the vessel. Placing the thumb loosely over the lower end of the tube and holding the tube as before, raise it gently until its lower edge is just below the level of the mercury, then press the thumb firmly on the bottom, lift the tube out, incline it in a nearly horizontal position, and allow the mercury to run very gently into the thin glass vessel by admitting air, a few bubbles at a time, into the bottom of the tube. Be sure that none of the mercury is spilled. Weigh the vessel with the mercury, and also weigh the empty vessel and compute the weight of the mercury. This gives the pressure of the atmosphere on each area equal to that of the cross-section of the tube. CALCULATION. To find the cross-section of the tube, divide the weight of the mercury by 13.6 to get the vol- ume, and this quotient in turn by the height, as in the ex- periment on the Cross-section of a Tube. To find the pressure per sq. cm., make the proportion A : 1 sq. cm. :: SPECIFIC GftAVtTT Off TWO LIQUIDS. 109 W : W. Where A is the area of the tube, W is the weight of the mercury, and W ' is the weight per sq. cm. EXERCISE 9. SPECIFIC GRAVITY OF TWO LIQUIDS BY BALANCING AGAINST THE ATMOSPHERIC PRESSURE. Preliminary. If we dip the lower end of a tube into a liquid and remove a portion of the air from the tube, the tension of the air remaining becomes less than that of the air outside, and a column of the liquid is forced up the tube, until its weight, plus the tension of the air above it, produces a pressure equal to the tension of the air outside. If we place the tube in another liquid and withdraw the same amount of air, then the second liquid-column formed has to furnish the same pressure as the first. The two columns, instead of being balanced against each other, as in Exercise 6, are balanced against the same pressure, that of the atmosphere, and must be of equal weight. So, as before, A X D = A 1 x />'. In the following exercise we wish to determine the spe- cific gravity of a liquid by this method. In order to have the same reduction of tension in each tube, both are con- nected with the same vessel, as in Fig. 67, and the air drawn out of that. If one liquid has a known density, we can determine the specific gravity of the other, by the same cal- culation as in Exercise 6. EXPERIMENT. Apparatus. Form shown in Fig. 67. Vaseline; meter-stick; water; solution of copper sulphate and some other solution. OBJECT. To determine the specific gravity of a liquid that will mix with water, by the method of balancing. no AND BPfiOifflO GRAVITY. MANIPULATION*. Arrange apparatus as in Fig. 67. Place water in one tumbler and in the other the copper sulphate- By applying the lips to the glass mouthpiece a, suck some air out of the bottle B, thus causing a column of liquid to rise in each tube. Without removing the mouthpiece from the lips, compress the tube tightly with the left hand, and while holding it in this manner, replace the mouth- piece by the solid plug (which may be covered with vaseline). On releasing the tube, the columns of the liquids will stand at a certain height in ^ach. By bringing a scale alongside the tube, the height of each column from the level of the liquid may be ob- tained. The specific gravity FIG. 67. is equal to the height of the water column divided by the height of the other column. Repeat several times with different heights. Tabulate result : Height of Water. Height of other Liquid. Specific Gravity. Keplace the water by some other liquid, and, taking the SPECIFIC G&AVITY OP TWO LfytflDS. HI copper sulphate as the liquid of known density, determine the specific gravity of the other liquid. QUESTIONS. How does this method differ in principle from Exercise 6 ? With sufficiently long tubes, could de- terminations of specific gravity be made in this way by entirely removing the air? Suggest a method of determin- ing specific gravity based upon Exercise 8. HEAT. The Bunsen Burner. The instrument commonly used for heating bodies is a burner, called the Bunsen Burner. This instrument (Fig. 68) is con- nected with the gas-pipe by a rub- ber tube, and consists of a pipe, a, provided with holes near the bot- tom, which can be closed, if desired, by turning the sleeve, S. The gas enters the bottom of the tube through a small opening, and, when lighted at the top of the tube, burns with a very hot blue flame, free from smoke. On shutting the air-holes, the flame becomes yellow and smoky. Never FIG. es. use the yellow flame except when specially instructed to do it. It will cover with a coating of lamp-black whatever is put in it. When turned down low, the flame sometimes runs down to the bottom of the tube, and burns at the point where the gas enters.* This is called " backing-down," and is often indicated by the flame taking a green color. Backing-down should be stopped at once, as it will make the lamp very hot, some- times even hot enough to melt the rubber tube. A smart blow of the fist on the rubber tube as it lies on the table will often cause the flame to jump to the top of the tube. If this fails, the gas must be turned off and relighted. * Partially closing the sleeve when the gas is turned low tends to prevent this. 113 ffOW SEAT TRAVELS. 113 Precautions in Heating. If a flask is nearly full of water, it is fairly safe to heat it directly, but care must be used that the flame strikes the glass nowhere above the level of the water. Test tubes are usually heated directly in the flame, with the same precautions. They may be held by a strip of paper, doubled three or four times, and passed around the tube near the top.* The bottom of any vessel to be heated should usually be held about three inches above the top of the burner. The safest way of heating a glass flask is by means of a shallow saucer of sheet-iron, filled with sand, in which the bottom of the flask rests. Such an arrangement is called a sand-bath, and, when the burner is placed under it, should be sup- ported three or four inches above the top of the tube. In- stead of a sand-bath, a piece of wire-gauze is often used. This is placed upon the ring of the ring-stand, and the bottom of the flask allowed to rest upon it. The flask may break, and should your hand happen to be beneath it, a severe scalding may result. Be careful. EXERCISE 1. HOW HEAT TRAVELS. Preliminary. In the following exercise we wish to ob- serve what happens when one portion of a body is raised to B.B. FIG. 69. a higher temperature than the other portions. We may use the apparatus shown in Fig. 69, which consists of a * Essentially as iu Fig. 48. 114 rod held by the support S, so that one end may be heated by the burner BB. Make some pellets of wax a little larger than the head of a pin, and place them at regular intervals along the upper side of the rod, as aa. Any con- siderable rise in temperature at any point on the rod will be indicated by the melting of the pellet there. We must try several rods of different materials, and vary the condi- tions by bringing two different substances in contact, in- stead of using different parts of the same substance. Fi- nally, we must try a liquid. The case of a liquid is a little different, because its particles are free to move among themselves, and we shall require some means of observing such motion if it occurs. EXPERIMENT 1. Apparatus. Exp. 1-3. Rod to be heated, with support; wax or paraffine; means of heating the rod. Exp. 4. Incandescent lamp that can be lighted. Exp. 5. Rods of wood, glass, and iron, with means of heating them. Exp. 6. Rod of Exp. 1; thin glass vessel; water; means of heating. Exp. 7. Ring-stand; lamp; wire-gauze or sand-bath; water; some crystals of potassium permanganate. OBJECT. To observe what happens when one portion of a solid is kept at a higher temperature than the rest. MANIPULATION. The rod being fastened so that the end to be heated is about 2 cm. above the top of the Bun- sen burner, close the air-holes o* the burner, light it, and turn off the gas until the flame is about .5 cm. high.* Heat one end of the rod with this low flame, and record your observations. If possible, note the time at which the melt- ing of each piece of wax begins. Write out all you have learned regarding what takes place when a portion of the rod is kept at a higher temperature than the rest of the rod. EXPERIMENT 2. OBJECT. To study the distribution of the heat in the rod. * This gives the yellow, smoky flame. HOW HEAT TRAVELS. 115 MANIPULATION. Remove the burner, and by the fingers or any convenient method test the temperature at different points of the rod, including the ends. Draw a line to rep- resent the rod, and illustrate the distribution of the heat by a line drawn around it. EXPERIMENT 3. OBJECT. To find if the rod loses heat. MANIPULATION. Replace the burner, open the air-holes, turn on the gas, and heat one end of the rod about two minutes. Remove the lamp and bring your hand near, but not touching the end that was heated. Does the rod seem to be losing heat? Is this loss in every direction? To test this latter point, hold the hand about .5 cm. from the heated end of the rod, above, below, on either side, and horizontally from the end. Write out what you have learned regarding the loss of heat. EXPERIMENT 4. OBJECT. To observe if the results in Exp. 3 can still be obtained in the absence of air. MANIPULATION. Observe an Edison lamp ; turn on the current and see if the heat from the hot carbon reaches your hand through the space in the globe from which the air has been exhausted. Record your answer to the ques- tion. EXPERIMENT 5. OBJECT. To find if all bodies behave in a similar man- ner when one portion of them is heated. MANIPULATION. Repeat Exp. 1 with rods of wood, iron, glass, etc., recording carefully the results in each case.* See if you can class together any substances that behave alike in this respect. Record results in tabular form. * Or the experiment can be tried by holding one end of the rod in the hand, heating the other end in the flame, and observing whether tlie end in. the hand bepoines heated or not f 116 HEAT. EXPERIMENT 6. OBJECT. To observe what happens when a heated body is brought in contact with a cooler body. MANIPULATION. Place about 50 cu.cm. of water in a glass vessel and note the degree of warmth by means of the finger. Heat one end of the copper rod for a few moments, plunge it into the water, stir it around, withdraw it, and again test warmth of the water. State your inference. EXPERIMENT 7. OBJECT. To observe what happens when one part of a liquid is heated hotter than the rest. MANIPULATION. Support the thin glass vessel used in Exp. 6 on a ring-stand, by means of a wire-gauze ; fill it three-quarters full of clean water. Have ready the burner turned down low, and adjust the ring-stand so that the vessel is supported about 3 cm. above the top of the burner. Drop into the water four crystals of the pink substance given you (which in dissolving colors the water), and at the same instant place the lamp under the vessel. Any motion of the liquid will be indicated by the motion of its colored portions. Watch carefully and draw a diagram representing your observations. Compare as carefully as possible the behavior of a solid with that of a liquid when one part is heated more than another. Definitions. The process by which heat is transferred from one part of a body to another part, or from one body to another in contact with it, is called Conduction. The process by which a body loses heat when in contact with no other body, as in the case of the electric light, is called Radiation. The process by which heat is distributed through a liquid or gas, as in Exp. 7, is called Convection. The condition of a body as regards its ability to give up heat is called its Temperature. The body giving up heat is said to have the higher temperature. The word "tern- TESTING THERMOMETERS. 117 perature " is used to indicate the relative degree to which a body possesses the property of causing the sensation that we call heat. It is always used with reference to the con- dition of some other body taken as a point of comparison. EXERCISE 2. TESTING THERMOMETERS. Preliminary. The fact that bodies expand when their temperature is raised and contract when it is lowered, is made use of in constructing instruments to measure changes in temperature. These instruments are called thermome- ters. They usually consist of some substance so arranged that changes in its volume may be observed on a scale. The instrument generally used in laboratory work is called a chemical thermometer. The substance used is mercury. It is contained in a glass bulb connected with a fine tube with thick walls. The scale is engraved on the walls, every ten degrees being numbered. The centigrade scale is gen- erally used. At the top of the instrument is a small glass eye by which it may be suspended. Such thermometers are usually provided with a case in which they should always be kept when not in actual use. The glass of the bulb is very thin, and great care should be used not to break it. When a thermometer is used to determine the temperature of a liquid, the bulb should not be allowed to come in contact with the sides or bottom of the containing vessel. When a thermometer has been at one temperature and is to be exposed to a very different one, as in changing from ice-water to steam, hold it in the air a moment before exposing it to the new temperature. For changes of a few degrees this precaution is not necessary. In reading a chemical thermometer, a white card held behind the glass makes the position of the top of the mercury column much more distinct. 118 HEAT. After thermometers have been used for a time, the posi- tion of the mercury at the temperature of melting ice does not always agree with the point on the scale, and some- times the position at 100 also changes. Hence the ther- mometer used in the following exercises should be tested, in order that, if necessary, corrections may be made in its readings. The correctness of the point is tested by plac- ing the thermometer in melting ice (whose temperature is always 0); the 100 point is tested by immersing the ther- mometer in steam (whose temperature is known).* EXPERIMENT. Apparatus. Thermometer to be tested; ice or snow; water; flask and ring-stand, and wire-gauze or sand-bath; tumbler; clamp; deliv- ery-tube; large glass tube 3 or 4 cm. longer than thermometer, corked at one end, the cork having a hole for the thermometer and another holding a piece of small glass tube for connecting with boiler. OBJECT. To test the correctness of the points on the scale of the thermometer which correspond to the temper- atures of melting ice and steam. MANIPULATION. Part I. Place the thermometer in the centre of some pounded ice or snow in a tumbler, the zero-pointf on the scale being just exposed. Allow it to remain there until the mercury has ceased to fall. Kecord the point on the scale at which the mercury comes to rest. This point is the true zero-point on the scale. Part II. Clamp the large tube in a vertical position, corked end up. Connect the delivery-tube from a flask about two-thirds full of water with the small tube in the cork. Thrust the thermometer through the other hole in the cork until the 100 point is just above the cork. Boil the water in the flask, thus surrounding the thermometer * Of course thermometers do not need testing every year or with ?rery class, f These instructions assume that the thermometer has a centigrade TEMPERATURE AND PHYSICAL FORM. 119 with steam, and note the reading of the mercury column when it comes to rest. Draw the thermometer up until the bulb only is below the cork, and see if it makes any difference in the reading whether all the mercury is heated or not. Read the barometer. The temperature of the steam corresponding to the atmospheric pressure may be calculated by calling the temperature corresponding to 760 mm. 100, and adding 1 for each 27 mm. above 760, or subtracting 1 for each 27 mm. below. Record the ther- mometer-reading, the true temperature of the steam, and the difference. EXERCISE 3. TEMPERATURE AND PHYSICAL FORM. Preliminary. We already know that when the tempera- ture of a solid is raised sufficiently, the solid changes to a liquid, and at a still higher temperature to a gas. That is, the physical form of a body is affected by its tem- perature. In the following exercise we wish to find out all we can about what goes on when a body is heated. Let us heat a body and note its changes in temperature, and also watch for any other changes. Ice is a good substance to work with. If we put some ice in a vessel, heat it, and note the temperature at regular inter- vals, we can see if there is any definite connection between temperature and physical form. At the beginning, some water must be added to the ice to get the temperature, as we could not thrust the thermometer directly into the ice. The contents of the vessel must be stirred in order to keep the temperature everywhere the same. We can weigh the vessel before and after heating to see if there is any change in weight. The apparatus used is shown in Fig. 70. A tin pail supported over the burner B.B. is filled with ice and water. The temperature is measured by the 120 HEAT. thermometer T, and the contents of the pail stirred by the paddle P. FIG. 70. EXPERIMENT. Apparat us. Ring-stand and burner; tin pail; paddle; thermome- ter; ice or snow; water; watch or clock; spring-balance or rough scales ; test-tube of cold water or plate of clean dry glass. OBJECT. To observe the effects of heating a body. MANIPULATION. Place about 100 cu. cm. of water in the pail; add enough ice or snow to fill the pail two-thirds full of the mixture ; weigh the pail and contents on the TEMPERATURE AND PHYSICAL FORM. 121 spring-balance.* Record the weight. If ice is used, it should first be wrapped in a cloth and pounded until it is fine. By means of the paddle stir the contents of the pail vigorously until the thermometer reads zero. Adjust the thermometer so that the bulb is well covered, and does not touch the sides or bottom of the pail. Place under the pail a very low flame,, turning the gas nearly off and almost closing the air holes in order to prevent backing- down. Stir vigorously, taking care that the solid and liquid are thoroughly mixed, and being careful not to break the bulb of the thermometer. Note the tempera- ture at one-minute intervals until four minutes after the water has boiled. The readings must be continuous from the beginning to the end of the experiment. When the readings are completed, weigh again. From time to time during the work hold over the pail a piece of clean dry glass, or a test-tube filled with cold water, and observe the results. In addition, note all that goes on, and record all your observations. Record results as follows : Weight before = Weight after = TABLE I. Time. Temperature. Remarks. Under "Time," place the hour and minute of each reading. Under " Temperature," place the thermometer- reading to 0.1 degree. Under "Remarks," place any observations that you made at the time of the reading. * A 64-oz. balance is the best. 122 HEAT. Note carefully changes of form, appearance, formation of bubbles, moisture, etc. QUESTIONS. 1. What effect has the addition of heat on the physical form of a solid ? 2. What effect has the addi- tion of heat on the physical form of a liquid ? 3. Is it possible to add heat to a body and not raise its tempera- ture ? 4. Under what circumstances ? 5. Under what circumstances does the addition of heat raise the tempera- ture ? 6. Is any change of weight produced ? 7 Why is it necessary to stir the mixture ? 8. When the tempera- ture rises, is the rise regular ? GRAPHIC REPRESENTATION OF RESULTS. CURVE PLOTTING. Where an experiment includes two sets of measure- ments, as the time and temperature measurements just made, the results are often expressed by means of a dia- gram. Suppose, for example, the following data have been obtained : Time. Temp. Time. Temp. 11 h. 3 m. 5 11 h. 23m. 4 5 7 25 3 7 4 21 2 9 3 29 4 11 3 31 5 13 5 33 6 15 8 35 5 17 6 37 4 19 7 39 3 21 5 41 To represent these results in a diagram, on a page of of your note-book, draw two lines at right angles, as AB and EC in Fig. 71. Let BO represent time and AB temperature. Divide the line BC into as many equal parts as there are observations recorded ; in this case, 18. GRAPHIC REPRESENTATION OF RESULTS. 123 Divide the line AB into as many equal parts as there are de- grees between the highest and lowest temperature noted; in this case, 8. From each of the points a draw lines parallel to BC and equal to it in length, and from the points c on BC draw lines parallel to AB, thus dividing the paper up into a number of rectangles. Starting at the point where the two lines first drawn meet, mark on dddddddd d d, 7 3 5 n (2) 11 13 15 17 19 21 23 25 27 29 31 FIG. 71. 35 37 39 AB the temperature 5, the first observation, by making a cross five spaces up the line. Then on the next vertical line, which marks the time of the next observation, make a cross at the intersection opposite the next recorded tem- perature. Proceed in this way until all the temperatures have been entered. Connect the centres of the crosses by straight lines, or by a regular curve. The line so obtained will represent the temperature at various times. By in- serting at the proper places on the curve any observations 124 HEAT. that may be noted as regards changes, etc., a complete graphic account of the results of the experiment is ob- tained. This process is called curve-plotting, and is much used to represent to the eye the results of experiments. Taking the results you obtained in the preceding experi- ment, plot a curve on one complete page of your note- book, representing the changes in temperature during the entire experiment. Enter at the proper points of the curve any phenomena that may have been observed. A curve like this is often called a temperature-curve. If BC be drawn the long way of the note-book page, the blue-ruled lines will be convenient for the vertical lines. The hori- zontal lines should be ruled very lightly with a pencil. Evidently any standard of length can be used in laying off the spaces. In Fig. 71, 1 cm. on the line BC represents two minutes of Time, and 2 cm. on the line AB represent one degree of Temperature if AB = 16 and BC = 19 cm. EXERCISE 4. LAWS OF COOLING. EXPERIMENT. Apparatus. A small beaker-glass; thermometer, and clamp to support it; watch or clock ; tin pail; water; ring-stand; and burner for heating the water. OBJECT. To observe the change in temperature in a cooling body. MANIPULATION. Place about 50 cu. cm. of hot water in a beaker glass, suspend the thermometer in the liquid, and observe the temperature every minute for twenty minutes. Every five minutes also observe the temperature of the room. Record results as follows: Temp. Time. Temp, of Room. Weight used. Repeat with 25 cu. cm. of water. MELTING AND BOILING POINTS. 125 QUESTIONS. 1. What have you observed regarding the changes in temperature when a body cools ? 2. Does the quantity of the body make any difference? 3. Plot curves showing the changes in temperature in each case. 4. Does the difference in temperature between the body and the air seem to affect the rate at which the temperature falls ? EXERCISE 5. MELTING AND BOILING POINTS. Preliminary. In the following exercise it is desired to observe the melting-points of some solids, and the boiling- points of some liquids. The melting-point of a solid is usually determined by immersing a small portion of it in some liquid having a sufficiently high boiling-point, heating the liquid, and noting its temperature when the solid melts. For bodies which it is supposed will melt below 100, water is used; for higher melting-points, other liquids. The solid is usually placed in a small tube, called a melting -tube, which is attached alongside the ther- mometer. A melting-tube is made by drawing out a piece of glass tubing in the flame of a Bunsen burner, as shown in Fig. 72. The tube should be about 10-15 cm. from the narrow neck to the upper end, and the small part about 3 cm. long. Melt some of the solid (paraffine, for instance) in a small dish, draw a little up into the tube, and after wiping the outside allow it to cool. In I determining the boiling-point of a liquid, a test- FIG. 72. tube, containing about 1 cu. cm. of the liquid takes the place of the melting-tube. EXPERIMENT 1. Apparatus. Ring-stand; sand-bath and burner; thermometer, and some means of supporting it; " melting-tubes;" wax or paraffine in small dish (if tubes are unprepared); water; stirring-rod; rubber bands. OBJECT. To determine the melting-point of a solid. MANIPULATION. Attach the tube containing the solid a 126 SEAT. to the thermometer by elastic bands or strings, as indicated in Fig. 73, the solid being on a level with the thermometer bulb, and support the whole so that the bulb is about in the centre of the dish of water. Heat the water slowly, stirring gently, and note the temperature either when the solid becomes transparent, or when it slides up the tube. Either of these may be taken as indicating the melting- point. The second gives a little higher temperature than the first. Add some cold water, and repeat with a fresh tube. If possible, try more than one substance. T FIG. 73. FIG. 74. EXPERIMENT 2. OBJECT. To determine the boiling-point of a liquid. MANIPULATION". Place about 1 cu. cm. of the liquid in a test-tube and support the tube in the beaker, which has been filled with cold water, so that the liquid is in the centre of the water, as in Fig. 74. Warm the water slowly, BEAT CAPACITY. 127 stirring gently with the thermometer, and note the tem- perature at which the liquid begins to boil. It is best to shake the tube gently while heating. Make two deter- minations with one liquid, and, if possible, repeat with another liquid. Alcohol, ether, etc., are very inflammable, and should be kept away from the fire. EXERCISE 6. HEAT CAPACITY. Preliminary. In the following exercise we wish to study the conditions affecting the rise in temperature of bodies when heated. We already know that the longer a body is heated, the more its temperature rises,* provided no change of form takes place, and that the greater the difference in temperature between the source of heat and the body, the more rapid will be the change. f In the following exercise we wish to see if the nature and quantity of the body heated have any effect.^ EXPERIMENT. Appara tits. Part I: Test-tube, with perforated cork; thermom- eter; tin pail; ring-stand; burner; water; scales and weights; a bu- rette or graduated cylinder. Part II.: Three test-tubes with corks; mercury; alcohol; empty tumbler; also the apparatus for Part I. OBJECT. To observe the effect on the rise of tempera- ture in a body produced by (a) quantity, (b) material. MANIPULATION. Part I. Effect of Quantity : Place 4 grams of water in the test-tube, close the mouth of the tube by a cork through which the thermometer passes, the bulb being immersed in the liquid. Have ready the large vessel in which the water is about 50, place the tube in the water, stir it gently, and observe the time required for the thermom- * Ex. 3. f Ex. 4. \ Let each pupil prepare a statement of the conditions under which such an exercise must be conducted. 128 BEAT. eter to rise 10 degrees. Repeat the experiment with twice the weight of water. Part II. Effect of Material : Weigh out in three tubes 15 grams, respectively, of water, mercury, and alcohol. Cork the tubes, and stand them upright in an empty tumbler until ready for use. Take the tube containing the water and substitute for its cork the one bearing the ther- mometer. Having the thermometer bulb immersed in the water, read the temperature of the liquid and then plunge it into the heated water. Shake it gently, and observe the time required for the thermometer to rise 2 degrees. Re- peat the experiment with the other liquids. Tabulate the results as follows : Wt. used. Original Temp. Final Temp. Time of Immersion. Body. QUESTIONS. 1. For a given substance, can you make out any relation between the rise of temperature and the weight used ? 2. Will exposure to the same temperature for the same time cause the same rise in temperature in all bodies ? EXERCISE 7. DETERMINATION OF SPECIFIC HEAT. Preliminary. We observed in the preceding experiment that when equal weights of various bodies were exposed to the same temperature for the same time, the temperature of some rose more rapidly than that of others. This is in- dicated by saying that they have different heat capacities. The lower the heat capacity, the higher the temperature rose; and the less the temperature rose, the greater the heat capacity. Which has the greater heat capacity water or mercury? DETERMINATION OF SPECIFIC HEAT. 129 The unit of heat quantity is the heat required to raise a unit of weight of water from to 1 on a temperature scale- hence the quantity of heat taken by any quantity of water is found by multiplying the weight of the water by its rise in temperature, or H= W X Rise in temp. Evidently we can have several units of heat, according to the unit of weight taken and the thermometer scale used. The units of weight generally used are metric, the kilo- gram and the gram, and the scale used is the centigrade. The corresponding unit of heat is called the calorie. When kilograms are used the calorie is designated by a capital C\ when grams are used, by a small c. In order to be able to use these heat-units for all bodies, we must compare their heat capacities with that of water, which is taken as the standard. This comparison is ex- pressed as the ratio of the heat capacity of the body to that of water, and this ratio is called the Specific Heat of the body. As the specific gravity of a body expresses how many times its density is that of water, so the specific heat of a body expresses how many times its heat capacity is that of water. The simplest way to determine specific heat would be to take equal weights of water and the body to be tested, expose them for the same length of time to the same tem- perature, and note the rise of temperature. The higher the temperature of the body rose, the less would be its heat capacity. If, for example, the temperature of the body rose twice as much as that of the water, its capacity would be half as much, and its specific heat one half; if it rose half as much, its specific heat would be 2, etc. Calculate from the data of the preceding exercise the specific heat of mercury. 130 HEAT. Specific heat is usually determined by what is called the "method of mixture." This consists in heating the body to a known temperature, and then bringing it in contact with water in a vessel, called a calorimeter, which will not lose heat by radiation. The body will lose heat and the water will gain it, until both are at the same temperature. Then the quantity of heat gained by the water will equal the quantity of heat lost by the body. If we know the weight of water in the calorimeter, and how many degrees it was raised, we can calculate how much heat was gained by the water, or, the equivalent, that lost by the body. If we also know the weight of the body, and the number of degrees it cooled, we can determine how many heat-units would be given out by one gram of the body cooled 1. Dividing this by the amount of heat that would be given off by one gram of water cooled 1, we can get the specific heat. In the following exercise we use an iron ball of known weight, heated in boiling water to 100. Taking a known weight of water and noting the rise in temperature, we calculate the specific heat. EXPERIMENT. Apparatus. Body whose specific heat is to be determined. Tin pail; ring-stand and burner; water; thermometer with white card; scales and weights; calorimeter; three corks; thread. OBJECT. To determine the specific heat of a given solid. MANIPULATION. Fill the pail about three-fourths full of water, and light the burner under it. Weigh the calo- rimeter, fill it about two-thirds full of water,* and weigh * The point is iiot to get so much water in the calorimeter that it will overflow when the body is put in, but yet to have enough to completely cover it. A preliminary trial may be needed. Place the body in the calorimeter, and then add water enough to fill the calo- rimeter to about 5 cm. of the top. On withdrawing the body, the amount of water for good working conditions remains, and may be weighed. DETERMINATION OF SPECIFIC HEAT. 131 again. Support the calorimeter on the corks upon the table at some distance from the heating apparatus, and put the thermometer into it. Weigh the solid under examina- tion. When the water in the pail boils, suspend the solid in the centre by means of a thread, and allow it to remain there until it has assumed the temperature of the water (100 approximately). This will take about four minutes. Then read the thermometer and quickly transfer the solid to the calorimeter. Stir gently with the thermometer and read it to 0.2 at intervals of half a minute (record these readings) until the temperature of the water begins to fall. The highest reading of the thermometer is the temperature to which the solid heats the water. If time allows, repeat with different quantities of water in the calorimeter. Record results as follows: Weight of body = Calorimeter -+- water = Calorimeter alone = Water alone Temperature of body before immersion = " " water in cal. after body is in = " " " " " before body was in = Increase in temp, of water in calorimeter = Fall in temp, of body = QUESTIONS. Explain why the space between the walls of the calorimeter is filled with excelsior. Suggest some other substances that would do as well. Why should the solid be suspended by a thread rather than by a wire? What error is introduced by doing so ? What error is in- troduced in calling the original temperature of the ball 100? 132 HEAT. CALCULATION. Call the weight of the body W and the weight of water in the calorimeter W, the original tempera- ture of the water t and the final temperature t' . Then W grammes of the body in cooling from 100 to t' degrees gave off sufficient heat to raise W grammes of water from t degrees to t' degrees, or raised it t' t degrees; the amount of heat given up was WX (t'-t). As the heat was given up by W grammes of the body cooled from 100 to t' degrees, the amount of heat given out by one gram cooled one degree was W X (t' - t) W'X (100-*')" Since this also represents the amount of heat that would be required to raise one gram of the body 1, we can get the specific heat of the body by dividing this value by the amount of heat that would be required to raise 1 gram of water 1 or \c\ so W X (t f - t) ., , W X (100 - t') Specific heat = ^ '. j-C By substituting in this equation the values obtained in the experiment, the specific heat of the body may be calculated. In this calculation we have neglected to take into ac- count the heat that went into the calorimeter, which was itself heated. To make this correction, weigh the vessel that formed the inside of the calorimeter.* This gives the weight which was heated from the original tempera- ture of the water to its final temperature, or t' t\ and so the heat that went into the calorimeter = Wt. cal. X t 9 t X the specific heat of the material of the calorimeter.! * Or, if a metallic calorimeter be used, weigh the whole vessel, f Glass, 0.198; brass, 0.858; iron, 0.1124. LATENT HEAT. 133 The total heat given out by the body equals that which went into the water plus that which went into the calorim- eter. The corrected formula, then, would be: SPECIFIC HEAT = [W X (f t)] + [wt. cal. X (f t) X sp. heat of cal.] W ' X (100 - t') Re-calculate your value for specific heat with the correction for the calorimeter. EXERCISE 8. LATENT HEAT. Preliminary. The name latent heat is given to the heat which is required to change a solid to a liquid, or a liquid to a gas, without altering its temperature. Latent heat is usually determined (1) by measuring the heat given out by a known weight of vapor at the boiling-point of the liquid when condensed at that point, or (2) by deter- mining the heat absorbed by a known weight of the solid at the melting-point when changed to a liquid at that tem- perature. In this exercise, the number of heat-units given off by one gram of steam at 100 when changed to water at that temperature is to be ascertained. The steam is con- densed under such conditions that the heat given off will raise the temperature of a known weight of water. If we know the weight of steam condensed, the weight of water heated, and the number of degrees that it was raised by the condensed steam, we can calculate the latent heat. The apparatus used in the first method consists of a glass vessel D y Fig. 75, holding the water, and containing a glass coil E, which terminates in a tube that projects from the bottom of the vessel. This coil is connected by the tube C with the flask A, which furnishes steam. K is an arrange- ment to prevent any condensed steam from passing into 134 HEAT. the coil. The tube C is thickly wound with cloth to stop any loss of heat and resulting condensation of steam before reaching E. When steam from A reaches E it condenses, FIG. 75. and so raises the temperature of the water in D. The con- densed steam runs out into a vessel, and the weight of water so formed gives us the weight of steam condensed. EXPERIMENT 1 . Apparatus. Ring-stand ; wire-gauze; burner; small beaker-glass; scales and weights; thermometer; liter and half-liter flasks; paddle; apparatus as in Fig. 75. OBJECT. To determine the number of heat-units re- quired to change one gram of steam at 100 to water at 100. MANIPULATION. Fill the flask A about two-thirds full of water and set it to boiling, the delivery-tube being dis- connected at H. Place a measured quantity of water in D * (2 to 4 liters, according to size), and suspend the ther- * The object, of course, is to get a known weight of water in D. This could be done by weighing D, filling it with water, and weigh- ing it again. It is much more convenient, however, to measure the LATENT HEAT. 135 mometer in the liquid. As 1 cu. cm. of water = 1 gram, you now know the weight of water in D. Weigh the small glass vessel F. When "live steam" comes out of the de- livery-tube at H, connect it with the glass coil and allow it to run for three minutes, meantime stirring the water in D with the paddle.* Eead the temperature of the water in D, and immediately place the small glass vessel under the end of the glass coil to catch the distilled water. " Let the apparatus run from 15 to 20 minutes, stirring the water in D gently all the time; then remove the glass ves- sel containing the condensed steam, and immediately read the temperature of the water in D. Disconnect the steam- pipe and turn out the gas under A. Weigh the vessel containing the condensed steam. Arrange the results afc follows: Water in the condenser = Original temperature = Final temperature = Kise in temperature = Vessel -j- condensed steam = Vessel alone = Weight of steam condensed = CALCULATION. Call JFthe weight of water in the con- denser, W the weight of steam condensed, t the original temperature of the water in /), and t' the temperature to which it was raised. Then W X (t f t) = the heat gained water. It is best to fill D within about 5 cm. of the top, and it is convenient to take a volume which can be measured by liter or half -liter flasks. * In stirring, care should be used not to break the glass coil, and to continually stir the water up from the bottom, at which point the colder water will always collect. The thorough stirring of the water js an important point all through the experiment. 136 HEAT. by the water in D during the experiment. This amount of heat includes not only the heat given out by the steam at 100 when condensed to water at 100, but also the heat given out by the water so formed in cooling from 100 to the temperature of the water in Z>, which varied from t degrees at the beginning to t f degrees at the end of the experiment. The average temperature to which this water /' 4- t was cooled was - and the amount of heat given off by 6 the water formed from the steam in cooling was * W x (100 - So that the heat gained due to the condensation of steam alone is [Wx(f- 1)] - [w x (100 - ^J-)], and the amount of heat per gram is [Tf X (t' - t)] - [V X lOO - W There are two errors that still need correcting for, if the results are to be at all accurate. (1) The glass vessel D and the glass coil E are raised from t degrees to t' degrees, as well as the water inside; hence the value taken for the heat given out is too small by the amount that went into the glass. To correct for this, weigh D and the coil to- gether. Calling this weight G, the heat that went into the * The original temperature being 100, the average fall in tempera- ture would be 100 ~~. & LATENT HEAT. 137 glass is G X (f f) X specific heat of glass.* If this quantity be added to the value taken before for the heat given up to D, it will give more accurate results. (2) Dur- ing the experiment the water in D was losing heat to the air in the room.f This error can be avoided by filling D with water a number of degrees below the temperature of the room,]; and stopping the experiment when it is heated as much above the temperature of the air as it started below. Then the water in D takes as much heat from the air while below its temperature as it gains while above, and so this error cancels out. The corrected calculation, then, is LATENT HEAT = [Gx(t'-t) X sp. heat glass] -f [Wx (<'-<)]- W X -~-\ I SUBSTITUTE EXPERIMENT. Preliminary. The apparatus is shown in Fig. 76. Steam is generated in the flask, and passes through the covered tube into the calorimeter contain- ing a known weight of water. The temperature of this water is ob- served before and after running in steam, and the increase in weight of the calorimeter gives the weight of steam condensed. The tube is cov- ered with cloth to prevent conden- sation. The calorimeter is sup- ported on a block or box, so that FIG. 76. by removing the support, the calorimeter can be quickly * This may be taken as 0.198. f For another method of correcting for this error, see Worthing- ton, p. 190. t This can usually be done by taking water from the faucet after letting it run awhile, where there is a water service; otherwise, a little ice or snow may be added. 138 HEAT. dropped down so as to clear the end of the delivery-tube without disturbing the flask. Apparatus. Ring-stand; wire-gauze; burner; flask with cork and delivery-tube; scales and weights; calorimeter and thermom- eter with white card; support for calorimeter (books, block of wood or small box). OBJECT. To determine the amount of heat given out by one gram of steam at 100 in condensing to water at 100. MANIPULATION. Weigh the vessel to be used as a calo- rimeter, add about 300 cu. cm. of water, weigh again, and place the thermometer in the vessel. Fill the flask two- thirds full of water and heat. After the steam has escaped freely from the delivery-tube for three or four minutes, note the temperature of the water in the calorimeter, and as quickly as possible plunge the delivery-tube nearly to the bottom of it. While the steam is condensing, stir gently with the thermometer, noticing the temperature from time to time. When the temperature of the water in the calo- rimeter is 8 or 10 above that of the room, withdraw the delivery-tube as rapidly as possible, and remove the lamp from beneath the flask. Note the temperature of the water in the calorimeter, and weigh the latter. Eecord the re- sults as follows: Calorimeter -f water = Steam condensed = " = Temp, before Water Temp, after Calorimeter + water after = Gain in temp. = Calorimeter + " before = EXERCISE 9. COEFFICIENT OF LINEAR EXPANSION. Preliminary. We know that when a body is heated it expands. The fraction of its length at that it expands COEFFICIENT OF LINEAR EXPANSION. 139 when heated 1 is called its coefficient of linear expansion, or the linear coefficient of expansion. The fraction of its bulk at that it expands when heated 1 is called its coeffi- cient of cubical expansion, or the cubical coefficient of expan- sion. Evidently fluids would have no coefficient of linear expansion, but solids would have both.* In the following exercise we wish to determine the average linear coefficient of a metallic rod. First Method. The apparatus is shown in Fig. 77. The rod c is surrounded by a large tube ee, which is first filled with ice-water and then with steam, thus heating the rod FIG. 77. 100. The changes in length are magnified by the lever p, which reads on the scale S. In this way we can meas- ure the change in length of the rod when heated from to 100 and determine the required coefficient. * Suggestion: Give the principles on which such measurements would be based. 140 EXPERIMENT 1. Apparatus. As shown in Fig. 77. Also, water; ice; funnel; tin pail; meter-stick; flask; ring-stand; burner; connecting tubes. OBJECT. To determine the linear coefficient of expan- sion of a solid. MANIPULATION. The chief error in this experiment is in the determination of length, since only the part of the rod inside the corks is at exactly the measured tempera- tures, though the rest of it becomes heated by conduction and expands to some extent. If we take the length be- tween the outsides of the corks, we shall come very near the truth. To get the length at zero. Attach the glass funnel to the rubber tube L, place a vessel under the exit-tube A", and pour ice-water through the apparatus until the ther- mometer T has read zero for several minutes. Read care- fully the position of the pointer on the scale, and measure the length of the rod between the outsides of the corks. Allow the water to run out. Connect with the flask F, and run steam through the apparatus until the pointer again comes to rest; then note its position. If time allows, again pour ice- water through, and see if the pointer comes back to its first position. If so, repeat the experiment; if not, record the fact. To find increase in length. By means of compasses, measure carefully the distance between the two pivots, re- peating several times, and recording each measurement. Measure also the distance from the lower pivot to the point on the needle at which you took your reading. The aver- age length of the "long arm" divided by the average length of the "short arm" gives the magnifying-power of the pointer. Record results as follows: Length of rod = Mag. -power of the pointer = COEFFICIENT Off LINE AH EXPANSION. 141 TABLE OF MEASUREMENTS. 1st Trial. 2d. 3d. Av. Short arm, Long arm, Magnify ing-power = Reading pointer at = " " " 100 = Increase on pointer = True increase = Coefficient CALCULATION". Substract the smaller reading of the pointer from the larger; this gives the space traversed by the pointer. This, divided by the magnifying-power of the pointer, gives the true increase in the length of the rod. This increase, divided by the length of the rod at zero, gives the coefficient of linear expansion as a decimal which is to be carried out to the fourth place of significant figures. Or, calling L the length of rod at 0, M the mag- nifying-power of the pointer, S the reading of the pointer at 0, S' the reading of the pointer at 100, Increase, 100 = 8 ' ~ S Increase, 1 = Linear coefficient of expansion = M S' - S a MX ioo ; 8' -8 M X 100* Second Method. The apparatus used is shown in Fig. 78. The rod is inside the tin jacket R, which can be filled 142 HEAT. with either steam or ice-water, thus changing the tempera- ture of the rod 100. For measuring the increase in length, the pointer P, moving on the clock face, is attached to a screw, D, which advances a known distance for each turn. The end of this screw is in line with the end of the rod, and the screw is connected with one wire FIG. 78. leading from a source of electricity, while the rod is con- nected with the other wire. When the end of the screw touches the end of the rod the circuit is completed, and this fact is indicated by some instrument placed in the circuit. If we know how far the screw advances at one turn, the change in length of the rod may be very accu- COEFFICIENT OF LINEAR EXPANSION. 143 rately measured by finding how many turns of the screw move its end enough to make contact with the end of the rod first at and then at 100. EXPERIMENT 2. Apparatus. As shown in Fig. 78. Also, ice-water; tumbler; meter- stick; boiler, burner, and ring stand; current of electricity and some instrument to indicate when the circuit is completed (galvanometer; lamp; sounder). OBJECT. To determine the linear coefficient of expan> sion of a metallic rod. MANIPULATION. Arrange the apparatus as in Fig. 78, connecting the glass vessel V with the jacket R, as shown. Turn the pointer, P, until the end of the screw, D, is just in contact with the end of the rod. Place a vessel* under the end of the exit-tube, fill V with ice- water, and allow it to run through the jacket, thus sur- rounding the rod with water at 0. As the rod contracts, turn the pointer so as to just keep contact between the end of the screw and the end of the rod, and continue until there is no further change in length. During this time keep ice-water constantly running through the jacket. When the rod has ceased to contract, read the position of the pointer at which the end of the screw just touches the end of the rod, and turn the pointer back half a revolu- tion or so. Replace V by a flask two-thirds full of water, and connect it with the jacket R. With a Bunsen burner heat the flask and pass the steam through the jacket. During this operation turn the pointer back as fast as contact is made by the expansion of the rod. The expan- sion will be very rapid. When the rod has ceased to ex- pand, note the position of the pointer at which contact is just made, and record the total number of minutes on the * When this vessel is full, the contents are to be poured back into V. It is well to have a little ice in it to hold the temperature of the water at 0. 144 BOAT. clock face which the pointer was turned back from its po- sition when the rod was at 0. This number, multiplied by the decimal of a millimeter which the end of the screw moves for 1 minute on the scale, gives the increase in length of the rod when heated from to 100. Again at- tach the glass vessel V, run in ice-water, cool the rod to 0, and ascertain the number of minutes on the scale which the pointer must be turned to get contact again. These numbers should be very nearly the same. Average them, and calculate the coefficient of linear expansion of the rod for one degree, taking for the length of the rod the dis- tance between the outer ends of the jacket corks. Ar- range results as follows : Eeading pointer at = min. " " " 100 = " Pointer moved " Beading pointer at 100 = " tf (( (S A (f Pointer moved in cooling " Average CALCULATION. Call the length of the rod L, the num- ber of minutes that the pointer moved m, and the distance screw moved for 1 m., a. Then the increase for 100 = m X a, and the coefficient for 100 = j. , and the coefficient for 1 = - _z/ 100 6WBICAL COEFFICIENT 0# A LIQUID. 145 EXERCISE 10. CUBICAL COEFFICIENT OF A LIQUID. EXPERIMENT. Apparatus. Alcohol of known specific gravity ; test-tube with perforated cork, and glass tube, with scale; tin pail; ice-water; ring-stand ; lamp ; thermometer. OBJECT. To determine the cubical coefficient of expan- sion of alcohol. MANIPULATION. Put some ice and water in the tin pail, and while the mixture is cooling weigh the test-tube with the cork and small tube. Fill the test-tube nearly full of alcohol and crowd the stopper in tight, thus forcing a col- umn of alcohol up the small tube. This column should not be over 4 or 5 cm. high, and no air-bubbles should re- main in the test-tube. Weigh again. The increase in weight represents the weight of alcohol in the apparatus. The volume is found by dividing this weight by the specific gravity of the alcohol (marked on the bottle from which it was taken). Immerse the test-tube iu the ice-water, allow it to remain there until the alcohol column has come to rest, and note the position of the top of the column on the scale. Remove the ice and slowly heat the contents of the pail, stirring gently with the thermometer until the alcohol column has risen four or five cm. Stop heating, and note when the alcohol column ceases to rise. Read its position on the scale, and at the same time note the temperature of the water. You have now the distance which the al- cohol rose in the tube when heated from to the final tem- perature of the water in the pail. CALCULATION. To determine the increase in volume, multiply the rise on the scale by the volume corresponding to a rise of 1 cm. as given on the card attached to the in- strument. This gives the increase in volume. Record re- sults as follows : 146 Weight of apparatus + alcohol = " empty = " " alcohol =~~ . Volume of alcohol = Alcohol column read at = (t ff (( f( 4- __ No. of degrees alcohol was heated = From the data, calculate the cubical coefficient of alcohol for 1. EXERCISE 11. COEFFICIENT OF EXPANSION OF A GAS AT CONSTANT PRESSURE. EXPERIMENT 1. Apparatus, The special form in Fig. 79 ; ice or snow-water ; tin pail ; ring-stand ; thermometer ; meter-stick. If apparatus is not calibrated there will be required in addition : scales and weights ; mercury ; small vessel for weighing mercury ; burette or balances that can weigh 300 to 400 grams. OBJECT. To determine the coefficient of a gas under constant pressure. MANIPULATION". To find the volume of the gas used. Having no water in B, Fig. 79, remove the gas-holder A, and by means of a burette determine its volume in cu. cm.* Dry, and place inside B, as shown, and connect with the tube DC when full. The volume of gas under test is really that in A plus a little in the tube ; but since the cork occupies some room in A, it will be near enough to the truth to call the volume that of A alone. Fill B with water to about 3 in. above the level of A ; add some ice or snow. In a short time the temperature of the liquid should be 0. While it is cooling, find the volume repre- sented by 1 cm. on the tube DC. Detach the tube at E, and draw a column of mercury into it. Lay the tube on a * Or, weigh A empty and then full of water. From the weight of water contained in A, calculate the volume. COEFFICIENT OF EXPANSION OF A GAS. 147 scale and measure the length of the column. Call this length L. Weigh a small dish; pour into it the mercury from the tube ; weigh the whole, and compute the weight of the mercury alone. Call this weight W. Then if J* = specific gravity of mercury, f the number of cu. cm. contained in length W L is -p and the volume in the tube, per W cm. of length, -ry . Put this down, B ir|i=E:jl- labelled "Volume per cm. in tube." It is best to repeat this several times and use the average values obtained. FIG. 79. Next, draw a small globule of mercury about 1 cm. long]; into the tube, and get it near E by gently inclining the tube and keeping the finger over one end. This is used as an index. Attach the tube at E, and read the position of the inner end of the index on the scale F. Before reading it is advisable to tap gently with a pencil on the tube over the index, as the index is liable to catch a little. If now the water in B is at 0, add a little warm water to it, and stir thoroughly with the thermometer until a rise of one or two degrees in temperature takes place. As the gas in 4 increases in bulk the index will move out on the scale. When the index has assumed a constant position after tap- ping, and the thermometer is also constant (at t), the dis- * This sign is called delta. f Say 13.6. \ The tube must be dry, and also the mercury, end of the meniscus, Read from the 148 HEAT. tance moved by the index represents the increase in volume A of a cu. cm. of gas heated from to t. From these data calculate what decimal of its bulk at a gas increases per degree centigrade. Put this down, carried out to the fourth decimal place, and label it " Coefficient of Expan- sion." Add ice to J9, and repeat experiment several times with different temperatures (t). Kecord results as follows : Volume of gas taken = Vessel weighed TABLE I. Trial. Length Mercury Col. Wt. Mercury Col. Vol. Vol. per Cm. Average volume per cm. = TABLE II. Index read atO. Index read at< Distance moved by Index. Volume corresponding Coefficient of Exp. for 1. Average value of coefficient = A Second Method. The apparatus is shown in Fig. 80. The tube & is closed at one end, and contains a drop of mercury, g, to serve as an index. The air whose expansion is to be measured is contained between the closed end of the tube and the index. This tube passes through a cork in one end of a larger tube, aa, which is provided with an inlet tube T, and an outlet tube T. The gas can be cooled to by filling the large tube with ice- water, and EXPANSION OF A GAS AT CONSTANT PRESSURE. 149 heated to 100 by running in steam. By measuring the movements of the index, the coefficient may be calculated, as in the preceding experiment. \Jc 11 FIG. 80. EXPERIMENT 2. Apparatus. Special form as shown in Fig. 80. Flask and con- nections; ring-stand; gauze and burner; ice- or snow-water; funnel, and vessel to hold ice-water; meter-stick. OBJECT. To determine the cubical coefficient of expan- sion of a gas at a constant pressure. MANIPULATION. Run steam into the large tube act. As the index is forced out, push the tube in, keeping the inner end of the index just inside the outer edge of the cork. When the index remains stationary after tapping with a pencil, measure the distance from the inner end of the index to the outer end of the tube. Disconnect the stearn, allow the apparatus to cool for a moment, and then connect the large tube with a funnel, and run ice-water through until the index again comes to rest, when kept just outside of the cork as above. After tapping again, measure the distance from inner end of the index to the outer end of the tube. Eemove the tube and measure the distance from its open end to the inner side of the closet end. Record results as follows: Dist. index from end of tube at 100 = te (t tf t( a (t * y. A good illustration of this is where a carriage is pulled by a ~^ y span of horses. In this case it FIG. 87. is evident that the two forces have different points of application, and that the resultant has a still different point. Forces applied in this way are called parallel forces. To investigate the case of parallel forces the apparatus shown in Fig. 88 is used. By pulling dowi on the balances B and (?, parallel forces act on the meter-stick, and the combined pull of the two is taken by balance A. The readings of B and C give the magnitudes of the components, and the reading of A the magnitude of a force which is equal and opposite to the resultant (as in Ex. 3), and whose point of application is the same as that of the resultant. With these data we can investigate the relations, as regards magnitude, point of application, etc., of parallel components and resultant. EXPERIMENT 1 . Apparatus. Three 24-lb. balances; meter-stick; fish-line; means of suspending meter-stick (the whole arranged as in Fig. 90). OBJECT. When two parallel forces act on a rigid body, to determine (1) the relation of the resultant to the com- ponents in magnitude and direction; (2) the position of the point of application of the resultant with reference to those of the components; (3) under what conditions equi- librium may be obtained; and (4) under what conditions the body tends to rotate. PARALLEL FORCES. 167 MANIPULATION. The readings of B and (7, Fig. 88, when forces are applied will not represent the true forces, because the balances themselves weigh something, and alone FIG. 88. exert a slight downward pull. To correct for this error, detach the apparatus from the balance A, slip the loops of string off from the meter-stick, and weigh balances B and G on A. Take half the weight so obtained as the weight of one balance.* Again, since balance A has to support the weight of the meter-stick in addition to the forces used, the weight of the meter-stick must be found. Remove balances B and G from A, suspend the meter-stick alone, and record the reading of A. Since this reading also gives A's increased reading due to the zero, error, we have the total amount to be subtracted from each subsequent read- ing in order to get the true force exerted on A by the com- bined pulla of B and G. When ready for work, the table of errors should stand something like this: Correction for weight, B .... G. . . .A . . . . " to zero, B....C Record on which side of the pointer the readings were taken. Slide the loops of the strings from B and G to such * These weighings could be still better performed with a 04-02. 168 DYNAMICS. points on the stick that the distance of each loop from the centre is over 10 cm. Pull down steadily on the two lower balances, being careful to pull vertically, until each balance reads more than five Ibs. Read the three balances, and note the direction of balance A. Place the loops at different points on the stick, and try again. Try a case where the distance on one side is twice that on the other. Try a case where the distances are both alike. Try other cases, mak- ing six in all. Great care must be used in reading the balances as accurately as possible, and always from the side of the pointer used in getting the readings for errors. Tabulate the results as follows : TABLE I. Read. A. Read. B. Dist. B. Read. C. Dist. C. Direc. A. Trial. While you have equilibrium, increase the pull of one balance. Note what happens. Decrease, and note again. CALCULATION'. The balance-readings have three errors for which corrections must be made: (1) Owing to use, tlje balances all read high; (2) A reads high because of the weight of the apparatus; (3) The readings of B and show the forces applied less the weight of the balances them- selves and their zero-errors. Correct A by subtracting total weight-error. Correct B and for zero-error, and add their-weight. Record the results as follows, giving cor- rected readings: TABLE II. Read. A. Read. B. Read. C. Dist. B. Dist. C. CxDc BXDb The values obtained by multiplying the magnitudes of parallel forces by their " leverage/' that is, the distance of THE INCLINED PLANE. 169 the point of application of each force from the same point of reference, as G X Cd, Fig. 88, are called the moments of the forces. QUESTIONS. 1. Can you see any relation between A, B, and O as regards (a) direction; (b) magnitude? 2. Is anything noticeable on comparing the moments of B and C for each case ? 3. Can you make out any relation between B and Db that also exists between C and DC ? 4. When the stick is at rest, how do the moments of B and C com- pare? 5. When the moment of one force was made larger than the other, by suddenly pulling down on one balance, what happened ? 6. Can you name a case in which the principle of this experiment is used ? EXERCISE 5. THE INCLINED PLANE. Preliminary. We know that machines enable us to make a small force overcome a greater one, but do they save work ? When a force is overcome by the aid of a ma- chine, is any less work done than when the force is over- come directly ? For example, if a weight is lifted directly 10 ft., or lifted the same distance by a machine, is the work done in the former case any more than that done in the latter ? To answer this question, we may raise a known weight a known vertical distance by means of a machine, say an inclined plane, and compare the work done in this case with that done in lifting the body vertically the same distance. For this purpose the apparatus illustrated in Fig. 89 may be used. The board B forms the inclined plane, and may be set at any angle by adjusting the rod R of the support S. The weight to be raised is the loaded carriage (7, and the force required to pull it up the plane may be obtained from the reading of the balance B. We can get the work done in raising the body vertically by multiplying the total weight of the body by the distance it 170 DYNAMICS. is raised (say db in the figure), and the work done in rais- ing it by the plane by multiplying the force required to pull FIG. 89. the body up the plane by the distance that, it must travel on the plane, cb in the figure, to reach the required height. EXPERIMENT. Apparatus. Board of Exercise 2; support; weighted carriage; 24 -Ib. balance; cross-stick and cord; meter-stick; T-square or plumb-line. OBJECT. 1. To study the laws of the inclined plane. 2. To see if a machine, taking the inclined plane as an exam- ple, saves work. MANIPULATION. Get the weight of the carriage and load together.* In case no suitable scales can be had, the weight may be found with sufficient accuracy by means of the spring-balance. Adjust the support so that the board B is inclined at an angle of about 30 degrees. Hook the balance into the loop at the end of the cord connected with the carriage. Let one student hold the balance firmly in both hands, and draw the carriage up the plane at a uni- form rate of speed. The back of one hand should rest on the board upon which it slides, and his entire attention should be devoted to holding the balance firmly, and pull- ing the carriage at a uniform rate. He should pull exactly parallel to the plane, and hold the balance so that it will not bind, keeping his eyes away from the balance altogether. * This weight may be determined once for all, and marked upon the carriage. THE INCLINED PLANE. 171 Meantime let the second student keep his eye directly over the balance and. take as many readings as possible. Owing to little inequalities in the board, etc., these readings will vary slightly, and the average position of the index must be determined as accurately as possible. A number of trials should be made, the students alternating in reading the balance, etc., and different parts of the board being used. The average of these trials, after the following corrections have been made, will give very closely the force required to pull the carriage and load up the plane. The force used to pull the body up the plane is not the true force required, because a portion of it is expended in overcoming the friction of the carriage- wheels, etc. To correct for this slight excess in the reading of the balance, let the body slide down the plane at the same rate of speed at which it was pulled up, reading the balance as before. When the necessary correction for the zero error of the balance has been made, the average of the two readings will be very nearly the true force required. Carefully measure the distance the body must travel on the board for a vertical rise of one foot, ab in the figure, or any vertical distance suitable to the apparatus. If a " T-square " can be obtained, the vertical rise taken may be marked off upon one side of it, starting from the outer edge of the cross-piece. The T-square is then placed ver- tically upon the table resting against the board, as shown in Fig. 90, and slid along until the mark indicating the vertical distance coincides with the lower edge of the board. The distance from this point to the lower cor- ner of the board is the length of the plane to be measured. If no T-square is available, a plumb-line of the required length may be FlG dropped from the lower edge of the board and slid down 172 DYNAMICS. until it just touches the table. The method with the T- square is the best. Change the angle of the board and repeat the experi- ment. Tabulate results as follows: TABLE I. Approx. Angle of Board. Up-force. Down-force. Vertical Rise of Body. Distance on Plane. CALCULATION. From the results of Table I, calculate and arrange the data under the following headings, where W= the weight of the body, F = the true force required to pull the body up the plane, Dv = the distance the body was raised vertically, and Dp = the distance the body moved on the plane for this vertical rise. TABLE II. w. F. Dv. Dp. QUESTIONS. 1. What effect has the angle of the board on the force required to pull the body up the plane ? 2. What effect has the angle of the board on the distance the body must travel on the plane for a given vertical rise? 3. Can you make out any relation between JFand F that also exists between Dv and Dp ? 4. Calculate for each case the work done in raising the body the given ver- tical distance, say 1 ft., and the work done in raising it the same distance by means of the plane.* 5. Can any rela- * In the first case, this equals and in the other Fx Dp. These may be calculated in any units of work, but the same units must be used in each case. Compare the values so obtained. THE WEDGE AND THE SCREW. 173 tion be made out between the work done in raising a body a certain distance vertically and the work done in raising it the same distance by the plane ? Does this hold for more than one angle of the plane ? 6. Does the machine save work ? (i.e., is less work done when the plane is used than when the body is lifted vertically?) 7. How does the machine help you ? EXERCISE 6. THE WEDGE AND THE SCREW. Preliminary. In the following exercise it is desired to discover whether the facts just observed also hold when the force used to draw the body up the plane is applied parallel to its base, as in the wedge and the screw, instead of to its length, as in the inclined plane. For this purpose the same apparatus may be used, the force being applied by pulling the balance parallel to the table instead of to the board. EXPERIMENT. OBJECT. 1. To study the laws of the wedge and screw. 2. To see if the inferences drawn for the inclined plane will hold for the wedge and screw. MANIPULATION*. Attached to the front of the carriage, C, Fig. 89, is a stick long enough to extend beyond the support at both sides. A second stick of the same length is connected with the first by cords, as shown by dotted lines, and the balance is attached to the centre of the second stick. As the connecting cords pass outside of the support, the body can be pulled up and down the plane without difficulty, by a force parallel to the table. Let one student hold the balance in both hands, face up, and pull the carriage up the plane, keeping the strings parallel to the table by raising his hands as the body rises on the plane. A second student should stand a short distance away, where he can see if the pull is actually parallel to the 174 DYNAMICS. table. The students should alternate in reading the bal- ance. Make the observations, records and corrections, and answer the questions, as in Ex. 5. EXERCISE 7. LAWS OF THE PENDULUM. Preliminary. The apparatus used in this exercise is s' shown in Fig. 91. Near the edge of the support S (which may be the edge of a table or R shelf) is screwed a spool S'. The screw is " set up " until the spool turns with considerable friction. A string is wound around the spool and is held in place by pass- ing through the slot of a screw, R, inserted horizontally in the edge of the support. The lower end of the string passes through a hole in a metallic ball B which forms the pendulum-bob. The length of the pendulum may be varied by turning the spool so as to wind or unwind the string. Small adjustments are best made Fro. 91. by gently turning the spool. EXPERIMENT. Apparatus. Two iron balls of different sizes, or iron, and wooden balls; apparatus for suspension (screw, spool, fish-line); callipers or rectangular blocks to get diameters; meter-stick; time-piece. OBJECT. To determine the effect on the number of vi- brations of a pendulum, of (1) length of arc, (2) length of pendulum, (3) weight of bob. MANIPULATION. Part 1. Length of arc. Make the length of the pendulum about 50 cm. Count the number LAWS Off TBB PMDVLUM. 175 of vibrations it makes in two minutes when swinging through an arc of not over 30 cm. Increase the arc to, say, 60 cm., the length of the swing being estimated by the eye. Determine as before the number of vibrations in two minutes. Compare the number of vibrations a minute in each case and draw your inference. Record the results as follows : TABLE I. Arc. No. Vibrations in 2 min. No. Vibrations per min. Long Short From the observation of the data, infer the effect of length of arc. Part 2. Length of pendulum. Observe the general ef- fect of changing the length of the pendulum. Eecord your observations and inference in general terms. To make the quantitative determination, we must com- pare the number of vibrations in equal times of pendulums of different measured lengths. The length of the pendu- lum is the distance from its centre of gravity to its point of support. The string having practically no weight, the centre of gravity of the pendulum corresponds with that of the ball, and is in the centre of the ball. To find the length of the pendulum, therefore, we must measure the distance along the string from the lower edge of the screw to the top of the ball, and add to it half the diameter of the ball. Place the lower end of the meter-stick on top of the .ball, and bring its graduated edge up to the string. Measure the distance to the edge of the screw three times, reading to millimeters. The average of these three read- ings will probably be nearly correct. Get the diameter of the ball, where the hole is, by placing it between the jaws 176 DYNAMICS. of the callipers and then applying the callipers to the scale. Repeat three times and average.* The length of the string plus half the diameter of the ball is the length of the pendulum. Set the pendulum swinging through an-arc of about 4 ins. Measure the number of vibrations in 1, 2, and 3 minutes. Reduce the length of the pendulum about half, measure exactly, and repeat the counting. Record results as follows : TABLE H. Length of String. Av. L. of String. Diam. of Ball. Av. D. D 2' True Length. No.Vib. Time. Av. No. Vib. Part III. Weight of the bob. Substitute for the ball on the pendulum a larger ball. Carefully determine the diameter of the second ball, as before. Make the length of the string such that the length of the pendulum is the same as before, i.e., the length of the string plus the radius of the ball equals one of the lengths used in Part II. De- termine the number of vibrations in 1, 2, and 3 minutes as before. Record as in Part II. Compare the average num- ber of vibrations per minute with that of similar length in Part II. CALCULATION. Divide the smaller length in Part II by the larger. Divide the smaller number of vibrations by the larger. Compare the ratios so obtained. If they do not agree, try squaring or cubing one of the ratios, and find the values approximating most closely. Infer the law, and ex- press it as a formula. * Or use the method given in notes on Mensuration. ACTION AND REACTION. 177 EXERCISE 8. ACTION AND REACTION. Preliminary. In this exercise we experiment with two bodies by giving them various amounts of energy and allowing them to collide. The special point of the experi- ment is to compare (1) the energy possessed by each body before and after the collision, (2) the energy lost by one with that gained by the other, and (3) the results of trying elastic and non-elastic bodies. The apparatus used is shown FIG. 92. in Fig. 92. Two ivory balls, A and B, are so suspended that they can swing in one plane only, and will collide at the lowest point of their arc. They may be drawn aside any desired distance and held there by the electro-magnets CC, and released by breaking the circuit. The distances 178 DYNAMICS. they are drawn aside may be read on the scale by aid of the cards bb. The momentum in each case is taken as the product of the weight of the ball multiplied by the distance it moved. EXPERIMENT 1. Apparatus. Two ivory balls; No. 30 wire; electro-magnets; board; two meter-sticks; electric current; circuit-breaker; tacks; made into apparatus as shown; scales and weights (if balls are not of known weight). OBJECT. To compare (1) the algebraic sums of the ener- gies possessed by two bodies before and after collision, (2) the results of trying elastic and non-elastic bodies, (3) the direction of the action and reaction, (4) the energy lost -by one with that gained by the other. MANIPULATION". A little adjustment of the magnets as regards their position in the plane of oscillation will enable the student to release the balls so that they will strike squarely upon each other. By means of the index-cards cc, determine on the meter-stick the position of the balls when at rest. One ball being at rest, place the magnet so as to hold the other ball about 10 or 15 cm. aside. Kead the position of this ball by the index-card b. Break the circuit, thus allowing one ball to strike the other, and notice the dis- tance traversed by each ball after collision. Place an index- card at each of these points, and repeat the experiment. Sighting across each index, note the exact position reached by the centre of the corresponding ball, and place the index at this point. Try again until each index marks the exact position reached by centre of the corresponding ball after collision. As the magnet remains in the same place all the time, the distance traversed by the ball before collision is always the same, and need not be measured again. Follow- ing this method, try the following cases, calling the small ball B y and the large ball A : Case 1. A in motion, B at rest. Try two cases, and re- peat with B in motion and A at rest. ACTION AND REACTION. 179 . Eelease both balls at once. Try covering one ball with a thin layer of putty. The weights of the balls should be determined in each case. Compare the momenta before and after collision in each case. Distinguish between the behavior of elastic and in- elastic substances under these circumstances. In calculat- ing the momenta, call the movement towards the right hand -f, towards the left hand . Tabulate results as follows : Weight of A... Weight of B.... l . tra ter c ed coll From the above data calculate the momenta before and after collision in each case, being careful to keep the proper signs. Arrange results as follows : Case 1. Momentum of A before collision = " " A after " = " B before " = " B after " = Algebraic sum = From these data answer the questions given in the object. SUBSTITUTE EXPERIMENT. Apparatus. Two pint tin pails, suspended and adjusted as shown; heavy bodies to load pails; cotton string; candle; two meter-sticks; coarse scales. OBJECT. (1) To compare the values of action and re- action when two bodies are acted upon by the same force, and (2) to study the effect of varying the weight of the bodies, 180 DYNAMICS. MANIPULATION. Set up the apparatus as shown in Fig. 93. Call the pail with the spring A, and the other B. Detach B from the wires, and make it weigh 250 grams (cover on). Compress the spring and tie it with a string.* FIG. 93. In the same way make A weigh 500 grams. Attach both the pails to the wires, being sure that they hang vertically. Holding the eye directly above the outer edge of each pail in turn, read its position on the meter-stick underneath, and record. Now place a meter-stick under the edge of each pail, and burn the string. As the pails swing out keep a pencil directly under the outer edge of each one, and stop them at the extreme point of the swing. While the pails return, hold the pencils steady at these points, read their positions on the meter-sticks, and record. Re- peat three times; then make pail B 500 grm., and try again, say three times more. If possible, try again with 750 grm. Tabulate results as follows : * It is a good plan to hold the hand between the pails when they come together, so that they will not strike each other with a heavy blow. THE FORGE OF TENACITY. 181 TABLE I. Wt. A. Wt. B. Read. A at rest. Read. B at rest. Read. A at end of swing. Read. B at end of swing. From the data in Table I calculate the following table: TABLE II. Wt. A. Wt. B. Dist. A moved. Dist. B moved. Wt. A x Dist. A. Wt. B x Dist. B. QUESTIONS. 1. Can any relation be made out between the weights of the pails and the distances that they moved ? 2. What relations appear between the numbers in the last two columns in Table II? 3. Calling w and W the weights of the two pails, and d and D the distances moved, can the results be expressed as a formula ? 4. Can any law be inferred for the relation of action and reaction re- garding (a) direction, (b) extent of motion ? EXERCISE 9. THE FORCE OF TENACITY. EXPERIMENT. Apparatus. Wire of two sizes and two materials; half -spool screwed to table; 24-lb. spring-balance; meter-stick. OBJECT. To study the effect of length, cross-section, and material on the force of tenacity. MANIPULATION. Part I. Effect of Length. Pass one end of the wire twice around the half-spool with a "round turn," making it lie close to the spool all the way; then twist the end of the wire around its main part, as 182 DYNAMICS. indicated in Fig. 94. FIG. 94. The spool is screwed to the table. Cut off the wire about one meter from the spool, and attach the end to the balance-hook, precisely as shown in Fig. 94. Ex- amine the wire to make sure that it is free from " kinks/ 7 and measure its length. Then, holding the balance hori- zontally in the palm, move the hand along with its back on the table so as to produce a steady pull on the wire. Steadily increase the pull until the wire breaks, meantime watching the index of the balance all the time so as to know where it stands when the wire breaks. The first trial will tell about what part of the scale to watch in sub- sequent trials. Make four trials besides the first, and try to read to lb., especially in the third and fourth trials. Take a different length for each trial, and record the length of each piece. Part II. Effect of Cross-section. In the same manner determine the tenacity of the second size of wire, making four trials. Part III. Effect of Material. Determine in the same way the tenacity of the wires of different material, making four trials. Tabulate results as follows : No. Trial. Length of Wire. Cross-section. Bk.Wt. on Bal. Correct Bk.Wt. The values in the last column are the balance-readings corrected for zero and position errors. QUESTIONS. 1. Can you make out any relation between length and tenacity ? 2. Between cross-section and tenac- ity ? 3. Has material any effect ? 4. What cross-section THE FORCE OF ELASTICITY. 183 E of one wire would give the same tenacity as another wire of different cross-section and material ? EXERCISE 10. THE FORCE OF ELASTICITY. Preliminary. A body whose shape has been changed by the action of a force is said to be distorted. A body which tends to take its former shape when distorted is said to be elastic. The force with which a distorted elastic body tends to resume its original shape is called the force of elas- ticity. A body which may be considerably distorted with very little force is said to be very elastic, or to have low elasticity. Rubber is an example of low elasticity. A body which gives considerable force of elasticity on small distor- tion is said to have high elasticity. Steel is an example of high elasticity. The following exercise investigates the effect of (1) degree of distortion, (2) cross - section, and (3) length on the magnitude of the force of elasticity in a solid. For this purpose the apparatus in Fig. 95 is used. The rubber strip S is fastened at its upper end, and may be stretched (distorted) by weights placed in the scale-pan E, which is attached to its lower end. Since, after the strip has stretched and is at rest, the up pull due to the elasticity of the rub- ber, and the down pull due to the weights, must be equal, the weights measure the force of elasticity. The total amount of distortion is measured by reading the position of the point a on the meter-stick, by means of the reading-card C. The distortion of two lengths, one twice the other, may be compared by reading first from the point a, and then from point b. The position of FIG. 95. 184 DYNAMICS. the card C may be changed by slipping off the rubber bands RR, and sliding it along the meter-stick. EXPERIMENT. Apparatus. Apparatus for the experiment as shown ; weights 10 to 200 g. ; screw -driver. OBJECT. (1) To see if any relation can be found between the amounts of distortion of an elastic body and the cor- responding magnitudes of the force of elasticity. (2) To observe the effect (a) of cross-section, (b) of length. MANIPULATION. Part I. Adjust C so that the upper edge of the card touches the lower edge of the mark a on the rubber strip. Hold it there by hand or by the rubber bands, and read and record the position of the upper edge of the card on the meter-stick. Gently place 20 gr. on the scale-pan, and after the strip has come to rest, again adjust C, and read the position of a and record. Eepeat with 40 gr. in the pan, and so proceed for ten readings in all (up to 200 gr.). Eecord as follows: Weight used. Position of a. Distortion of S.* Part II. Eepeat Part I, reading from b, and record in the same way. Part III. Detach the strip used in Part II, and substi- tute the wide one. Eepeat with this strip. When read from the mark upon it, this gives the same length and cross-section as the one in Parts I and II. QUESTIONS. What effect have length and cross-section ? 2. Are all bodies equally elastic ? (Answer from your gen- * The position of a for each weight minus that for no weight. BOYLE'S LAW. 185 eral knowledge.) 3. What conditions have you found to affect the magnitude of the force of elasticity ? Plot a cure from the data of Part I. EXERCISE 11. BOYLE'S LAW. Preliminary. We know that when pressure is exerted on a confined volume of gas its volume becomes less, and that when the pressure is diminished the volume increases. In the following exercise we wish to see if we can find any relation between different pressures and the corresponding volumes.* The apparatus used is shown in Fig. 96. A glass tube, ab, is bent as shown. The short arm is closed at the top, the long arm open. The gas to be experimented upon is confined at b in the short arm by pour- ing mercury into the long arm. The pressures can be changed by using different depths of mercury, the volume of gas can be read on the scale d, and the depths of mercury on the scales d and e. The two cards ff help in reading the levels. As we know from the laws of liquid pressure, the depth of mercury causing the pressure will be the difference in the heights of the two columns; and since the atmospheric CZ pressure is exerted on the top of the column in , the total pressures will equal the FIG. 96. Suggest a method for such an experiment. 186 DYNAMICS. height of mercury, causing the pressure plus the height of the barometer, whose reading must be known. Since changes of temperature affect the volume, the tempera- ture must be practically uniform during the exercise. EXPERIMENT. Apparatus. As shown (tube; support; scales; reading-cards); about 500 gr. mercury (clean and dry); barometer; feather and rod to remove air. OBJECT. To discover some relation between the volume of a confined body of gas and the pressure exerted upon it. MANIPULATION". Eead the barometer. (See the card of instructions tacked over the instrument, with instruc- tions for reading vernier, etc.) The barometer reads in inches; as the other readings will be in centimeters, con- vert the barometer-reading to centimeters by the following formula : Bar. -read, in inches ^ , . ~ Bar. -read, in cm. Eead the thermometer. Place the glass funnel (be sure that it is clean and dry) in the open end of the long arm, and carefully pour in mercury until the bend is cov- ered and the mercury stands two or three cm. higher in the long arm than in the short arm. Tip to the left the appa- ratus as it stands in Fig. 96, and allow some air to escape from the short arm; place the apparatus upright again, note the levels, and, if necessary, repeat until the mercury stands at about the same level in both arms. If the level of the mercury in the short arm is still below the upper edge of the horizontal part of the tube, add a little more mercury. If too much air has been allowed to escape, tip the apparatus to the right and let some air run in. Work- BOYLE'S LAW. 187 ing in this way, get the level of the mercury in the short arm above the curve, and the mercury in the long arm from 1 to 3 cm. higher. Then read the position of the top of the meniscus of each mercury-column on its scale. Place the funnel again in the top of the tube, and carefully pour in 'ercury until the level of the column in the long arm has m raised about 15 cm. Eemove the air-bubbles and ,ain read the heights in both arms on the scales. With uae same precautions add another 15 to 20 cm. height to the long-arm column. Again read the levels. So proceed till the difference in the levels of the columns in the two arms is about 75 to 85 cm. Again read the barometer, and if you find any difference in the barometer-readings before and after these operations, use the average of the two. Read the thermometer, and if you find a small change in temperature, average the readings; if a large change, report the fact at once. During the progress of the experiment, watch the thermometer and note any change of tempera- ture. Now you have the following data : (a) Barometer-reading before and after. (b) Thermometer-reading before and aftei (c) Levels of mercury in the short arm. (d) " " " " " long " Arrange (c) and (d) in a table as follows: TABLE I. Height in Short Arm. Height in Long Arm. No. Trial. 188 DYNAMICS. CALCULATION. Arrange the results of the calculation in a table of five columns, as follows : TABLE II. Volumes. Pressure. Whole Press. Ratios of Vol. Ratios of Press. The figures in column 1 are obtained from the card attached to the apparatus, the volumes in cubic centi- meter corresponding to each reading on the short-arm scale, The higher the number on the scale the less the volume of air represented. The figures in column 2 are obtained by subtracting the readings of the short arm from those of the long arm. The figures in column 3 are ob- tained by adding to each number in the second column the height of the barometer in centimeters. This gives the total pressure of mercury in centimeters. The figures in column 4 are obtained by dividing each volume in turn by the smallest volume. The figures in column 5 are obtained by dividing each pressure (column 3) in turn by the small- est pressure. Carry out both these ratios to the second place of decimals. QUESTIONS. 1. Is there any law as regards the ratio of the volume to the pressure of a gas, the temperature being constant ? 2. If so, what is it ? 3. Why read the barome- ter twice ? 4. Why read the thermometer twice ? 5. What keeps the mercury from completely filling the small arm ? 6. Is it of the nature of a push? 7. Is it a force? 8. What is the name of that force ? 9. In this experiment what is the stress? 10. In this experiment what is the strain? 11. What sort of elasticity has a gas ? 12. What princi- SPECIFIC GRAVITY WITHOUT SCALES OR WEIGHTS. 189 pies, learned in previous experiments, have you made use of in this one ? Plot a curve from the data. EXERCISE 12. SPECIFIC GRAVITY WITHOUT SCALES OR WEIGHTS. EXPERIMENT 1. Apparatus. Suspended meter-stick; two stones or other bodies of about equal weight; cords; vessel of water. OBJECT. To determine the specific gravity of a solid by the principle of moments. MANIPULATION. Call the body whose specific gravity is to be determined A, and the other B. Suspend A about 25 cm. from end of the meter-stick, Fig. 97, having the loop of the suspending string tight enough not to slip during the experiment, Slide the weight along un- til it balances A, and note its distance from the sup- port S. Bring a vessel of water under A, and when A is completely submerge*!, and clear of the sides ana bottom of the vessel, move B until it balances it again, and note its distance from S. You have now the data for determining the specific gravity of A. CALCULATION. In Fig. 97 aS represents the weight in air, bS represents the weight in water; so aS bS or ab represents the loss of weight, and specific gravity = j-. 100 DYNAMICS. EXPERIMENT 2. Apparatus. Long spiral spring; meter-stick; clamp; body whose specific gravity is to be deter- A B G mined ; vessel of water; string or wire. OBJECT. To determine the specific gravity of a solid body. MANIPULATION. Note length of spring, with sus- pended wire only attached, Fig. 98, 0. Attach the body to the lower end, as in Fig. 98, A, and record the length of spring. Bring the vessel of water under the body, immerse the body with the usual pre- cautions, and again record the length of the spring B. CALCULATIONS. Reading of reference-marks : Spring alone = With body attached = Body immersed = ac represents wt. in air. ab " " " water, and ac ab represents loss of wt. in water, and Specific gravity = PIG. 98. ac _ ac ac ab be In same way find specific gravity of some liquid. LIGHT. EXERCISE 1. FOCI OF LENSES. Preliminary. When the light from a luminous body passes through a double convex lens, the point at which all the light is concentrated is called the focus of the lens. The distance from the centre of the lens to the focus is called the focal length. The following exercise investigates the effect on the focal length of the distance of the object from the lens. The apparatus shown in Fig. 99 is used. s ^ <0 A JUJ-L ^uuu^ fZ FIG. 99. For the luminous object near the lens we use a light A, represented as a candle mounted upon a block C", which slides upon the meter-stick M. The lens L and the screen 8 are similarly arranged. The position of the lens can be so adjusted that the image of A falls on S when A is at different distances from the lens, and the distances AL and L8 can be read on the meter-stick. EXPERIMENT. Apparatus. As in Fig. 99, so arranged that an image of an object at a considerable distance may be obtained. OBJECT. To study the effect of the distance of the ob- ject from the lens on its focal length. 191 192 LIGHT. MANIPULATION'. Bring the outer ends of blocks C and G" even with the ends of the meter-stick. Light A, place it in the centre of block C", and move the lens to a point about 20 cm. from A. Slowly slide the block G' towards S until a position is found which gives a sharp image of A on the screen. Eecord the readings of the right-hand sides of S and D and of block C" (in this case, 0). Move the lens towards 8 until the image is lost, then slowly move it back towards A until a sharp image is again obtained, and take the reading of D as before. Gently slide block C" 10 cm. nearer the lens, and repeat. So continue at in- tervals of 10 cm. until an image can no longer be obtained. To test the case when the object is as far from the lens as possible, extinguish the light and remove it, together with block C". Arrange the rest of the apparatus so that the light from some distant object * can pass through the lens and fall upon the screen. Find as above the position of D that gives a sharp image. Kecord as follows: TABLE I. Bead, of 8. Read, of D. Read, of A. R. L. Av. In the first and third columns place the readings of right- hand sides of C" and 8, respectively. In the second col- umn R and L are the readings of the right-hand side of D when moved from the right or from the" left to the posi- tion giving a sharp image. QUESTIONS. 1. Is the distance of the lens from the * The distance of this object, which should be over 30 meters from the lens, should be recorded, whether measured or estimated by the eye. FOCI OF LENSES. 193 screen the same whatever the distance of the luminous object from the lens? 2. What other inferences can you draw from the results of the experiment ? When the object is so distant that the rays of light from it are practically parallel where they strike the lens, as in the case of the distant object in the experiment, the dis- tance from the centre of the lens to the image is called the true focal length of the lens. When the object is so near the lens that the rays of light are not parallel, this distance is called the conjugate focal length. CORRECTIONS. In order to make any exact comparisons, it is necessary that the true positions of A and of the lens should be determined. To get the true position of A, add one half the length of block C" to the readings of A in Table I. For the position of the centre of the lens add one half the width of the board D to the average readings for D in the same table. Eecord as follows : TABLE II. True pos. A. True pos. L. Pos. 8. Dist. AL. Dist. LS. CALCULATION. Taking the first case, express the frac- tion -r-j as a decimal carried out to four significant fig- ures. Express the fractions ^-^ and ^ T -^ - * in the LS Focal length same way. Do the same for the other cases. Tabulate as follows : * As obtained in the trial with the distant object. 194 LIGHT. TABLE in. 1 1 1 AL Ta Sum of the two. F.L. QUESTIONS. 1. From the study of Table III can you make out any relation between the distance of the object from the lens (AL), the conjugate focal length (LS), and the true focal length of the lens ? If so, letting F true focal length, /= conjugate focal length, arid D = the dis- ance of the object from the lens, express your inference as a formula. EXERCISE 2. DISTANCE AND INTENSITY OF LIGHT. Preliminary. By the intensity of light is meant not the brightness of the source of light itself, as a lamp-flame, white-hot carbon, etc., but the degree to which its light illuminates a given body. It is a well-known fact that the illuminating power of a light decreases as the distance of the illuminated body from it increases. The light from a large lamp and from a candle may be of equal intensity if the il- luminated body be much nearer to the candle than to the lamp. The following exercise investigates the effect of dis- tance on intensity of light, with a view to seeing if any fixed relation can be made out between them. In order to do this, we determine the distances at which lights of different known powers give light of the same intensity. For this purpose we use an instrument called a Bunsen Photometer, whose operation is based upon the fact that when a piece of paper having a paraffin e spot in the centre is equally lighted on both sides, the spot can no longer be seen. The form used is shown in Fig. 100. The lights are placed upon the DISTANCE AND INTENSITY OF LIGHT. 195 blocks C and E and the paper upon the block B. All the blocks slide upon the meter-stick. For lights of different intensities we use different numbers of candles, assuming that two candles give twice as powerful a light as one. Taking lights of different intensities, and finding the dis- Fia. 100. tance from each light to the paper when the paper has been placed so that the spot in its centre is no longer visi- ble, we have the distances required for the different lights to give the same degree of intensity. EXPERIMENT. Apparatus Bunsen photometer, as in Fig. 100; 5 candles, 3 or 4 in. long; matches; scissors for trimming candle-wicks. OBJECT. To see what relation exists between the intens- ity of a light and its distance from the lighted object. MANIPULATION. Arrange blocks C and E at the ends of the meter-stick, as in the preceding exercise. Place one lighted candle on the block C and one on block E. Move the block B towards G y , watching it from that side until the spot shows plainly; then slowly move it away until the spot just disappears. Have the eye about level with the spot, and the line of sight at an angle of about 30 with the meter-stick. If possible, shield the eye from the direct light of the candles by card-board screens. Head the position of the right-hand side of D. Next looking at A from the left-hand side, move B within 20 cm. of E\ then back towards C until the spot just disappears. Ee- cord the reading of D. Move B within 20 cm. of C, and again determine the position where the spot is invisible when looked at from the right-hand side, as in the first case. Working in this way from each side alternately, 196 LIGHT. make about ten readings in all. During the operation keep the candle-flames burning evenly, trimming the wicks if necessarj 7 .* In order that the effect of a variation in flame may be still more reduced, it is advisable to change the candles end for end of the apparatus, moving blocks and all. If this be done, take twelve readings in all. Repeat these readings first with two and then with four candles on C, setting the candles about 1 cm. apart in a line at right angles to the length of the meter-stick. Tabulate results as follows: TABLE I. Reading of B. Pos. of Centre of L. Pos. of Centre of L'. R. L. Av. CALCULATION. The readings for B are practically cor- rect. The positions of the centres of the candles are found as in the preceding exercise. Record corrections as follows: TABLE II. Inten. of L.t Inten. of Z/.t Dist. LD. Dist. L'D. The numbers in the last two columns are the distances from the centres of the candles to D. QUESTIONS. 1. How would the distances compare if nine candles were used ? Sixteen ? Twenty-five ? 2. Can you make out any uniform relation between the distances * To protect the caudles from draughts, lamp-chimneys may be placed over them, supported, of course, so that air may enter from the bottom. f That is, number of candles used in each case. RADIATION OF LIGHT. 197 and the intensities ? If so, using / and /' for the intensi- ties and D and D' for the distances, express your inference as a formula. EXERCISE 3. RADIATION OF LIGHT. Preliminary. It is generally known that light radiates, or spreads out in every direction, from a luminous point. The following exercise investigates the effect of distance from the light upon the degree of radiation. The light from a luminous body is allowed to pass through a small opening, and the degree to which it spreads is determined by letting it fall upon a screen whose distance from the light may be varied. In order that the light should radiate from as nearly a point as possible, the light is placed in a box with a small hole opposite the flame on the side towards the screen. EXPERIMENT. Apparatus. As in Fig. 99, the lens being removed and a piece of paper with a hole 2 cm. square tacked over the hole in Z>; a box fitted to hold the light; a short mm. scale; sharp pencil; some pieces of writing-paper about 3x3 in., one of which is pinned on the screen at the beginning of the exercise. OBJECT. To see if there is any uniform relation between the degree of radiation and the distance from the point of radiation. MANIPULATION. Light the candle and adjust the block supporting it so that the reading of the opening in the box through which the light passes is 5 or 10 cm. on the scale.* Place D 25 cm. and 8 35 cm. from the hole. If the light is properly adjusted, a well-defined square of light will be thrown on the screen. Holding the screen firmly, place a ruler upon it, and with a sharp pencil rule a vertical line 2 * One method of doing this would be to hold the ruler firmly against the side of the box facing the screen, and adjust so that the right-hand edge of the ruler would come on the 5 or 10 cm. mark on the meter- stick. 198 LIGHT. or 3 cm. long on the left-hand edge of the square of light, using great care to get the lines exactly on the edge. Mark the right-hand edge in the same way. Set the screen 40 cm. from the hole, and rule two more lines. So proceed up to 60 cm. from the hole. Remove the square of paper pinned on the screen, pin on a fresh square and get an- other set of lines, working back from 60 to 35. Get four sets of lines in all, working back and forth twice. Meas- ure carefully on all four pieces of pieces of paper the dis- tance between the pairs of lines obtained for each position of the screen. Record as follows : TABLE I. Pos. of Point. Pos. of Screen. Dist. between Lines. 1st. 2d. 3d. 4th. Av. v From these results calculate TABLE n. Dist. from Point to Screen. Increase. Av. Width of Square of Light. Increase. In the first column place the reading of the screen minus the reading of the left-hand side of the box. The figures in the second column are obtained by getting the differences between the different readings of the screen. In the third column place the average values obtained from Table I for the distance between the pairs of lines corre- sponding to each position of the screen, and in the fourth column obtain the differences in the same way as indicated for the second column. QUESTIONS. 1. What inference can you draw regarding CANDLE-POWER BY THE RVMFORD PHOTOMETER. 199 the relations of distance and degree of radiation ? 2. If D and D r be any two distances, and I and 1' the corre- sponding intensities, can you combine them in a formula ? Eemember that for each distance the same amount of light will spread over a surface whose area would be proportional to the squares of the width of the square of light, and that the intensity of the light will become less in proportion to the surface illuminated. EXERCISE 4. CANDLE-POWER BY THE RUMFORD PHOTOMETER. Preliminary. The unit used in comparing the light-in- tensities is called one candle-power, written c. p. Candle- power is measured by determining the distances at which the source of light to be tested, and a standard candle specified by law, give lights of equal intensity. For ex- ample, if the light to be measured and the standard candle must be at the same distance in order to give light of equal intensity, the light of required intensity would be 1 c. p. The form of photometer used in this exercise is shown FIG. 101. in Fig. 101, and is called the Rumford Photometer. Two meter-sticks MM carry two blocks LL' 9 one of which supports the standard reference-candle, the other the light to be measured, represented here by two candles. These 200 LIGHT. blocks can be moved to any position on the meter-sticks. A card-board screen 8' is placed between them, and an up- right rod R at the left-hand ends of the meter-sticks. Each light will cast a shadow from this rod upon the screen at the left. When these shadows are equally black, both lights are of equal intensity at the screen. EXPERIMENT. Apparatus. Rumford photometer as in Fig. 101; candle; light to be tested; scissors. OBJECT. To determine the candle-power of a light by the Rumford photometer. MANIPULATION. Place one candle on block L', light it, and set the block 30 cm. from the rod. Place on L the light to be tested. Allow the lights to burn for a few moments, and then move L towards the screen until the two shadows cast by the rod are equally dark. Read the position of the right-hand side of L. Move L towards the screen until its shadow is decidedly the darker (recollect that the shadows cross), then move it towards the right until the shadows are equal, and again record the reading of L. Move L' 10 cm. nearer R and repeat. Repeat again with L' 10 cm. still nearer. Record as follows: Pos. of L'. True Pos. of Candle. Pos. of L. True Pos. of Light.* Dist. from Screen to* Candle. Dist. from Screen to Light. R. L. Av. CALCULATION. Using the formula of Ex. 2, all the values are given in the table above, except the intensity of the light to be tested, the intensity of the candle L' being taken as 1 c. p. Substitute these values for each case, taking the intensity of the light to be tested as X. Average the values so obtained, and put them down as candle-power. * Distances of L and L' from rod, plus distance of rod from screen. SOUND. EXERCISE 1. CONDITIONS AFFECTING PITCH. Preliminary. The following exercise investigates the conditions affecting the pitch of the note given by the vibrating wire. For this purpose the apparatus shown in ^ VT iA^oem cA/^ ^^^^ FIG. 102. Fig. 102 is used. The wires WW of different sizes are stretched by the balances BB' f the lengths used being those between the triangular blocks CC'. In order that the tension may be the same for different lengths, a fifth block, D, may be placed under the string, the wire being pressed down on D by the finger H } as shown in the figure. Cords cc wound around nails aa hold the balances at any desired tension. EXPERIMENT. Apparatus. As in Fig. 102. Meter-stick. OBJECT. To observe the effect of (a) length, (b) tension, (c) size, on the pitch of the note given by a stretched wire. MANIPULATION. Part L The apparatus being arranged as in Fig. 102, hold balance B in the left hand, take a turn of the cord c around the right-hand nail a, steadily pull to the left on B, and at the same time pulling the cord with the right hand until B reads 8 Ibs. Eemove the left hand, and let the whole strain come upon the cord. Make the cord fast by four or five crossed turns around both nails. 201 202 SOUND. If the cord stretches so that the tension drops below 8 Ibs., the operation must be repeated. In like manner put W under the same tension. Bring D close to the left-hand block C\ measure the length of wire between D and right- hand block by laying the meter-stick on the blocks parallel to the wire. Press the finger on the wire to the left of D, as at H in Fig. 102, and sound W. Shorten W by moving D to the right, and look for positions that give the first and second octaves of the note first obtained, measuring the length in each case. Move D back to its original position, and calling the note given by W " do " on the scale, look for positions giving the other notes in the gamut. If pos- sible, carry these measurements through the second octave. Repeat, starting with a different length. Record as follows: TABLE I. Tension. Length. Note. Part II. Remove Z>, sound W, and change the length of W so that it gives the same note as W. Then find what tension on one half -length of W will give the same note as W. The note given by W is simply used as a reference ; hence the length of W need not be recorded. Shorten W 10 cm. by moving the block D, again set B at 8 Ibs., and repeat the whole operation. Do this for several lengths, and record. TABLE II. 1st Tension of W. Tension of W for same Note on 7iaZ/-length. Note that whole-length of W would give.* * See Part I. VELOCITY OF SOUftfi. 203 Part III. With a tension of 8 Ibs. on each string, and with equal length of wire, compare the notes. Do this for several lengths and tensions. Eecord TABLE III. Length W. Length W. Tension TFand W. Pitch of note. QUESTIONS. 1. Can you make out any relation between the length giving any note and that giving its octave? 2. Do the lengths giving the note on the scale bear any definite relations to the length giving the first note ? If so, what ? 3. Can you make out any connection between tension and pitch ? 4. Between size and pitch ? 5. Name some musical instruments in which these principles are used, and explain how they are applied. EXERCISE 2. VELOCITY OF SOUND. Preliminary. In the following exercise the velocity of sound is determined in two media air and carbon dioxide. The method used is based upon the fact that if a tuning- fork be sounded at the mouth of a tube closed at one end, the length of the air-column which will reinforce the sound of the fork is one quarter the wave-length. By using a fork of known number of vibrations, and finding by trial the length of air-column which will respond to the fork, the velocity may be calculated. EXPERIMENT. Apparatus. Resonant tube; tuning-fork; wash - bottle with water ; chemical generator ; marble ; muriatic acid ; meter-stick ; blocks of wood to support generator ; thermometer. OBJECT. To determine the velocity of sound, (a) in air, (l>) in carbon dioxide. 204 60VND. MANIPULATION". The tube being placed upon a firm surface, sound the fork holding it horizontally over its mouth, one prong directly above the other. By means of the wash-bottle, run water into the tube until the point of strongest reinforcement is found. When this point is ap- proached, add the water very cautiously, holding the deliv- ery-tube of the bottle close against the sides of the tube, taking care to wet the sides of the tube as little as possible. Place the meter-stick against the inner wall of the tube, and measure the distance from the level of the water to the top of the tube. Pour out some of the water and repeat, making four or five trials in all. Empty the tube com- pletely, and support the generator on blocks so that the end of the delivery-tube reaches nearly to the bottom of the tube. Pour about 20 cm. of acid into the generator and allow it to run for three or four minutes; then proceed as above. Kecord the temperature. Tabulate : Substance used. Length of air-column. Average. CALCULATION. Average separately the values of the quarter wave-length obtained for air and for carbon di oxide. By substituting these values and the number of vibrations of the fork in the formula V = No. of vibr. X 4 (length of air-col. + J- diam. of tube) calculate the velocity of sound in each medium. INDEX. ^- Numbers above 204 refer to teachers' edition. Abbreviations, metric, 59 Absorption and radiation, 150; exp. 151; app. 218; notes and ref. 268 Action of acid on bodies, exp. 17; attracted body on magnet, 4; exp. 5; notes and ref. 256; currents on magnets, exp. 25; notes and ref. 257; force, exp. 153; app. 220, 247; notes and ref. 269; magnet free to move, exp. 5 Action and reaction, 6; exp. 178, 179; app. Ill, 180, 220, 249; notes and ref. 271 Ampere's law, 27; exp. on, 25 Angular forces, composition and resolution of, 160 Apparatus, 6, 207; construction of: density and specific gravity, 242; dynamics, 247; electricity, 225; heat, 244; light, 252; magnetism, 224; mensuration, 237; sound, 254; lists of: den- sity and specific gravity, 217; dynamics, 220; electricity, 214; heat, 218; light, 222; magnet- ism, 214; mensuration, 216; sound, 222 Archimedes' principle, exp. 93; notes and ref. 261 Atmospheric pressure, exp. 107; app. 217, 243; notes and ref. Balance, 79, 217, 238, 239; spring, 82, 85, 217, 219, 220; substitute for, 247 Battery, 30; fluid, 215, 227 Binding-posts, 223; substitute, 230; English, 231 Boiling-point, exp. 126; notes and ref. 267 Boyle's law, 185; exp. 186; app. 185, 220, 250; notes and ref. 271 ; calibration of tube, 251 Breaking circuit, 29; magnets, exp. 8; notes and ref. 256 Bunsen burner, 112, 218; pho- tometer, 194 Burette, 71, 216; substitute, 237 Calibration of a tube, 146, 251 Calorie, 129 Calorimeter, 130, 218 Caudle-power, 199; exp. 200; app. 199, 222, 254 Cell: see Galvanic Cell. Cells, methods of connecting, exp. 36; notes and ref. 258 Centre of gravity, of pendulum, 175 Changing systems of units, 58 Chemical change, exp. 87; notes and ref. 261; thermometer, 117, 218 Circuit, 24; introducing into, 29 Coefficient of cubical expansion, 139; gas, exp. 146; app. 218, 205 206 244; notes and ref. 261 ; liquid, exp. 145; app. 218, 245; notes and ref. 261; linear expansion, 188; exp. 140, 141; app. 139, 142, 218, 246; notes and ref. 268 Coils of wire, 32, 214, 232 Components, 160; of angular forces, 160; parallel forces, 166 Compass, 6, 7; substitute, 214, 224 Composition of angular forces, 160; exp. 162; app. 220, 247; notes and ref. 270; parallel forces, exp. 166; app. 220, 248; notes and ref. 270 Conductors, 24; in series or par- allel, 33 Conduction of heat, 116 Conjugate focal length, 193 Constant errors, 85 Conditions affecting electrical resistance, 29; exp. 30; app. 32, 214, 232; notes and ref. 257; pitch, exp. 201; app. 201, 222, 254; notes and ref. 272 Connector, 215 Convection, 116 Cost of equipment, 207 Counterpoising, 82 Cross-section of tube, exp. 76; app. 216; notes and ref. 260 Current, electric, 20, 24; revers- er, 225 Currents, induced, 52; exp. 53; app. 52, 214; notes and ref. 259 Curve plotting, 122, 124 Density, 89; unit of, 91;0zp. 90; app. 217; notes and ref. 261; and specific gravity, app. con- struction, 242; lists, 217; notes and ref. 261 Determination of length, 59, 62; volume, 67; diameter of a sphere, 61 Diagrams, 21 Direction of current, 24 Distance and intensity of light, 194; exp. 195; app. 195, 222, 252; notes and ref. 272 Distribution of heat in a rod, exp. 114; of magnetism, 2 Dynamics, Exercise 1, 153; notes and ref. 269; construction, 247; list of, 220 Dynamo, 54; model, 233 Dynamometer,83; substitute, 247 Edison current, 208; uses of, 210 Elasticity, force of, 183; of a gas, 186 (see Boyle's law); of a solid, exp. 184; app. 183, 220, 252; notes and ref. 271; spe- cific gravity by exp. 190; app. 190, 220, 252 Electricity, 17; construction, 225; lists of, 214 Electro-magnetism, exp. 50; app. 214; notes and ref. 259 Electro-motive force, 49; exp. 48; app. 214; notes and ref. 259; standard, 49 Electric current, 20; circuit, 29 Electrical resistance, 33; exp. 34; notes and ref. 258; conditions affecting exp. 29; relative, 40 Elements of cell, 23 English units, 57; measure, 57 Equilibrium, 156 Equipment, cost of, 207; gen- eral, 223 Errors, 85 Essays, 206 Exciting fluid, 23 Expansion, suggestions for illus- trating, 265; coefficients of, 139 Field of magnet, 12 Float, 72 Focal length of lenses, 191 Focii of lenses, exp. 191; app. 191, 222, 252; notes and ref. 271 Focus of lens, 191 Force, 4, 269; action on a body, 153; composition of, 160; exp. 162, 166; notes and ref. 270; form of lines of, 15; graphical representation of, 158; measure- ment of, 157; of elasticity, in a solid, 183; exp. 184; notes and ref. 271; in a gas, exp. 186; notes and ref. 271; of friction, 207 156; exp. 156; app. 220, 247; notes and ref. 269; of tenacity, exp. 181; notes and ref. 271 Forces, direction indicated by signs, 159; geometrical addi- tion and subtraction of, 159; by algebra, 159; parallelogram of, 163; exp. 164; parallel, composition of, 166 Formula for changing system of linear units, 58, 186; cubical coefficient of a gas, 150; den- sity, 90; diameter of circle from area, 78; heat quantity, 129; latent heat, 186, 137; lin- ear coefficient of expansion, 141, 144; number grins, in an oz., 83; number ins. in a meter, 63; specific gravity by elasticity, 190; by moments, 189; of li- quids, 93; by balancing, 104, 106, 109; of solids, 97, 98; specific heat, 132, 133; work (inclined plane), 172 French units, 57 Friction, force of, 156 Galvanic cell, 23; diagram of, 24; direction of current in, 24; construction of, 214, 227, 236 Galvanometer, 27; construction of, 215, 229; diagram of, 28; precautions, 28; sensitive, 215, 231 Gas, temporary piping, 211 Gases, elasticity of (see Boyle's law), 185 General laboratory equipment, 211, 223; method, 34, 205; sug- gestions, 205, Preface; study of a magnet, exp. 1; app. 214; notes and ref. 256 Glass cutting, 208 Graduated cylinder, 67; use, 70; flask, 72 Graphical representation o f forces, 158; of results, 122 Heat, app. 218; construction, 244; notes and ref. 264; capacity, 127, exp. 127; app. 218, notes and ref. 269; conduction of, 116; how it travels, exp. 113; app. 113, 218; notes and ref. 265; radiation of, 116; specific, 128 Heating, precautions in, 113 Induction, 6 Induced magnetism, exp. 8; notes and ref. 256; currents, exp. 52; app. 216; notes and ref. 259 Inducing magnet, 10 Inclined plane, 169; exp. 170; app. 170, 220, 248; notes andref. 270; as wedge and screw, 173 Intensity of light, 194 Irregular body, volume of, exp. 74 Laboratory work, preparation of, 207, Preface; equipment, 223 Latent heat, 133; exp. 134, 137; app. 134, 219, 224; notes and ref. 267 Law, 6; of cooling, exp. 124; notes and ref. 266; of induced poles, exp. 8; magnets, 10; notes and ref. 256; of magnet, 6 Lectures, 206 Length, determination of, 59; units of, 56; of pendulum, 175; units of, 57 Lenses, focal length, 193; conju- gate, 193 Light, app. construction, 252; list, 222; notes andref. 271; in- tensity of,194; effect of distance on, exp. 195; app. 195, 222, 253; notes and ref. 272; radia- tion of, 197; exp. 197; app. 222, 253; notes and ref. 272; unit of, 199; exp, 200; app. 199, 222, 254; notes and ref. 272 Lines of magnetic force, 12; exp. 13; app. 214; notes and ref. 256 Lin ear measurements, 57; scales, English, 59; French, 59; read- ing, 60; pracitce in use of, exp. 62 Liquid pressure due to weight, 99; exp. 100; app. 217, 242; notes andref. 262; weighing, 81 208 INDEX. Machines, 169 Magnet, general study of, exp A; bar, 2; action of attracted body on, exp. 4; of currents on, exp. 25; notes and ref. 257 Magnets, breaking, exp. 8; notes and ref. 256; law of, induced, exp. 10; notes and ref. 256; mutual action of two, exp. 6; notes and ref. 256 Magnetism, app. 224; lists, 214; induced, exp. 8; notes and ref. 256 Magnetic force, lines of, exp. 12; field, 12; poles, 6 Measurement, of forces, 157; of resistance, exp. 42, 45; app. 226; notes and ref. 258; notes on, 56 Measuring vessels, 67, 71, 72; substitutes, 237 Melting point, exp. 125; notes and ref. 267; tubes, 125 Meniscus, 68 Mensuration, app. 237; notes and ref. 260; list, 216 Mercury, 214, 218, 220; care of, 210; calibration by, 237, 251; cups, 214, 230 Meter, 57; sticks, 216 Metric system, 57; abbreviations, 59; units, 57; values, estima- tion of, exp. 84; notes and ref. 261; weights, 79 Moment of a force, 169; specific gravity by, exp. 189 Motor, principle, exp. 54; model, 233 Multiple arc, 33 Naming of poles, 6 Notes, form of, 205; on errors, 85; on measurement, 56 Ohm.39 Parallel forces, exp. 166 Pendulum, exp. 174; app. 174, 220; notes and ref. 270 Personal errors, 85 Phenomenon, 2 Photometer, Bunsen, 194; Rum- ford, 199 Physical and chemical change, exp. 86; notes and ref. 261; app. 216 Plates, positive and negative, 24 Polarity, 3, 4 Poles, 4; naming, 6; action of one on another, 6; induced, exp. 8 ; law of, exp. 10 Practice in determining volume, exp. 62; app. 216; notes and rej. 260; estimating metric values exp. 84; notes and ref. 261; use of linear scales, exp. 62; app. 216; notes and ref. 260; weigh- ing, exp. 83; app. 216; notes and ref. 261 Qualitative experiment, 4 Quantitative experiment, 4 Rack with wires, 41, 215, 231 Radiation of heat, 116; and ab- sorption, 150; exp. 151; app. 218; notes and ref. 268; of light, 197; exp. 197; app. 222, 253; notes and ref. 272 Ratio, 89 Reading by reversal, 29; linear scales, 61; pointer against scale, 62; volumes, 68 Relation of circumference to di- ameter, exp. 64; app. 216; notes and ref. 260 Relative resistance, exp. 40; app. 41, 215, 231; notes and ref. 258 Residual magnetism, 10 Resistance, 40; unit of, 39; con- ditions affecting, 29, 33; meas- urement of, exp. 42, 45; box, 39, 40, 215, 225 Retentivity of steel, 10 Resultant, 160; of forces, exps. 162, 166 Reverser, 215, 225 Rheostat, 39, 208 Scales, linear, 57; balances, 79, 217; substitutes; 239; of spring balances, 82 Sections, size of, 208 Solution, exp. 152; notes and ref. 268 200 Sound; app. 254; list, 222; notes and ref. 272; pitch of, exp. 201; velocity of, exp. 203 Special method, 34, 205; con- dition of wire, 20 Specific gravity, of a liquid, by bottle, 92; exp. 92; app. 217; notes and ref. 261; balancing, 103; exp. 104; app. 205, 217, 243; notes and ref. 263; atmos- pheric tension, 109; exp. 109; app. 110, 217, 243; notes and ref. 264; by floating body, exp. 107; app. 217; notes and ref. 263, of solids. 96; exp. 96; app. 217; notes and ref. 262; bottle, 93, 94, 217; without scales or weights, exp. 189; app. 220, 252; notes and ref. 271 Specific heat, 128, 129; exp. 130; app. 218 ; notes and ref. 267 Spring balance, 82, 217, 220; error, 85; substitute, 247 Square measure, 58 Sulphate of copper cell, 236, 259 Substitutes, balances, 239; bind- ing post, 230; compasses, 224; dynamometer, 247; measuring vessels, 237; weights, 241 Support, for apparatus, 251 Surface measure, 58 T square, 171, 220 Temperature, 116; and physical form, 119; exp. 120; app. 119, 218; notes and ref. 266 Tenacity, exp. 181 Testing thermometers, exp. 118; app. 218, 244; notes and ref, 265 Thermometers, 117, 218, 244; wps. 266 Tumbler cell, 23, 215, 237 True focal length, 193 Unit of force, 158; of length, 57; of surface, 58; of volume, 58; of measure, 56; English, 57; French, 57; change from one system to another, 57; theory of, 56. Useful books, 212 Velocity of sound, exp. 203; app. 222; notes and ref. 272 Vibration of pendulum, exp. 174, wires, exp. 201 Voltaic electricity, 17; produc- tion, exp. 18; notes and ref. 257 Volume, units, 58; scales, 67, 71; practice in determination of, 74 Weighing, proper method of, 80; of liquids, 81; solid in liquid, 95; by counterpoising, 82 Weight, units of, 78; determina- tion of, 78; by spring balance, 82; in chemical and physical change, 86; liquid pressure due to, exp. 99; apparatus for, 99, 217, 242; of liquid displaced by floating body, exp. on 106; app. 217; notes and ref. 260; lost by a body immersed in a liquid, 93; exp. 94; notes and ref. 261 Weights, 79, 217, 241 Wheatstone's bridge, measure ment of resistance by, 45; app 215, 225; Wire, 223; coils of 214, 232, rack with, 214, 231 Zinc, amalgamated, 18 YB 36012