UC-NRLF UNIVERSITY OF CALIFORNIA LIBRARY OF THE DEPARTMENT OP PHYSIC'S > Received *J>..:........ / Accessions No. ....... ./ ...... Book No. GIFT OF LOWER DIVISION PRACTICAL MEASUREMENTS IN MAGNETISM AND ELECTRICITY BY GEORGE A. HOADLEY, A.M., C.E, PROFESSOR OF PHYSICS IN SWARTHMORE COLLEGE AUTHOR OF "A BRIEF COURSE IN PHYSICS" NEW YORK-:- CINCINNATI.:- CHICAGO AMERICAN BOOK COMPANY I COPYRIGHT, 1904, BY GEORGE A. HOADLEY. ENTERED AT STATIONERS' HALL, LONDON. HOADLEY'S MEAS. W. P. I -. INTRODUCTORY IN preparing this book, the purpose has been to meet the requirements of students in the scientific courses in high, preparatory, and manual training schools, and in the introduction to more advanced work in college, as well as those of the practical man who wishes to become familiar with the foundation principles of the subject. The greatest benefit that can be derived from experi- mental work is that obtained from the careful and pains- taking observation of the experimenter ; for this reason the directions given for the experiments are in outline, rather than in detail. The student who makes these experiments should keep careful notes, adding to the apparatus recommended any- thing that may seem desirable, varying the manipulation, and drawing such conclusions as the experiment teaches. He should also keep a full set of notes on observations made. The accuracy and fullness of these notes will be an index of the benefit that he is receiving from the work. No attempt has been made to cover more than a small part of the field; but the belief is entertained that a thorough familiarity with the principles and experiments outlined in this book will provide a good foundation for a more extended study, or for the practical application of these principles to the requirements of practice. 328841 CONTENTS PAGE MAGNETISM . . . . ... . . . . 5 ELECTRICITY , . ... .,..._ , . 35 Galvanometers , . . . . . . . 46 Batteries . . . . . . ... 54 Resistance . . . . . . . . ; . 60 Current, etc. . , .. . . . , , . 87 APPENDIX : Resistance of pure copper wire . . . . " . ' . 105 Relative resistance of different substances .... 106 Relative properties of copper and aluminum . . . 107 Equivalents ....'.. .' . . . 107 Answers to problems . . . * . . . . 108 INDEX 109 CHAPTER I MAGNETISM 1. Magnetic and Non-magnetic Substances. Substances may be divided into classes, according to their action when in the presence of a strong bar magnet. Those that cling to the magnet are called magnetic substances; those that do not are called non-magnetic. EXPERIMKNT 1. To separate magnetic from non-magnetic sub- stances. Apparatus. A strong bar magnet ; twenty or thirty objects made of different substances, such as screws, matches, copper rivets, bicycle balls, etc. Manipulation. Place these objects upon MAGNETIC Nails NON-MAGNETIC Matches a table and touch each of them with the end of the bar magnet. Make a table like the one suggested, classifying the different articles as mag- netic or non-magnetic. Are any of the magnetic substances non- metallic? Are all the metals magnetic? A further examination of different substances will prove that, besides iron and steel, nickel and cobalt are magnetic. This may. be shown by bringing the end of a bar magnet in contact with these metals or some of their ores. Of the ores of iron, some, like magnetite, are magnetic, while others, like sphalerite, are not. If, however, a piece of sphalerite is heated under a blowpipe, it becomes magnetic. 5 MAGNETISM ^ -' ' f 1 r -- 1 "' . 2. The Poles of a Magnet. Every bar magnet exerts a greater attractive power near its ends than at any other point. These points of maximum attraction are called the poles of the magnet. EXPERIMENT 2. To locate the poles of a bar magnet. Apparatus. A bar magnet and a box of small nails or tacks. Manipulation. Pour the nails upon a table, dip one end of the magnet into them, and then raise it vertically. Do the same with the other end. Spread the nails out in a line as long as the magnet, lay the magnet down upon its side in the nails, and then raise it vertically as in the figure. FIG. 1 The position of the poles is indicated by the number of nails that cling to the magnet at different points. Locate as definitely as you can the distance of each pole from the end. 3. Names of the Magnetic Poles. EXPERIMENT 3. To name the poles of a magnet. Apparatus. A small bar magnet ; silk thread. Manipulation. Suspend the magnet from the middle by the thread in such a manner that it can swing freely in a horizontal plane, and let it come to rest. A magnet suspended or supported in this way constitutes a magnetic needle. THE MUTUAL ACTION OF MAGNETS FIG. 2 The line in which it finally comes to rest is called the magnetic meridian. The end of the needle that points to the magnetic north is called the north, the JV, or the + pole, and the other _^ Er/c ^ the south, the $, or the pole. The strictly accurate, though less convenient, names would be the north-seeking pole and the south- seeking pole. 4. The Mutual Action of Magnets. EXPERIMENT 4. To investigate the law of mutual action. Apparatus. The bar magnet used in Experiment 3 ; also a small magnetic needle. Manipulation. Holding the magnet by the S end, bring the N end near the TV end of the needle after it has come to rest. Bring it near the & end. Reverse the magnet and repeat both tests. From the results obtained formulate a law that shall state the mutual action of like and of unlike poles. This "law of mutual action" is an extremely important one and explains many of the phenomena that are observed in magnetism. 5. The Poles of a Horseshoe Magnet. - When a bar magnet is bent in the middle and its ends are brought near each other, it is called a horseshoe magnet. A piece of soft iron placed across the ends is called the armature. If the magnet is formed of a single bar, it is a simple magnet (Fig. 3) ; but if it is made up of a number of thin magnets fastened together, it is a compound horseshoe magnet (Fig. 4). FIG. 3 FIG 8 MAGNETISM EXPERIMENT 5. To locate the poles of a horseshoe magnet. Apparatus. A horseshoe magnet; a magnetic needle. Manipulation. Bring the different parts of the magnet near the N end of the needle and observe the effect. Name the poles of the magnet by applying the law that was deter- mined in the preceding experiment. 6. Magnetic Induction. EXPERIMENT 6. To show the in- ductive effect of a bar magnet. Apparatus. A long bar magnet ; a soft iron rod 3 or 4 in. long ; and iron filings. Manipulation. Bring one end of the soft iron rod near the end of the magnet, and while it is in that position put the other end of the rod into the iron filings. Raise the rod from the filings and then slowly move the magnet away from the rod. This changing of an iron rod into a magnet in the presence of a magnet is the result of what is known as magnetic induction. If the experiment is extended by placing a succession of iron rods in the _i_ i- - -h - + - + - FlGr 5 axis of the magnet as in Fig. 5, an examination of the polarity of each will show that it is as marked in the figure. The position of the poles is determined by the law of mutual action. 7. Inductive Action of the Earth. The fact that a magnetic needle will always come to rest in a fixed direc- tion shows that the earth itself acts like a great magnet. The line in which the needle comes to rest is called, as has been said, the magnetic meridian, and the points toward which all the different magnetic meridians converge are called the magnetic poles of the earth. EXPERIMENT 7. To show the inductive action of the earth's magnetism. Apparatus. A bar of soft iron about 3 ft. long and an inch in diameter ; a magnetic needle mounted on a stand, MAGNETIC INDUCTION 9 Manipulation. After the needle has come to rest, bring one end of the iron bar near the N end of the needle, keeping the bar in the horizontal plane and in an east-and-west line, as in Fig. 6. Make the same experiment with each end of the bar upon each end of the needle. If the bar is of soft iron, attraction should take place in each case. Now bring the iron bar into the magnetic meridian, raise the southern end until the bar makes an angle of about 70 degrees with the horizon, and *r bring its lower end near one " ^ side of the N end of the needle. Make the same experiment on the S end of the needle. Reverse /w FIG. 6 the bar and repeat. This experiment if carefully made is most striking and instructive, its results showing that the inductive action of the earth determines the polarity of the bar in both positions. EXPERIMENT 8. An extension of Experiment 7. Apparatus. The iron bar and needle used in Experiment 7, and a hammer. Manipulation. Bring the bar into the position in which it produces the greatest deflection of the needle and then strike it two or three sharp blows with the hammer. Hold it in the horizontal plane and test it for polarity. Hold it in the magnetic eastand-west line and again strike it a few blows. Test it once more for polarity. In making a test for polarity the only acceptable proof is repulsion, not attraction. The results of these tests show that if an iron bar is jarred mechan- ically while it is magnetized by induction it will retain a certain amount of magnetism. If the bar were of steel, it would become a permanent magnet. The demagnetization of the iron bar that takes place when it is struck while in the magnetic east-and-west line is possibly due to its being magnetized transversely. EXPERIMENT 9. To test vertical iron rods for magnetic 'polarity. Apparatus. A magnetic needle, retort stand, and any vertical iron rods or pipes that may be in the laboratory or its vicinity. 10 MAGNETISM Manipulation. Hold the needle near the top of the retort stand and determine the polarity. Lower the needle slowly until the foot of the stand is reached. Determine the polarity of the stand along its entire length and mark, on a drawing, the point at which it changes. An examination of steam pipes, iron fence posts., and in fact any iron or steel rods that have stood for some time in an approximately vertical position, shows that they are magnetized. It also shows that the upper end of each is a south pole and that the lower end is a north pole. Why? QUESTIONS 1. Is an ordinary tin plate magnetic or non-magnetic? Why? 2. Is the pole of a bar magnet nearer the end in a long, thin mag- net, or in a short, thick one ? 3. Give illustrations of the mutual action of magnets. State the law. 4. Make a drawing of a horseshoe magnet with its armature nearly touching the ends of the magnet. Mark the polarity of both the magnet and the armature. 5. -What kind of magnetic polarity has the north magnetic pole of the earth ? What two experiments prove it ? 6. Why are steel tools. frequently found to be magnetized? 7. Why is attraction no proof of polarity ? 8. Making a Magnetic Needle. EXPERIMENT 10. To mag- netize a piece of steel. Apparatus. A piece of watch spring or a sewing needle; a bar magnet ; and a magnetic needle. Manipulation. Straighten the watch spring by drawing it between the fingers. Holding the spring firmly upon some flat surface, draw the N end of the magnet from the middle to one end. Do this at least twenty times. Draw the S end of the magnet along the other end of the spring an equal number of times. Determine the polarity of the spring by testing it with the magnetic needle. State the kind of polarity produced by drawing the N end of a magnet along one end of a piece of steel. 9. Demagnetization. The demagnetization of a magnet may be accomplished in several ways, one of which is shown in the following experiment. DEM A GNETIZA T1ON 11 EXPERIMENT 11. To demagnetize a magnet by heat. Apparatus. The magnetic needle made in Experiment 10 ; a cop- per wire about 6 in. long; a Bunsen burner; and a magnetic needle. Manipulation. Wind one end of the copper wire around the middle of the watch-spring needle and hold the needle in the flarne of the Bunsen burner until it is white hot. Remove it from the flame, allow it to cool, and examine it for polarity. Heat it again, plunge it into water, and magnetize it again as in Experiment 10. Conclusion. The increased rate of molecular vibration due to the heating of the needle changes it from a magnet to a magnetic sub- stance, or demagnetizes it. Compare this result with that obtained by striking the iron bar in Experiment 8. 10. The Effect of High Temperatures upon Magnets. EXPERIMENT 12. An extension of Experiment 11. Apparatus. A bar magnet ; a knitting-needle magnet ; a support- ing stand ; and a Bunsen burner. Manipulation. Suspend the knitting- needle magnet by a wire in such a way that it will diverge some degrees from the magnetic merid- ian. This can be done by twisting the wire suspension at the top. Fix the bar magnet as shown in the figure, when the attraction of the magnet for the needle will overcome the tor- sion of the wire and bring the unlike ends in contact with each other. Now apply the flarne of the Bunsen burner to the end of the needle that is nearest the magnet, and when this begins to get red hot the needle will swing back away from contact with the magnet. 12 MAGNETISM Experiment has proved that the temperature at which this result takes place, is about 785 Centigrade. This means that at this temperature and above, iron is a non- magnetic substance. 11. Magnetic Lines of Force. From the results of the experiment on induction it is evident that the space sur- rounding a magnet differs from the space surrounding a bar of iron. Around the magnet there is what is called a magnetic field, and through this there extend lines of mag- netic force. These lines of force are closed circuits passing externally from the north to the south pole, and internally from the south to the north pole. They pass more readily through magnetic substances than through non-magnetic ; constantly tend to shorten their paths like stretched rub- ber bands ; and, if parallel and in the same direction, repel each other. In direction each line of force is the path along which an isolated north pole would be repelled by the magnet, were such an isolation possible. EXPERIMENT 13. To determine the direction of the lines of force. Apparatus. A bar magnet ; a very short magnetic needle ; a sheet of paper ; window glass ; iron filings ; and a sieve made of fine woven wire or of thin muslin. Manipulation. Place the bar magnet on its side upon a table and over it lay a sheet of paper. Lay the sheet of glass over this and sift a light coat of iron filings over its upper surface. Rap the glass lightly with a lead pencil, and the filings will arrange themselves in curves that indicate the paths of the lines of force and the comparative in- tensity of the magnetic field. Determine the direction of the lines of force by suspending at different points above the curves a very short magnetic needle and observing the direction in which the north pole is repelled. The most satisfactory record of these curves can be made by carry- ing out the experiment in a dark room, using the film surface of a MAGNETIC LINES OF FORCE 13 photographic dry plate as a support for the filings. When the desired curves are obtained, the plate is exposed by burning a match, held a foot or more above it, and is then developed in the usual way. A slow plate is best for this purpose, and the prints are much more accurate than drawings, as is shown in Fig. 8. FIG. 8 Let negatives and prints of the following fields be made : 1. Side of bar magnet ; 2. End of bar magnet; 3. Side of horseshoe magnet ; 4. End of horseshoe magnet ; 5. Two horseshoe magnets, one inch apart, like poles opposite ; 6. Two horseshoe magnets, one inch apart, unlike poles opposite; 7. Horseshoe and bar magnet, one inch apart ; 8. Bar magnet and iron bar, one inch apart, showing induction ; 9. Field devised by the student ; 10. Field devised by the student 14 MAGNETISM 12. Geometrical Construction of the Direction of Lines of Force. A very important equation, which expresses the value of the force between two bodies that act mutually ff upon each other, is F = *~. In the case of two magnets this expression takes the form F = ~T^ in which m and m' are the strengths of two magnetic poles, and d is the distance between them. The sign + is used when there is mutual repulsion, as between like poles; the sign when there is mutual attraction, as between unlike poles. The application of this equation to the geometrical con- struction of the direction of lines of force is as follows: Let NS (Fig. 9) represent a long, thin magnet. Let A be the mid- dle of a small magnetic needle placed 8 in. from S and 12 in. from N. What position will the needle assume when it comes to rest ? N FIG. 9 Suppose the poles of the magnet NS to be 12 in. apart, and that ns is so short that its length may be disregarded. Let 50 represent the magnetic strength of N and of S, and 3 that of n and of s. There will THE EFFECT OF BREAKING A MAGNET 15 50 x 3 be two forces acting upon n, one of ^ acting from N toward A, and one of * ' acting from A toward S ; hence we can write : Repulsion of N : Attraction of S : : : 144 64 Repulsion of N : Attraction of S :: 64 : 144 Repulsion of N : Attraction of S : : 4 : 9 To find the position of the needle, lay off on NA prolonged, and on AS, distances AB and AC proportional respectively to 4 and 9. Complete the parallelogram ABDC, and the diagonal AD will be the position of the half needle An, considered independently. But a similar construction would show the position of the other half of the needle As to be the prolongation of nA (let the student prove this) ; hence no further construction is necessary. The needle ns is tangent to the direction of the line of force at the point A. The position of other tangent lines may be found by selecting other values for AN and AS and constructing the position of the needle as before. Let the position be found at the following distances : 1. AN 14, AS 6. 2. AN 9, AS 9. 3. AN 4, AS 10. 4. AN 2, AS 15. Verification. Upon the drawing made in the foregoing construc- tion, lay a magnet with its poles 12 in. apart and just over the poles of the drawing. Place a short magnetic needle at the point A and turn the board until the needle coincides with n.s, when the needle will be found to be in the magnetic meridian. Why? NOTE. For convenience in the verification it will be well to make the distance NS in the drawing equal to the distance between the poles of some magnet that you have used. 13. The Effect of Breaking a Magnet. EXPERIMENT 14. To show that each piece of a broken magnet is polarized. Apparatus. A knitting needle ; a magnet ; a magnetic needle ; iron filings; and a three-cornered file. Manipulation. File a notch in the middle of the knitting needle and break it in two. Magneti/e one half of it as in Experiment 10 16 MAGNETISM so that the point will be +. Test it for magnetism with the filings and determine its polarity with the needle. File a notch in the middle of the half-needle magnet and break again. Test as before. Break the pointed end in two and test again. Carry the experiment as far as possible, or until you can not break the needle again. + - 4- - 4- FIG. 10 The results obtained, shown in Fig. 10, suggest the results of induction in Experiment 6. Can you break off a piece of the magnet so short that it will not be polarized ? 14. Explanation of Induction. Since the shortest piece that we can obtain by breaking a magnet is found to be polarized, the hypothesis has been made that each mole- cule of a magnetic substance is a magnet. The difference between a piece of soft iron and a steel magnet is that in the magnet the molecular magnets are practically parallel to one another and all in the same direction, while in the soft iron they are in positions that are determined by their mutual attractions and repulsions. If a strong bar magnet is brought near a soft iron bar, the molecular magnets of which the bar is composed are drawn around into lines that are practically parallel in direction, and we say that the iron is polarized by induction. EXPERIMENT 15. To represent induction in soft iron. Apparatus. Watch spring; bar magnet; pins; sheet of lead; steel punch; Bunsen burner; wire; and hammer. Manipulation. Break from the watch spring twenty or more pieces each an inch long, heat them in the Bunsen flame, and make a slight depression in the middle of one side of each with the punch. Cut from the sheet of lead twenty or more disks each an inch in diameter and drive a pin through the middle of each. Harden the EXPLANATION OF INDUCTION 17 springs by heating them to a red heat and plunging them into cold water. Magnetize and mount each on one of the pins as a stand (Fig. 11). Place them upon a table, symmetrically arranged in the form of a long rectangle. Observe the position taken by each and make a sketch of the group. Now bring one end of a bar magnet near one end of the rectangle, keeping the axis of the magnet in the direction of the length of the rectangle. Observe the change in the directions of the needles, and after they have come to rest sketch the group again. Figure 12 represents such positions as the small needles will assume when they come to rest under the FIG. 11 FIG. 12 influence of their mutual at- tractions and repulsions alone. In this condition they represent the molecules of soft iron when they neutral- ize one another and exert no magnetic force as a whole. If, however, a strong bar magnet is brought near the small magnets, their mutual action is overpowered, and the result is shown in Fig. 13. FIG. 13 In this position they represent the molecules of an iron bar polar- ized by induction. Instead of the form of needles described above, the pieces of watch spring may be magnetized and then placed upon a piece of glass, resting on their convex sides. It will be difficult, however, to pre- vent their coming in contact with one another. A better arrange- ment is to use a number of small magnetic compasses which can be placed in any desired position. 15. The Lifting Power of a Magnet. EXPERIMENT 16. To determine the lifting power of a magnet. Apparatus. Single and compound horseshoe magnets ; pail ; sand ; and a pair of scales. ELEC. AND MAG. 2 18 MAGNETISM Manipulation. Fix the single horseshoe magnet in such a posi- tion that the armature will hang vertically downward. Suspend the pail from the armature and pour sand into it until the armature is pulled from the magnet. Weigh the armature, pail, and sand, and make a record of the weight. Make the experiment three times and take the average of the weights for the lifting power of the magnet. Suspend the pail from the armature of the same magnet and pour into it almost as much sand as was .supported in the first experiment. Leave it suspended for an hour ; at the end of that time pour in a little more sand, and repeat this at the end of each hour until the armature is pulled off. Find the weight and compare it with that supported in the first experiment. Suspend the pail again and pour in sand until the armature is again pulled off. Weigh the load and again compare with the first. Weigh the magnet and compare its weight with that of its maximum load. The results show that by gradually building up the load on a magnet its lifting power is increased. They also show that the in- crease is not permanent. Make the same experiments with the compound magnet. Is the lifting power of a compound magnet formed of ten single magnets of equal strength, ten times as great as the lifting power of one of them ? Give the reason for your answer. 16. The Action of the Earth upon a Magnetic Needle. - EXPERIMENT 17. To show that the action of the earth upon a mag- netic needle is simply directive. Apparatus. Beaker of water; sewing needle; magnet; and wire. Manipulation. Magnetize the sewing needle in such a manner that its point is a north pole. Draw it between the fingers and lay it carefully upon the surface of the water, using the wire, bent into a loop, for that purpose. It will come to rest in the magnetic meridian. Deflect it from that position by bringing one end of the magnet toward the side of the beaker. Repeat, and observe that every time it comes to rest it simply turns into the north and 'south line without moving either to the south or to the north. Conclusion. Since the needle moves neither to the north nor to the south, the action of the earth upon a magnetic needle is directive only. Bring a bar magnet near the beaker and explain the action. THE EARTH S MAGNETIC FORCE 19 17. The Terrestrial Magnetic Couple. A study of Fig. 14 will show the reason for the results obtained in Experi- ment 17. Let NS represent the magnetic meridian and ns a needle that is deflected from it by the angle a. By the law for the mutual action of r, mm' magnets, the force acting on n is F = - , and that acting on s is F= -\ , in which m and m' are the respective strengths of the north pole of the needle and of the earth. Since these forces are parallel and opposite in direction, they form a mechanical couple the only effect of which is to turn the needle ns on its axis at 0. There will be a similar expression for the action between the south pole of the earth and the needle. Since the distance is inde- terminate, we will call the horizontal effect of the earth's magnetism If. The forces acting upon n and s will then be each mH. The moment of each force will be mffx nb, and the total moment will be ZmHxnb. But nb = nOs'u\ a. Hence F= mHx2nO sin a. Let I = 2 nO, the length between the poles of the needle ; then F=mHl sin a. But ml is the magnetic moment of the needle ; call this M^ and F = MH sin a. 18. Components of the Earth's Magnetic Force. EXPERI- MENT 18. To show the direction of the earth's magnetic force. Apparatus. Knitting needle; small cork; sewing needle; and two beakers of equal height. Manipulation. Thrust the knitting needle lengthwise through the cork and thrust the sewing needle through at a right angle to its length and close to the knitting needle. Support the ends of the sewing needle on the edges of the beakers, so that it may serve as an axis, arranging the beakers in such positions that the knitting needle will be in the magnetic meridian. Push the knitting needle 20 MAGNETISM back and forth through the cork until it will balance in a horizontal position. Magnetize the knitting needle carefully so as not to change its position in the cork. Support it on the beakers as before arid observe the position in which it comes to rest. The fact that the needle no longer remains balanced horizontally after it has been magnetized shows that the maximum directive force of the earth is not horizontal. Let AB (Fig. 15) represent the intensity and direction of the earth's magnetic force. This may be resolved into two component forces, one AC horizontal, and the other AD vertical. Let these forces be represented by J, H, and V respec- tively, and let a represent the angle CAB ; and we may write H=I cos a; F~=Zsin a. The component H is the force that determines the position of all needles moving in a horizontal plane ; it is called the horizontal component of the earth's magnetism. FIG. 15 19. The Angle of Dip. The Dipping Needle. The angle CAB in Fig. 15, which measures the inclination of the earth's magnetic force below the hori- zontal line passing through the needle, is called the angle of dip. A con- venient and simple form of dipping needle with which the angle of dip can be determined at any place is shown in Fig. 16. The axis of the needle is supported by braces attached FIG. 16 THE ANGLE OF DIP 21 to a graduated ring which is itself supported by an axis at a right angle to the axis of the needle. The semicircular arms which support the axis of the ring are mounted at the top of a vertical standard capable of rotating on its axis. At the base of the standard is a horizontal circle gradu- ated to degrees. A pointer attached to the standard determines its position on the graduated circle. Three leveling screws are provided in the base of the instru- ment for adjustment. EXPERIMENT 19. To determine the angle of dip. Apparatus. Dipping needle, and long magnetic needle. Manipulation. Set up the magnetic needle in the middle of a table and, by sighting across the ends of the needle, mark two points in the magnetic meridian, one at each end of the table. Remove the needle and draw a chalk line from one mark to the other. Set np the dipping needle in the middle of this line and turn the graduated ring into the vertical plane. Bring it into the meridian by reference to the chalk line and turn the graduated circle at the base of the standard until the pointer marks zero. The needle is now in the posi- tion to give the reading of the angle of dip. Read both the upper and the lower end of the needle. Turn the ring through 180 degrees and read again. Turn the standard through 180 degrees and take four readings as before. In all these readings care should be taken that the needle moves freely upon its axis and does not come to rest too soon. Make a record, as shown in the table, and take an average of the readings. The average is the angle of dip for the locality. EXPERIMENT 20. To determine the angle of dip in vertical planes not in the magnetic meridian. Apparatus. The dipping needle used in the last experiment. Manipulation. Turn the stand- ard of the instrument through 90 degrees, taking a reading of the needle every five degrees, and make a table of the results. POSITION END OF NEEDLE RKADIXG No. 1 { Upper . . 1. Lower . . No. 2 j Upper . . ! Lower . . No. 3 /Upper . .' [ Lower . . / No. 4 /Upper .... [ Lower . . Average, 22 MAGNETISM Make a curve having for the horizontal axis the angle through which the standard is turned, and for the vertical axis the reading of the dipping needle. 20. The Graphical Method of Recording an Experiment. One of the most satisfactory methods of recording the AMJI.K DIP CHANGE ANGLE DIP CHANGE AN<;L i: DIP CHANGE 71.50 35 75.75 1.00 70 84.00 1.25 5 71.75 .25 40 76.75 1.00 75 85.50 1.25 10 72.00 .25 45 77.75 1.00 80 87.00 1.50 15 72.75 .75 50 79.00 1.25 85 88.75 1.75 20 73 50 .75 55 80.00 1.00 90 90.00 1.25 26 74.00 .50 CO 81.50 1.50 :JO 74.75 .75 65 82.75 1.25 70 10 30 40 50 60 DECLINATION FROM THE MERIDIAN FIG. 17 70 80" results of an experiment is the graphical method, or curve. This is made by laying off on cross-section paper one set of conditions in one direction, and at a right angle to it the results that are to be compared with them. Two lines are usually selected as axes, the horizontal being THE GRAPHICAL METHOD 23 called the axis of X and the vertical the axis of Y. Figure 17 gives the curve for Experiment 20. An inspec- tion of this curve, and a comparison of it with the table from which it was formed, will show how it was drawn. One advantage of this form of record is that points not determined by the experiment are interpolated by the curve. 21. Application of the Dipping Needle to Finding the Poles of a Bar Magnet. Since the direction of a short dipping needle at any point is parallel to the direction of the magnetic lines of force at that point, it is possible to locate the poles of a bar magnet as follows : EXPERIMENT 21. To locate the poles of a bar magnet. Apparatus. A dipping needle, supported as shown in Fig. 18, and a long bar magnet. FIG. 18 Manipulation. Draw a line across the middle of the magnet and call it zero. Draw similar lines across the magnet at intervals of a centimeter, numbering them from the middle toward each end. Lay the magnet upon a table in the magnetic meridian and place the base of the dipping-needle stand which should be an even num- ber of centimeters in length in such a position that the axis of the needle is vertically above the middle of the magnet. Move the magnet lengthwise one centimeter at a time, and take a reading of both ends of the needle for each position. Tabulate the results, and from the table thus formed construct a curve that shall have the distance of the middle of the needle from the middle of the magnet laid off along the axis of X, and the angle of dip laid off along the axis of Y. 24 MAGNETISM The location of the poles will be indicated by those points of the curve that correspond to a dip of 90 degrees. It will be observed that the position which the dipping needle takes is in every case due to the resultant of the magnetic forces of both the earth and the magnet under consideration. A curve made from the average of two sets of readings, one taken when the bar magnet lies with its N pole to the magnetic north, and one when it lies with its S pole to the magnetic north, will give the most accurate result. 22. Magnetic Declination. Observation shows that in most places the magnetic meridian and the geographical meridian do not coincide. In the eastern part of the United States the needle points to the west, and in the western part to the east, of the true north. The angle which measures the difference is called the declination. It changes slowly from year to year, and is also subject to a slight daily change and to acci- dental changes. These are called variations FIG. 19 in the declination. 23. Measurement of the Decimation. The method of determining the declination is generally that of determin- ing the true north by reference to the position of the North Star. If this star, Polaris, were at the exact north pole of the heavens, it would give the direction of the true meridian at all times ; but as it is nearly one and one quarter degrees away, it is on the meridian only twice in twenty-four hours, when it is directly above and when it is directly below the pole, as in Fig. 20 at A and C. At points midway between these, as at B and Z>, it is at its greatest elongation either east or west. The full line in Fig. 20 represents a photograph made MAGNETIC DECLINATION 25 by exposing a plate in a camera for nearly twelve hours, and letting the trail of Polaris fall upon it. The dotted line gives its path for the remaining hours of the day. In order to give an idea of the distance of Polaris from the north pole, a representation of the moon on the same scale is placed here for comparison. MOON ON SAME SCALE FIG. 20 EXPERIMENT 22. To measure the magnetic declination. Apparatus. A surveyor's compass or transit. Manipulation. Set up and level the transit in a room in such a position that the North Star can be seen through an open window. Choose such a time of night that the constellation of the Great Bear is either east or west of Polaris. Bring the vertical cross hair of the instrument to cover the star, and watch it until it seems to stand still, moving neither to the right nor to the left. When this position is found, it is in position either B or D (Fig. 20). Release the compass needle on the transit and let it come to rest. Read the position of the needle; this reading, corrected for the angular distance of Polaris from the North Pole, will be the declination. By leaving the transit undisturbed in its position until morning, both the geographic and the magnetic meridian can be laid out per- manently. 26 MAGNETISM To find the True Meridian. Make the correction for the angular distance of Polaris, and place a mark in the floor vertically under the instrument. Place another on a stone set in the ground at a distance of a hundred yards, and in the line determined by the vertical cross hair. To determine the Magnetic Meridian. Bring "the needle to read zero, and then determine a mark in a second stone. NOTE. If the Great Bear does not come to the east or west of .Polaris at a convenient hour, the reading can be taken when it is in the position shown in Fig. 21. The north pole is in the meridian of Polaris when the vertical cross hair passes through both Polaris and the second star in the handle of the Dipper as shown. X FIG. 21 The angular distance of Polaris from the north pole is diminishing at the rate of about twenty seconds of arc per year. In 1900 its distance was 1 13' 32". In 1915 it will be 1 8' 53". The fol- lowing table gives the times of greatest elongation for the first day of each month of the year : MAXIMUM ELONGATIONS OF POLARIS MONTH EASTERN WESTERN MONTH EASTERN WESTERN Jan. 0.27 P.M. 0.19 A.M. July 0.35 A.M. 0.23 P.M. Feb. 10.24 A.M. 10. 13 P.M. Aug. 10.30 P.M. 10.22 A.M. Mar. 8.34 A.M. 8.22 P.M. Sept. 8.28 P.M. 8.20 A.M. Apr. 6.32 A.M. 6.20 P.M. Oct. 6.30 P.M. 6.22 A.M. May 4.34 A.M. 4.22 P.M. Nov. 4.28 P.M. 4.21 A.M. June 2.33 A.M. 2.21 P.M. Dec. 2.30 P.M. 2.22 A.M. It will be observed that at times approximately six hours earlier or six hours later than those given above Polaris will be in the position represented by Fig. 21, or by that figure inverted. DISTRIBUTION OF MAGNETISM 27 24. Distribution of Magnetism along a Bar Magnet. One of the methods employed for measuring the magnetic intensity at any point is that of vibrating a magnetic needle at that point, and is called the method of vibrations. Whenever a magnetic needle is deflected from its position of rest, it will set up a series of vibrations which, like those of a pendulum, are made in equal times. The intensity of any magnetic field is directly propor- tional to the square of the number of vibrations per minute of a magnetic needle suspended in that field. If a needle vibrates N times per minute when acted upon by both a bar magnet and the earth, and n times when acted upon by the earth alone, then the intensity of the magnetic field due .to the magnet alone will be proportional to N 2 n 2 at that point. EXPERIMENT 23. To determine the distribution of magnetism along a bar magnet. Apparatus. Two bar magnets ; a magnetic needle suspended so as to be free from air currents (an Erlenmeyer flask will answer) ; and a support for the magnet. In- crease the weight of the needle by splitting a lead ball and pinching it on as in a, Fig. 22. Manipulation. Place the support for the magnet which must be made without using either iron or steel so that a line drawn across the middle of the op will be in the magnetic meridian. Place the flask containing the _, needle upon the line and make sure that there is no twist in the suspension ; the needle will then come to rest directly over the line. Deflect the needle by bringing bar magnet No. 1 toward the flask MAGNETISM POSITION OF NEEDLE NUMBER OF VIBRATIONS COMPARATIVE INTENSITIES Earth alone 71 = 5 n 2 = 25 End of mag. 1st mark 2V =23 N=25 /V 2 -w 2 = 504 N 2 -n 2 = 600 2d mark N=22 Ni-ri 2 = 45Q Figure from either the east or the west. Be careful that the needle does not swing as a pendulum. Determine the time it takes for 50 vibrations and compute the number per minute. Draw lines across bar magnet No. 2 at intervals of a half inch, beginning at each end, and fasten the mag- net on the side of the box, as shown in the figure, so that the needle will be on a level with the end. Put the needle in vibration as before and determine the number of vibrations per minute. Do this for every half inch of the magnet until the middle is reached. Turn the box around, reverse the magnet, and make the same experiments for the other half. Arrange the results as in the table, and make a graphical record of the 23 shows how the graphical record is made. First a drawing is made of the bar magnet, then from the end and from each half-inch mark distances &' aa', W, etc., are laid off to scale, representing the values of JV 2 ri 2 at the different positions on the magnet. By connecting the points a', &', c', etc., by a curved line, the figure will be made to represent the distribution of magnetic force along the magnet. By continuing the curve for the whole length of the needle, the position of each pole is shown to be at some distance from the end, and the question whether the magnetism is symmetrically distributed or not is determined. The above table and the curve of distribution FIG. 23 are from a part of the results of an experiment. 25. Action of a Magnet upon a Needle. It was shown in Section 17 that the expression for the terrestrial mag- netic couple that tends to bring the needle back into the meridian whenever it is deflected, is MH sin a, in which M is the magnetic moment of the needle, or the product ACTION OF A MAGNET UPON A NEEDLE 29 of the strength of one of its poles by the distance between them, H is the horizontal component of the earth's mag- netism, and a is the angle of the deflection. Suppose a magnet NS to be placed in an east-and-west line near a magnetic needle us, as in Fig. 24, and to keep it deflected from the magnetic meridian at the angle a. Let the strength of each pole of the magnet be w, and of the needle m 1 . Let the length of the magnet be 2 Z, of the needle 2 Z, and let the distance between their 2L- I FIG. 24 centers be d. Since I is small compared with d, the force acting between S and n will be -, and the force acting between N and n will be H mm mm mm (<* i ; , while the total force will be 4 mm 1 Ld rrn A.' The force acting (<* + )' (<*>-), (#; upon s will be H !^ m g - Since this force acts at nearly a right angle to the needle, the moment of the couple acting at n and s may be taken as 4 mm'Ld ,-, 7 8 mm'Itdl cos a 2 I cos a = As this is the moment of the deflecting force which keeps the needle in equilibrium, it must be equal to the moment of the magnetic couple of the earth ; hence. 30 MAGNETISM (d 2 - L 2 ) 2 8 mm'Ldl cos a (rf 2 - or 2 m'lffs'm a = i i XT- 4 7ft^>C? COS a ixi- from which we get //sin a = - ^yT' a reduces to = "^ tan a. Since 2mL = M, the mag- JZ ^ 6& iietic moment of ^ZViS, the equation becomes If d is great as compared with L, the equation reduces, as M d 3 an approximation, to = -tana, an expression which -TZ gives the ratio of the magnetic moment of a given magnet to the horizontal component of the earth's magnetism, in terms of the distance between the centers of the magnet and of the magnetic needle, and the tangent of the angle of deflection produced. This position of the magnet with relation to the needle, shown in Fig. 24, is called the "A tangent position of Gauss." In the "B tangent position" the magnet is placed parallel to the needle. P^XPERIMENT 24. To investigate the A tangent position. Apparatus. A small bar magnet ; meter scale ; and a deflection magnetometer or compass. Manipulation. Place the magnetometer in such a position that the needle will read zero when it conies to rest. Cut a short piece from the meter stick and fix the stick upon a support in an east-and- west line opposite the middle of the needle in such a position that the distances are laid off from that point. Place the bar magnet on the scale with its middle at the distance of one meter from the middle of the needle and read the deflection. Move the magnet along the scale THE VIBRATION OF A MAGNET 31 toward the needle and take a reading of the deflection at every centi- meter. Plot a curve from the results obtained, laying off distances along the axis of X and deflections along the axis of Y. A study of the curve obtained will show the change in the deflec- tion that takes place as the magnet is brought near the needle, and the varying rate of the change. A reflecting galvanometer with a short needle makes a good mag- netometer for this experiment. FIG. 25 Let AB represent the meter scale, fastened to a board with a groove in it, in which the magnet NS can slide. When the deflection of the needle is the angle OMC, the reading is for the angle OMD. If the distance OM is taken as unity, the reading of the scale OD will be the tangent of twice the angle of deflection. If the distance OM be one half a meter, the millimeter divisions on the scale OD will, for small deflections, be nearly the natural tangent of the angle of deflection. 26. The Vibration of a Magnet. A suspended magnet, or magnetic needle, vibrates with a simple harmonic motion like a pendulum. The time of its vibration is given by the expression t = TT^/ , in which I is the moment of inertia of the magnet, Mits magnetic moment, and H the horizontal component of the earth's magnetism. 32 MAGNETISM The moment of inertia can be calculated by the following rules : (a) For a cylindrical magnet supported as in Fig. 26, 1- FIG. 26 In this expression W is the mass, I the length, and r the radius of the magnet. (5) For a bar magnet of rectangu- lar cross section, suspended as in Fig. 27, 1= W 12 / and b are the dimensions of the horizontal sides. From the expression for the time of a vibration, we get t 2 = in which I MJf hence MH= 7T 2 / Ml? 7T 2 / t* ' EXPERIMENT 25. To determine the value of MH for a given magnet. Apparatus. A short bar magnet and vibration box, as shown in Fig. 28 ; and a brass bar of the same weight as the magnet. Manipulation. Set the box so that its sides shall be in the magnetic meridian. Place the JV brass bar in the stirrup and twist the suspension head until the bar is directly over the line Remove the brass bar and FIG. 28 NS, drawn on the bottom of the box. substitute the magnet for it. Put the magnet in vibration by bringing the end of another magnet up to the side. Determine the time of vibration. Repeat and take the- average. THE VIBRATION OF A MAGNET 33 By determining the time for several sets of vibrations the fact that they are isochronous will be observed. By computing the value of 7 by one of the rules given above, and substituting this value and the value of t determined in the experiment, the value of the product MH is determined. 27. The Determination of M and //. From the two formulas, Mff=^~, and ^= ( ^ ~^ 2)2 tan a, we obtain values for M and H as follows : From the first M = From the second M = ^- ~-L tan a. 2 d Equating these values of M and reducing, we get = ___^ X 1O T"ON and in a similar way M - By substituting in these formulas the results obtained in Experiments 24 and 25, the values of M and H are obtained. 28. To compare the Magnetic Moments of Two Magnets. - It is sometimes necessary to determine the comparative values of the moments of magnets. This may be done as follows : EXPERIMENT 26. To compare the values of M in magnets. Apparatus. The magnetometer used in Experiment 24 ; a stand- ard magnet ; and magnets to be compared. Manipulation. Place the standard magnet which should be a short magnet highly magnetized at such a distance from the needle, say 500 cm., that it will give a convenient deflection. Place one ELEC. AND MAG. 3 34 MAGNETISM of the other magnets on the opposite side of the magnetometer at such a distance that the deflection is brought back to zero. Let M be the moment of the standard magnet and d the distance of its center from the needle; then, from Section 25, = tana. In 71 jy x7/3 "^ w the same way - = tan a, in which M and d' are corresponding H 2 values for the second magnet. Combining these expressions, we get = ; that is, the magnetic moments of the magnets are directly M f d' B proportional to the cubes of the distances that give a zero deflection. PRACTICAL QUESTIONS AND PROBLEMS 1. Suppose that in some way the polarity of a magnetic needle has become reversed. With which pole of a magnet will you stroke the original north pole of the needle to restore it to its proper condition ? 2. Can you devise a form of experiment in which the change of the magnetic moment of a magnet due to a change of temperature can be shown and measured? 3. What is the value of the horizontal component of the earth's magnetism at a place where the dip is 71 27' and the intensity is .605 ? 4. Why does the dipping needle stand in a vertical direction when its axis is in the plane of the magnetic meridian ? 5. The blade of a steel table knife can be magnetized by laying it on a table and stroking it with one end of a fire poker held in a vertical direction. Why ? 6. In 1861 a survey was made of a quarter section 160 acres of land having the first line in the magnetic meridian. Show by a drawing the error that would be made by surveying the land accord- ing to the old minutes, in 1900, if the average annual increase in the western declination has been 7'. 7. A magnetic needle vibrated 6 times per minute in the place mentioned in Problem 3. 'What is the intensity of the field of a bar magnet, if the same needle vibrates 29 times per minute, due to both the earth and the magnet acting together ? 8. A certain magnet vibrates 32.2 times per minute in New York and 36 times in Philadelphia. What are the relative values of H in the two places ? CHAPTER II ELECTRICITY 29. The Electric Current. Whenever the ends of a wire are connected to the poles of a voltaic cell or battery, phe- nomena take place in and around the wire that are the effects of what is called an electric current in the wire. These effects may be grouped in three classes and are called: i 4 rpi - cc 1st. I he magnetic etiect; 2d. The chemical effect; 3d. The heating effect. It is worthy of notice that identical electric currents can be obtained in three ways, and that these currents are : 1st. The currents derived from an electrical conductor cutting lines of magnetic force ; 2d. The currents derived from chemical action ; 3d. The currents derived from the action of heat. The experiments that follow are designed to make the student familiar with the different effects of electric cur- rents, and to give some facility in the measurements of these effects. 30. Magnetic Effects of the Current EXPERIMENT 27. Oersted's experiment. Apparatus. Any form of galvanic cell ; a piece of insulated cop- per wire three feet long or more ; a magnetic needle. 35 36 ELECTRICITY Manipulation. Connect the ends of the wire to the terminals of the cell. Hold the wire above, and parallel to, the magnetic needle. Observe the action of the current upon the needle. Reverse the direc- tion of the current and observe. Place the wire below the needle. Repeat both experiments. Formulate a law that shall express the relation between the direction of the current and the direction of deflection of the north end of the needle. Assume that the current flows in the external circuit from the copper or carbon terminal to the zinc terminal. This makes the copper terminal the + pole, and the zinc terminal the pole. This experiment was first made by Oersted, a Danish physicist, in 1820, and. established the relation between electricity and magnetism. Ampere, who studied the experiment carefully, stated the law of deflection as fol- lows : If one considers himself a swimmer going along the wire in the same direction as the current and always facing the needle, the north end of the needle will be deflected toward the swimmer's left hand. A convenient statement of the law is : Let the fingers of the right hand point in the direction in which the cur- rent is going, with the palm always turned toward the needle ; then the north pole of the needle will be deflected toward the thumb. This law is fundamental and should be made very familiar. EXPERIMENT 28. An extension of Experiment 27. Apparatus. A magnetic needle ; a flat coil of wire long enough to inclose the needle; two cells of a battery; and a switch. Manipulation. Place the needle inside the coil, turning the coil until it is parallel to the needle when it comes to rest. Couple the terminals of one cell to the coil, close the switch, and observe the deflection. Compare it with the deflection obtained in Experiment 27. Couple both the cells in series with the coil and observe the deflection.. Compare it with the deflection when one cell was used. MAGNETIC EFFECTS OF THE CURRENT 37 Cells are coupled in series when the copper terminal of one is coupled to the zinc terminal of the other, as in Fig. 29. CELLS IN SERIES , I I + Cu X, \SS EXTERNAL CIRCUIT FIG. 29 They are coupled in parallel when the copper terminals are coupled together, and the zinc terminals are coupled together, as in Fig. 30. This experiment shows CELLS IN PARALLEL that a coil of wire carrying a current deflects a magnetic GoQQQOOQ needle through a greater EXTERNAL C.RCU.T angle than a single wire does, and that two cells produce a greater effect than one. One class of galvanometers, called galvanometers of the first class, makes use of the principle brought out in this experiment. EXPERIMENT 29. - An examination of deflection galvanometers. Apparatus. A cell; connecting wires; several galvanometers of the first class. Manipulation. Couple each galvanometer to the cell in turn and determine the direction of the deflection. From the observed deflec- tion determine the direction of winding in each galvanometer. Make a list of the galvanometers examined, and state why they are of the first class. EXPERIMENT 30. The principle of the solenoid galvanometer. Apparatus. The coil, iron core, and balance shown in Fig. 31; a number of cells ; and a switch. 88 ELECTRICITY Manipulation. Suspend the iron core from one scale pan of the balance so that its upper end shall be 2 in. or 3 in. above the top of the coil. Couple a cell to the coil, having a switch in the cir- cuit. Close the switch and send the current through the coil. Observe any change that takes place in the position of the iron core. Find the weight necessary to bring the beam back to a horizontal posi- tion. Couple two cells in series and re- peat the experiment. This experiment shows that an elec- tric current passing through a coil of wire tends to draw an iron core to its center. FlG 31 This is the prin- ciple upon which a second class of galvanometers operate. They are called solenoid gal- vanometers. EXPERIMENT 31. The effect of a current in a coil upon an iron core. Apparatus. Cells; insulated wire; switch; soft iron rod; and iron filings. Manipulation. Wind the wire closely around the iron rod and couple it to one of the cells, putting the switch in the circuit, as in Fig. 32. Dip the end of the iron rod in the iron filings to test it for mag- netism when the switch is open. Close the switch, sending the cur- MAGNETIC EFFECTS OF THE CURRENT 39 rent through the coil, and again test the rod for magnetism. Repeat with all the cells in series. The results of this experiment show that whenever a current of electricity passes through a coil of wire wound around an iron rod, the rod becomes magnetized, and that the strength of its magnetism increases with the strength of the current. NOTE. In all experiments in which the electric current is used, care should be taken that all contacts, at the binding posts and other couplings, are well made, since a poor contact either weakens the current or makes it unsteady. The current should be cut off by the switch as soon as the experiment is finished, since the current from many forms of cells grows weaker the longer they are used continu- ously. The student must not expect that the current from a battery will go from one point to another unless a conducting path is fur- nished. This path is usually a metallic conductor, such as a wire, and the student can form no better habit than that of tracing out the path of the current in every connection that he makes. EXPERIMENT 32. To determine the relation between the direc- tion of the current in a coil and the polarity of its core. Apparatus. The cells, coil, iron core, and switch used in Experi- ment 31 ; and a magnetic needle. Manipulation. Couple the apparatus as in the preceding experi- ment and send the current through the coil. Determine the polarity of the core by bringing each end alternately near the poles of the needle. Reverse the current in the coil and repeat. Formulate a law showing the relation between the direction of the current in the coil and the resulting polarity of the core. One statement of the law is as follows: If the coil is grasped in the right hand in such a manner that the fingers point in the same direction as that in which the current is pass- ing, then the thumb will point to the north pole of the core, as in Fig. 38. Does the experiment verify this law ? 40 ELECTRICITY 31. Electro-magnets. The combination of coil and iron core described in the last two experiments constitutes an electro-magnet. Electro-magnets are used for many pur- poses, in nearly all of which an important factor is the readiness with which the core becomes demagnetized on breaking the current. The form is usually that of a horseshoe magnet wound in such a way that one of the poles shall be -ZVand the other 8. The armature is a piece of soft iron placed directly in front of the poles. As long as the current is pass- ing through the coil, the armature is held against the poles; but when the FlG ^ circuit is broken and the current is consequently stopped, the armature is moved away by a spring, as shown in Fig. 34. 32. The Telegraph. The essential parts of a tele- graphic circuit are the main battery and line, the send- ing key, and the receiving instrument. The receiving instrument consists of a high resistance electro-magnet called a relay, and a local circuit. The function of the relay is to make and break the local circuit, which con- sists of the local battery and line and a low resistance electro-magnet called the sounder. EXPERIMENT 33. To set up and operate a telegraph line. Apparatus. Cells ; relays ; keys ; sounders ; and wire for the main and local circuits. Manipulation. Set up the instruments as shown in Fig. 35. This figure shows the instruments necessary for one station only. Study the operation of the relay and sounder when the circuit is made and broken by the key. In actual telegraphic work a single wire only is employed, the earth being used as one branch of the circuit. THE TELEGRAPH; THE ELECTRIC BELL 41 NOTE. Since this is a well-known and important method of com- munication, the student should study the circuits carefully and be able to explain fully the function of each part of the apparatus. LOCAL BATTERY MAIN BATTERY 'h FIG. 35 LOCAL CIRCUIT 33. The Electric Bell. Another familiar use to which the electro-magnet is put is in the electric bell. In the telegraph, the circuit is made and 'broken at the will of the operator by the use of the key ; but in the electric bell the circuit is made and broken automatically, as long as the button is pushed. EXPERIMENT 34. To set up and operate an electric bell. Apparatus. A cell ; push button ; connecting wires ; and an elec- tric bell. Manipulation. Couple the cell, push button, and bell in series, and study the action of the bell on closing the circuit with the push button. Make a drawing showing the path of the current in the circuit, and write a detailed description of the automatic action of the bell. EXPERIMENT 35. To determine whether electric bells should be coupled in series or in parallel. Apparatus. A second bell and push button, in addition to the apparatus used in Experiment 34. Manipulation. (a) Couple the two push buttons in such a way that either of them will ring bell No. 1. (ft) Couple the two bells in series and test them. (c) Couple them in parallel and test again. Write the results of experiments (a), (5), and (c), and explain why the bells will ring better with one coupling than with the other. 42 ELECTRICITY 34. The Polarized Bell. A bell having a bar magnet for its armature is called a polarized bell. This armature swings on a pivot at the middle and at this point carries a rod on the end of which is the bell hammer. There are two bells, as in Fig. 36, which are sounded by the alter- nate blows of the hammer caused by the vibrations of the rocking armature. The bell is operated by an alternating current, and is used in telephone calls and for testing the connections of electrical circuits. EXPERIMENT 36. The principle and operation of the polarized bell. Apparatus. A polarized bell; magneto; wires; cells; and the key shown in Fig. 37. This key consists of a brass spring wire KG, screwed to a block of wood at C, and looped into a handle at K. At A and B are pins con- nected to the opposite poles of the cells D and E. Manipulation. (a) Vibrate the free end of the key, touching the pins A and B alternately. (b) Rotate the magneto after coupling the bell to it. Show on a drawing the path of the current in (a) when the key touches A , and when it touches B. FIG. 36 THE POLAKIZED BELL 43 The results of the first part of the experiment (a) show that the direction of the current determines which of the bells is struck. Make a drawing of the bell with detailed winding, and determine from its' BELL FIG. 37 movement the N end of the armature. Verify this determination with a magnetic needle. The second experiment (b) differs from the first in the rapidity of the strokes only. NOTE. A magneto is a small dynamo having permanent magnets for its field and giving an alternating current. EXPERIMENT 37. The use of the polarized bell in tracing connec- tions. Apparatus. Insulated wire and a large tube of some insulating material. FIG. Manipulation. Cut a dozen wires, each a meter long, and run them through the insulating tube as in Fig. 38. Attach a label to each end of every wire, each having a different number, and by the use of the 44 ELECTRICITY magneto, or of the key used in Experiment 36, and the polarized bell, determine which terminals belong to the same wire. NOTE. This kind of work has to be done in finding the terminals of telephone circuits. The experiment can be made more interesting and useful if different kinds of wire are used and their contacts changed within the tube. 35. Magnetism of a Flat Coil. EXPERIMENT 38. To show the magnetic effect in a coil of one turn. Apparatus. Large brass wire; a stand shown in Fig. 39 made of half-inch board; a magnetic needle; cells; and a switch. Manipulation. Bend the brass wire into the form of a ring 6 in. in diameter, and fasten it to the upright part of the stand with __ staples. Connect the ends of the ring to a pair of binding posts; connect the cells and switch in series with the ring and close the switch. Bring one end of the magnetic needle in front of the ring at its middle and deter- mine the relation between the direc- tion of the current in the ring and the polarity of its axis. Bring the same end of the magnet to the other side of the ring, i.e. to the back of the upright support, and again observe the relation. Repeat with the other end of the needle. This experiment may be considered as an extension of Experiment 31, by reducing the coil used in that experiment to a single turn, and removing the iron core. The law for the relation between the direc- tion of the current and the resultant polarity holds in this case. It may also be expressed as follows : The north pole of the ring is facing the observer when the direction of the current is counter-clockwise. 36. The Lines of Force around a Conductor. If the space around a conductor is explored with iron filings, it will be found to be a magnetic field. EXPERIMENT 39. To find the direction of the lines of force around a conductor. FIG. 39 THE LINES OF FORCE AROUND A CONDUCTOR 45 Apparatus. A plate of glass or a smooth card with a wire running through it perpendicular to the surface; a source of electricity capa- ble of giving a current of twenty amperes; iron filings; and a sieve. Manipulation. Couple the wire to the source of current, and while the current is passing sift the filings upon the plate. Tap the plate lightly with a pencil and observe the direc- tion of the lines of force. The experiment shows that the lines of force are circles having the wire as a center. By placing a small compass on the plate near the wire the direction of the lines will be shown to be as in Fig. 40. This experiment is satisfactory with a small current if its effect upon a small magnetic needle alone is wanted, but in order to show the circular character of the lines of force by the use of iron filings a heavy cur- rent must be used. The same result can be obtained by winding a coil of twenty turns of No. 24 wire, threading them through a hole bored in a glass plate and supported as shown in Fig. 41. The hole in the glass plate can be bored with compara- tive ease by using a tube of iron or brass rotated by a vertical drill. Clarnp the glass plate between two boards, with a hole of the size of the tube to be used through the upper one, and feed the tube with fine emery or carborundum moistened with spirits of tur- FIG. 41 pentine in which camphor has been dissolved. Since an arrow is used conventionally to represent the direction in which an electric current is going, a small circle with a dot at its center, to represent the point of the arrow, is used for a current ^. coming toward the observer, while a circle with a cross within it, to represent the feathered end of the arrow, is used for a current going away from the observer (Fig. 42). 46 ELECTRICITY GALVANOMETERS 37. Current, Electro-motive Force, and Resistance. Whenever a conductor of electricity is connected to the terminals' of a battery or other electric generator an elec- tric current will flow along the conductor. The magni- tude of the current will depend upon the relation between the electro-motive force generated by the battery and the resistance offered by the conductor. The unit of current is called the ampere. Electro -motive force is analogous to water pressure in a system of pipes and may be called electrical pressure. The practical unit is the volt. The resistance of a conductor, as its name implies, is the resistance offered by a conductor to the flow of the electric current. It increases as the length of the con- ductor increases, and as the cross section diminishes. It also varies with the material used. The unit is the ohm. These definitions are given to enable us to study gal- vanometers intelligently ; the more complete definitions will be left for consideration later. 38. The Principles of Galvanometers. The three classes of galvanometers suggested by the preceding experiments depend upon the following principles : 1st. That a magnetic needle will be deflected when- ever an electric current is sent through a wire near it. 2d. That an iron core will be drawn toward the center of a coil whenever a current of electricity passes through the coil. 3d. That any coil of wire, however short, becomes a magnet with its poles lying in the axis of the coil when- ever an electric current is sent through it, and hence the GAL VA NOMETERS 47 coil, if properly suspended, will be deflected in the pres- ence of another magnet. The force that tends' to keep the reading of the galva- nometer at the zero point is called the controlling force, and is as follows in the three classes of instruments : Class 1. The horizontal component of the earth's mag- netism, or a bar magnet that can be placed in any desired position. Class 2. Gravity acting upon a weight at one end of a balance, or the pull of a spiral spring. Class 3. Either the tension of a wire suspending the coil, or the action of a flat spiral spring to which the coil is fastened. 39. The Tangent Galvanometer. The tangent galva- nometer is of the first class. In order that the law of the galvanometer may hold, the needle must be sup- ported in the middle of the vertical coil, and the diameter of the coil must be ten or twelve times the length of the needle. The general form of the instrument is shown in Fig. 43. When the galvanometer is in use, the plane of the ring must be vertical and in the magnetic meridian. Figure 44 is a horizon- tal section through the middle of the instrument, which, for the sake of simplicity, 48 ELECTRICITY FIG. 44 is supposed to have but a single turn of wire. The circles surrounding the wire represent the magnetic lines of force. By extending the lines of force until they reach the needle, it will be seen that with a short needle the deflecting force acts in an east-and-west direction, when the galvanometer is placed with its coil in the magnetic meridian. If ab (Fig. 45) represents the deflecting force acting on the -ZV^end of the needle, the component of this force that acts at a right angle to the needle will be ab cos x, in which x is the angle of the deflection. The controlling force is ad = H, and when the needle is in equilibrium, the component ae = H sin x is equal and opposite to ac. Hence we have ab cos x = If sin x, and ab = H tan x. Since ab is proportional to the current, ab = k =ff tan x, in which k is a constant depending upon the in- strument. For any other current C", kC' =ff tan x' \ hence 52 of the two points by put- ting the voltmeter in connection with them. EXPERIMENT 41. rTo classify voltmeters. Apparatus. Voltmeters of different makes; a resistance coil; cells; and a switch. Manipulation. Couple the cells in series to the switch and resist- ance coil, which should have a resistance of at least 1000 ohms. Connect each voltmeter in turn as a shunt to the terminals of the resistance coil. Examine the construction and test the deflection of each. Determine the class of galvanometer to which each instrument belongs. BATTERIES 48. Galvanic Batteries. The galvanic, or voltaic, cell is an electric generator in which the current is the result of the physical relations between the different materials of which the cell is composed. When a number of these cells are coupled together they form a battery. A cell can be made by inserting in a liquid any two solids, usually metals, upon which the liquid acts with different intensities. The accompanying table is arranged in such a way that if the substances are placed in dilute sulphuric acid, each will l- zinc 6 - Copper be electro-positive to the ones 2 ' Tin 7> Silver following it and electro-negative to those preceding it. Thus it 3. Lead 8. Gold 4. Iron 9. Platinum 5. Nickel 10. Graphite BATTERIES 55 will be seen that iron is electro-positive to copper and electro-negative to zinc. The order given in the table does not hold for other liquids. In potassium sulphide, for example, copper is electro-positive to iron. EXPERIMENT 42. A partial verification of the preceding table. Apparatus. A battery jar half full of dilute sulphuric acid; plates of copper, iron, and zinc ; strips of wood ; connecting wires ; and a voltmeter. Manipulation. Drill two holes in the end of each plate, and screw them to the strips of wood. Attach wires to each plate as shown in the figure. Test the voltage of each pair by coupling to the voltmeter. Arrange the metals in the order indicated by their difference of potential. Is the order the same as that in the table? Does the difference in voltage between the copper and the zinc equal the sum of differences between the copper and the iron, and the iron and the zinc ? NOTE. If metal A is electro-positive to metal B, when placed in a liquid, the current passes from A to B in the liquid, and from B to A in the external circuit. 49. The Gravity Cell. FIG. 54 This cell consists of a glass jar in the bottom of which is placed a copper plate, generally made of thin copper spread out to give greater surface, around which are packed crystals of copper sulphate. Water is poured into the jar to make a solution of the copper sul- phate, and upon this is poured a solution of zinc sulphate, or dilate sulphuric acid. Sus- pended from the edge of the 56 ELECTRICITY jar is a zinc plate, frequently in a form that gives the cell the name of the crowfoot cell. The general name of this cell is derived from the fact that the copper sulphate solution, being heavier than the zinc sulphate, is kept separated from it by the action of gravity. As a result of the action that takes place in the cell the zinc plate is destroyed, and the zinc sulphate is increased in amount, while the copper from the copper sulphate is deposited as metallic copper on the copper plate. In chemical symbols this action is expressed as follows : Zn + ZnSO 4 + CuSO 4 + Cu = 2 ZnSO 4 + 2 Cu. By substituting the atomic weights of the elements in this formula, we can find how much copper sulphate is needed to use up a given quantity of zinc. The gravity cell gives a nearly constant voltage and steady current and is much used on telegraph lines. The copper terminal is positive to the zinc terminal, and in the external circuit the current goes from the copper to the zinc. This means that the positive terminal is attached to the electro-negative plate and the negative terminal to the electro-positive plate. 50. The Leclanche Cell. This cell consists of a glass jar in which is placed a porous cup containing a carbon plate embedded in man- ganese dioxide and gas carbon, both in small pieces. The porous cup is sealed after the contents have been well packed together. After the porous cup is placed in the glass jar a solution of sal ammoniac is poured FIG. 55 in until the jar is two thirds full, and BATTERIES 57 a zinc rod is placed in the solution by the side of the por- ous cup. This cell is an open-circuit cell, and is used when the current is wanted for a short time only, as in electric bell lines. When a cell is capable of giving a steady current for some time, like the gravity cell, it is called a closed- circuit cell. 51. The Potassium Bichromate Cell. A common form of this cell is shown in Fig. 56. The two out- side plates are of carbon and are fixed to the cover of the cell. The middle plate is of zinc and can be lowered into the liquid or raised from it and clamped in place by the middle rod. As the action goes on in the cell whenever the zinc is in the liquid, the plate should be raised except when the cell is in use. A satisfactory formula for the liquid is : Pulverized potassium bichromate . . 1 Ib. Strong sulphuric acid . . . . . 2 Ib. Water . . . ., . ... . . 12 Ib. The bichromate must be added to the acid with con- stant stirring, after which the mixture is to be poured slowly into the water, also with constant stirring. An- other formula, more easily made up, is as follows : Commercial chromic acid . . 160 grams Water . . .... . . 1420 c.c. Sulphuric acid . . "-. . *". . 90 c.c. Dissolve the chromic acid in the water and then add 58 ELECTRICITY slowly the sulphuric acid, stirring the mixture with a glass rod. This is a convenient form of cell when a strong current is needed for a short time. A number of these cells are frequently arranged in such a way that the zincs can all be raised and lowered at the same time, thus forming a plunge battery. 52. The Dry Battery. A convenient form of portable cell is what is called the dry battery. The zinc plate forms the outer cup of the cell, and the carbon plate is packed in the middle, extending above the contents of the cell. This is a useful cell when the current is wanted but a little while at a time, and forms a ready means of obtaining a battery of high electro-motive force by coupling a FIG. 57 number of these cells in series. EXPERIMENT 43. To examine different kinds of cells. Apparatus. Cells of the above types ; a voltmeter. Manipulation. Measure the voltage of each cell by coupling a voltmeter directly to its terminals, take a record of each, and make a list of the voltages of the different classes. Observe whether the cells of each class have a common voltage. The voltage of these cells should be taken later in the year after they have had considerable laboratory use, and the readings compared with those now taken. EXPERIMENT 44. To study the effect upon the voltage of a cell, produced by taking a continuous current from it. Apparatus. One open-circuit and one closed-circuit cell; two low- resistance coils ; two voltmeters ; and two switches. Manipulation. Couple each cell with a low-resistance coil and a BATTERIES 59 switch, and couple a voltmeter to the terminals of each cell. Read the voltage of each cell before the switch has been closed, and for each five minutes afterward as long as it seems to be desirable, opening the switch each time just long enough to take the reading. From the record made for each cell make a curve that shall show the relation between the voltage of the cell and the time of observa- tion. The form of the curve should show clearly the different effects of polarization in the two cells. EXPERIMENT 45. -To find the voltage of cells coupled in series. Apparatus. Four or five cells of the same kind; a voltmeter. Manipulation. Take the voltage of each cell separately. Couple the cells in series, taking first two, then three, and so on until the whole number is used, and take the voltage of each set. The results of this experiment should show that when N cells are coupled in series, their combined voltage is the sum of their voltages taken separately. If the cells have a uniform voltage, the voltage of N cells will be N times the voltage of one. EXPERIMENT 46. To find the voltage of cells coupled in parallel. Apparatus. The cells and voltmeter used in Experiment 45. Manipulation. Couple the cells in parallel instead of in series as before, and take the voltage of each set. The results of this experiment should show that the voltage of any number of cells coupled in parallel is the same as the voltage of a single cell. The results of this and the previous experiment are as true for dynamos as for cells. 53. The Electro-motive Force of a Cell. EXPERIMENT 47. Does the size determine the voltage of a cell ? Apparatus. A potassium bichromate cell and a voltmeter. Manipulation. Couple the voltmeter to the cell and push down the rod carrying the zinc far enough so that the zinc will just touch the liquid. Read the voltmeter and make a record of the reading. Push down the zinc a half inch more, take the reading, and make a record. Repeat the process until the zinc is entirely submerged. The results of this experiment show that the size of a cell does not determine its voltage. By referring to the results of Experiment 43, 60 ELECTRICITY we see that different cells have different voltages ; hence we may say that the voltage of a cell does not depend upon its size, but upon the kind of plates used and the solution in which they are used. QUESTIONS AND PROBLEMS 1. The controlling force in a certain galvanometer is the earth's magnetism. In what position should the coil be when in use ? Why ? 2. Suppose an electro-magnet is to be used in a circuit in which there is a high resistance but a small current ; would you wind it with fine or with coarse wire ? Why ? 3. Make drawings for the connections of a "single stroke" bell, that is, one that will strike only once when the circuit is closed. 4. Make a drawing of the end of an ordinary horseshoe electro- magnet, showing the direction of the winding and the resulting polar- ity of each core. Do the same for the electro-magnet of a polarized bell. Compare the two drawings. 5. What is the difference between a galvanometer and a galvano- scope ? 6. A tangent galvanometer gives a deflection of 8 degrees ; what will be the deflection when the current strength is doubled? 7. A certain galvanometer has a figure of merit of .015, and its resistance is .023 ohm. What difference of potential at its terminals is necessary to produce a deflection of one scale division? 8. Suppose you have a current passing through a given resistance ; show the effect of coupling the voltmeter in series with the resistance instead of at its terminals. 9. How much copper sulphate must be taken in a gravity cell to use up a zinc plate weighing 3 Ib. ? 10. An incandescent -lamp in the hall of a house is to be turned on or off by a switch at the front door, and also by one on the second floor. Show by a drawing the arrangement of switches, lamp, and connecting wires. Verify the drawing by constructing a line that will fulfill the conditions. RESISTANCE 54. Electrical Contacts. In making the contacts for an electrical circuit, great care should be taken that they are firm and bring the parts into a real metallic contact. EESISTANCE 61 When two wires are to be connected permanently they should be soldered and not twisted together. Twisting the end of a wire to make a contact not only does not make a good contact, but it spoils the end of the wire for future use. EXPERIMENT 48. To show the value of a good contact. Apparatus. A brass chain fastened at one end and held at the other by one end of a lever, as in Fig. 58; cell; and gal- vanometer. Manipulation. Couple the chain, cell, and galvanometer in series. Notice the de- r IG. DO flection of the galvanometer, first when the chain is hanging loose, and then when it is drawn tight by pulling down on the free end of the lever. Does the poor contact made by the chain when loose increase or decrease the current flowing through the galvanometer? 55. Electrical Resistance. The resistance of an elec- trical conductor depends upon three things : its length, its cross section, and its material. The relation that each of these holds to the resistance will be shown in the follow- ing experiment. EXPERIMENT 49. To show how the resistance of a conductor varies. Apparatus. Insulated copper wire No. 18 and No. 30; German silver wire No. 30 ; cells ; and a galvanometer. Manipulation. Cut from the No. 18 wire a piece 10 ft. long, and couple it in series with the cells and the galvanometer. Read the deflection of the galvanometer. Repeat, using a piece of copper wire, No. 18, 30 ft. long, and then a piece of copper wire, No. 30, 30 ft. long. Do the same with a piece of the German silver wire 30 ft. long. Since the deflection of the galvanometer increases with an increase of the current, and since the current decreases with an increase of the resistance, the results of the experiment should show that an increase 62 ELECTRICITY in the length of a wire increases its resistance ; that an increase in its diameter decreases its resistance ; and that changing from a copper wire to a German silver wire of the same length and diameter in- creases the resistance. 56. Formula for the Resistance of a Wire. The rela- tion between the length, diameter, and material of a wire and its resistance may be expressed by a formula. Let R equal resistance. Let L equal length. Let A equal area of cross section. Let D equal diameter. Let k equal a constant depending upon the material of the wire, and called its specific resistance. This is the resistance of a cube of the material one unit in length. The resistance will then be expressed as follows : Since the areas of cross section of two wires are directly proportional to the squares of their diameters, the formula can be written R = k In a second wire in which the L' length is L' it becomes R = k Hence we can write R : R' = L : L'. Stated as a law this becomes : In wires of the same diameter and material the resistances are directly proportional to the lengths. In the same way we can derive R : R = D' 2 : D 2 , and R : R' = k : V. 57. Ohm's Law. The definite relation existing between electro-motive force, resistance, and current was investi- gated in a series of careful experiments by Ohm in 1827. Using the same conductor, he proved not only that the current varies with the electro-motive force, but that this RESISTANCE 63 variation is in a direct proportion. This means that the resistance of a conductor is the ratio of the electro-motive XT force to the current. The law as usually stated is C= E From this two other forms can be derived : R = , and C E RO. This is the foundation formula for these rela- tions, and should be made so familiar that it can be recog- nized in its various forms. 58. Resistance Boxes. A resistance box is a box con- taining coils of resistance wire with their ends connected FIG. 59 to terminals in such a way that they can be thrown into a circuit, or out of it, at will. Figure 59 shows a common form of resistance box, while the method of winding the coil double so that it shall - r^7 A be non-inductive, and of connecting its ends, is shown in Fig. 60. In using the plug resistance box care should be taken to put the plugs in with a slight twist so that there shall be no resistance introduced by poor contact. FlG> 00 64 ELECTRICITY 59. The Measurement of Resistance ; the Substitution Method. There are a number of ways in which the resist- ance of a conductor can be measured. One of the simplest of these is the method of substitution. It is not an accu- rate method, unless the contacts are very carefully made, but will give a close approximation. EXPERIMENT 50. To measure a resistance by the substitution method. Apparatus. A galvanometer; resistance box; two or more cells; the substitution board shown in the figure ; and the wire to be tested. Manipulation. Couple the resistance box and the wire to be tested to the cells and galvanometer by means of the substitution board, as shown in Fig. 61. Turn the switch so that the current will pass first through the coil cir- cuit, and observe the deflection of the gal- vanometer. Turn the switch so that the current will pass through the box cir- cuit, and regulate the resistance in the box so that the deflec- tion of the galvanom- eter shall be nearly FlG - 61 what it was in the first circuit. Throw the current from one circuit to the other, chan- ging the resistance in the box until the deflection of the galvanometer does not change on throwing the switch. When this condition is found, the reading of the box is the resistance of the coil. 60. The Fall of Potential along a Wire. Whenever there is an electric current passing along a wire, there will be a fall of potential along it that will be dependent RESISTANCE 65 upon the resistance of the wire. If this is of homogeneous material and of uniform cross section, the resistance will be the same for equal lengths, and the fall of potential will be proportional to the length. In order to measure this fall of potential the apparatus shown in Fig. 62 may be used. 19 18 1 FIG. 62 EXPERIMENT 51. To determine the fall of potential along a wire. Apparatus. A board with a German silver or iron wire 2 m. long stretched between the points C and D\ a number of cells; a voltmeter; an ammeter; a switch ; and connecting wires. Manipulation. Divide the distance CD into equal parts, as at 1, 2, etc. Couple the wire, cells, ammeter, and switch in series. Couple one terminal of the voltmeter to the point C, as shown, and its other terminal to the points /), 19, 18, etc., consecutively. Read the am- meter and voltmeter at the same time and tabulate the results. If the cells are of a kind that polarize easily, a variable resistance should be coupled in series with the wire, in order to keep the current of uniform value. A fairly good result can be obtained by omitting the ammeter and using the current only long enough at a time to read the voltmeter. Make a curve showing the relation between the length of a wire and the fall of potential along it, when a uniform difference of poten- tial is maintained at its ends. 61. The Measurement of Resistance ; the Fall of Potential Method. By applying Ohm's law to the case of a current ELEC. AND MAG. 5 66 ELECTRICITY flowing along a wire, we see that the current that passes depends upon the resistance of the wire and the difference of potential at its ends. This difference of potential at different points is, as the pre- vious experiment shows, the fall of potential along the wire. In order to measure the resistance of a conductor by this method, both an ammeter and a voltmeter must be used. Fig- ure 63 shows the coupling of the ammeter, voltmeter, cells, and resistance to be measured. The ammeter is coupled in series with the resistance, to measure the current, while the voltmeter is put in as a shunt to the coil, contact being made at its terminals. EXPERIMENT 52. To measure resistance by the fall of poten- tial method. Apparatus. An ammeter; voltmeter; switch; cells; and several coils of wire. Manipulation. Couple the apparatus as shown in the figure above. Read the instruments simultaneously, and compute the resist- ance of each coil from the expression FIG. 63 This method is a convenient one for practical work in electrical stations, since it requires only the apparatus RESISTANCE 67 with which every station is provided. With sensitive instruments it is a rapid and accurate method. The resistance of the voltmeter should be so high that the cur- rent that passes through it is very small, so small in fact that the reading of the ammeter may be taken as the true value of the current in the coil. If the resistance of the volt- meter is small, it can still be used, but must be coupled to the terminals of the am- meter and coil in series as shown in Fig. 64. The resist- ance measured with this coupling will be the sum of the resistances of the coil and the ammeter. The resistance of the ammeter is usually known and can be subtracted from the sum to obtain the required resistance. EXPERIMENT 53. To show the influence of the voltmeter resist- ance. Apparatus. A coil of wire; an ammeter; and two voltmeters, one of high and one of low resistance. Manipulation. Measure the resistance of the coil by the fall of potential method, with the high -re si stance voltmeter, and then with the low-resistance voltmeter, using the coupling of Fig. 63. Explain the difference in the results. Measure again with the low-resistance voltmeter, using the method of Fig. 64. Explain the difference between this result and that of the last measurement. 62. The Wheatstone Bridge. If an electric current is going from the point A to the point 5, through the two FIG. 64 68 ELECTRICITY y i < III) V \ \ 11 1 IT paths AxB and AyB, in Fig. 65, it is evident that there is the same fall of potential in each branch, since they begin and end at the same point. If a point x in the x upper branch is con- nected by a conduct- ing wire to some point of the lower branch, as y, the direction of the current in the wire xy will depend upon the difference of FlG ' 65 potential between the points x and y. If the point is chosen at z and the fall of potential from A to z is less than from A to x, then the current will go from z to x. If the point is chosen at w, so that the fall of potential from A to w is greater than that from A to #, the current will go from x to w. It is evident that a position may be chosen such that the fall of potential from A to y will be the same as from A to x. When this position is found, there will be no current in the conductor xy. The relation between the potential differences at the several points can now be written : The potential difference between A and x _ The potential difference between A and y The potential difference between x and B The potential difference between y and B We have already learned that potential differences in conductors are proportional to their resistances ; hence we can state the proportion : The resistance of Ax _The resistance of xB The resistance of Ay The resistance of yB THE WHEATSTONE BRIDGE 69 Or, letting r, r\ r", r'" represent the various resistances, r : r = r : r If we substitute a wire of uniform cross section for the lower branches, as in Fig. 66, the proportion becomes r:Z=r':Z'; whence rl' = r'l. By putting a galvanometer Q- in the conductor xy, the position in which there is no difference of potential between x and y is determined when there is no deflection of the galvanometer. One form given to the Wheatstone bridge for practical work is shown in diagram in Fig. 67. In this form the FIG. 67 wire A C is a meter long and is fastened to the base of the instrument at the points A and C. This wire forms one side of a rectangle, the other sides of which are formed by a copper strap which has two gaps in it at EF and TH. One of these gaps is bridged by the resistance to be meas- 70 ELECTRICITY ured, and the other by the resistance box. The battery is connected at the points L and Jf, while the galvanometer is coupled permanently at JV, contact with the wire being made by the key K. By referring to Figs. 66 and 67, we see that Ml' = Bl ; i.e. the products of the cross multi- plications of the branches of the bridge are equal. While this is theoretically true for any values of I and Z', it is much better practice to keep the key as near the middle of the wire as possible. If it is kept at the exact middle, the resistance of the box is a measure of the unknown resist- ance. It is readily seen that for accurate measurements a sensitive galvanometer must be employed, since the potential difference between N and K is never large. The most sensitive arrangement of the bridge is when the resistances of the four arms are equal. As the accu- racy of the method depends upon the uniform resistance of the bridge wire, great care should be exercised in making contact with the key K, not to press it down so hard as to bend the wire. The Wheatstone bridge is an accurate instrument when understood and properly used. The student should make numerous measurements with it, as in no other way can its capabilities and limitations be discovered. 63. The Portable Testing Set A design of Wheatstone bridge in which the parts of the bridge wire are replaced by plug resistance boxes, and which also contains a bat- tery, galvanometer, and rheostat in a convenient carrying case, is known as a Portable Testing Set. It is capable of a wide range of measurements and is accurate for practical purposes. The connection of the several resistance boxes to the battery and galvanometer is made through a part of the DIVISION THE PORTABLE TESTING SET 71 apparatus called the commutator. This consists of four heavy brass blocks that serve as connections to the arms of the bridge, A and 2?, the known resistance R, and the unknown resistance -X". Figure 68 shows diagrammatically the connections, from which it may be seen that the function of the commutator is to reverse the relative positions of R and X with respect FIG. 68 to A and B, the arms of the bridge. When the resistance to be measured is high, the commutator plugs are placed as in Fig. 68, connecting A with R and B with X, in 7} which case A : B = R : X, and X = R. A If a small resistance is to be measured, the plugs are placed in the other diagonal, connecting A with X and B with R. In this case A : B = X : R, and X= ^.R. Jj The bridge boxes A and B have each three resistance coils, of 1, 10, and 100 ohms, and of 10, 100, and 1000 ohms, 72 ELECTRICITY respectively ; hence the value of X is always obtained by multiplying the value of R by some power of 10. In using any particular testing set, certain directions for the method of procedure are furnished by the maker, together with the values of resistances in the bridge and rheostats that should be used to secure the greatest accuracy. In general, the procedure is to plug the commutator connection in the diagonal H or X, depending upon the estimate of the resistance of X as high or low, unplug the 100-ohm coil in each of the bridge arms A and 5, and then unplug resistances in the rheostat until its total resistance is equal to the estimate of the resistance of X. Hold the batter}*- key down, then press the galvanometer key, and from the movement of the needle determine whether the resistance in the rheostat is too great or too small. When a balance has been obtained, greater accuracy should be secured by including all the cells of the battery and making the ratio of the resistances in A and B such as is given in the table furnished with the instrument. 64. The Measurement of Resistance ; Differential Gal- vanometer Method. Resistances can be measured by the use of a differential galvanometer as follows : EXPERIMENT 54. To measure a resistance with the differential galvanometer. Apparatus. A differential galvanometer ; resistance box ; cells; switch ; and the coil to be tested. Manipulation. Couple the apparatus as shown in Fig. 69, and regulate the resistance of FJG 6Q the box until there is no deflec- tion of the needle. When this condition is secured, the reading of the box is the resistance of the coil. THE RESISTANCE OF PARALLEL CIRCUITS 73 As this is a nil method, it is better adapted to the measurement of non-inductive than of inductive resist- ances. If inductive resistances are to be measured, the current must be allowed to flow until there is a steady current in order to overcome the influence of the self-induction. 65. The Resistance of Parallel Circuits. When two points, as A and B (Fig. 70), are connected by two con- ductors, the proportion of the total current that 1 I will pass through each will depend upon its FlG> 70 resistance. If these resistances are equal, the currents will be equal, and each will be one half the total current. If, however, the resistances are unequal, the current in each will be proportional to the resistance in the other. This may be expressed by the proportion 0' : C" = R" : R', in which C' and R 1 are the current and resistance of X, and C" and R" are the current and resistance of Y. Since the potential difference between A and B is the same in both wires, the respective currents, may be expressed by the equations <,_2 -a a-.", ro . ru> _ n ni . n" 7?" 7?' -j^i - ^77' -U.K. The part of the current passing through X will be given by the proportion C' : O = R' 1 : R 1 ' + R 1 , in which C is the total current. The combined or parallel resistance of X and Y is equal to the product of the resistances divided by their 74 ELECT1UCITY R' R' f sum ; that is, R p = - For when the electro-motive ./t -\- .K force is 1, 0'=, and 0" = - ; therefore -it All tf' + tf"=-l 1 = R' + R". R' R" R'R" and since C' + O" = (7, the whole current, hence 0= R ^"^ ; 1 R 1 R ff and since R p , therefore R p = - - C l> -j- /t For example, if R' = 3 ohms and J?" = 5 ohms, then For more than two branches, three for example, the value ill 1 R'R'R" _1_ J_ J_ " ^'^" + .B' JK" ; + #"72"' ' #' #" #'" This may be stated as follows : The parallel resistance of several circuits may be obtained by dividing the product of all the resistances by the sum of the products of each resistance by all the others taken separately ; or it is the reciprocal of the sum of the reciprocals of all the resistances taken separately. EXPERIMENT 55. To measure the parallel resistance of lamps. Apparatus. A lamp board with a half dozen lamp bases and binding posts as shown in the figure; a half dozen lamps of different candle power. Ma nipulation. Measure the resistance of each lamp separately. Measure the resistance of the lamps in parallel in groups of two at a time, then in groups of three at a time, and so on. Com- pare the measured resistances with those obtained by substituting the separate resistances in the above formula. SHUNTS 75 The results of this experiment should show agreement within nar- row limits. The parallel resistance of two conductors is always less than the resistance of either taken alone. 66. Shunts. The principle of divided or parallel cir- cuits is applicable in the case of shunts. If it is desired to measure a current greater than can be measured by the galvanometer or ammeter, a part of the current can be sent through a resistance in parallel with the instrument, and this is called a shunt. The parallel coupling of a galvanometer and its shunt is shown in Fig. 72. The ratio of the currents in the two circuits will be expressed by the proportion O ff :O s = R s : R g , while the ratio of the galvanom- eter current to the total current will be C g : C = R s :R g A convenient arrangement is to have the current in the galvanometer one tenth of the whole current; then the resistance of the shunt will be one tenth of the sum of the two. In this case, R s : R g + R s = 1 : 10, hence R q + R s = 10 R s , and 9 R s = R g , or R s = R g . This is what is called a tenth shunt, for the whole current will be obtained by multiplying the galvanometer current by 10. - In the same way, a hundredth shunt can be shown to be one in which R s = ^ R g . EXPERIMENT 56. To make a tenth shunt for a galvanometer. Apparatus. A low-reading galvanometer, and a spool of high- resistance wire. Manipulation. Measure the resistance of the galvanometer. Cut from the spool of wire a piece 10 ft. long and measure its resist- ance. Compute the length of wire required to make a tenth shunt. Cut from the spool a piece 2 ft. longer than the computation calls 76 ELECTRICITY for. Measure its resistance and reduce the length of the wire, measuring the resistance each time, until the exact length is found. Wind this wire into a non-inductive resistance coil by winding it on a spool double, beginning at the middle. This method of winding is a convenient one, since it brings both ends of the coil on the outside. In order to verify the accuracy of the work, it will be well to compare the readings of the shunted galvanometer with those of a reliable ammeter. What change has been made in the usefulness of the galvanometer ? 67. The Internal Resistance of Batteries. The fact that a battery is a generator makes it more difficult to measure its resistance than it is to measure the resistance of a coil of wire. The following are some of the methods used : EXPERIMENT 57. (a) The three-cell method. Apparatus. Three cells, two of which have the same electro- motive force ; the substitution board used in Experiment 50 ; a resist- ance box ; and a galvanometer. Manipulation. Consider the cell A (Fig. 73) as the source of E. M. F., while the two equal cells B and C are coupled so as to oppose each other. Connect these cells and the resistance box as in the substitution method of measuring resist- ance, and find their resistance. The method will not be accurate unless the' cells C and B, when coupled as in the figure, give no current. It is not a method that can be relied upon for the greatest accuracy under any circumstances. EXPERIMENT 58. (ft) Mance's method. Apparatus. The cell, the resistance of which is to be measured; a Wheatstone bridge ; connecting wires ; and a contact key. THE INTERNAL RESISTANCE OF BATTERIES 77 Manipulation. Place the cell in one of the arms of the bridge, as shown, and place the key between A and D instead of in the galva- nometer circuit BC. Vary the resistance of the box until such a resistance is found that the opening and closing of the key makes no difference in the deflection of the galva- A nometer. When such a resist- ance is found, it is equal to the resistance of the cell, pro- vided that AB is one half of AD. This is a satisfactory method except that it requires a different form of coupling for the bridge, and takes considerable time to complete. EXPERIMENT 59. (c) The voltmeter method. Apparatus. A low-reading voltmeter; ammeter; resistance box; a two-way switch; and the cell the resistance of which is to be measured. Manipulation. Couple the apparatus as in the figure and take the reading of the voltmeter. Throw the switch from the voltmeter to the ammeter circuit and take the reading of the ammeter as soon as possible. Substi- tute these readings in the E expression R = and find C the value of R. This gives the resistance of the ammeter circuit. Subtract the resist- A ance of the ammeter, resist- ance box, leading wires, and switch, and the remainder gives the resistance of the cell. This method assumes that the difference of potential at the ter- minals of the cell, measured by the voltmeter, is the E. M. F. of the cell. With a voltmeter that can be read to the hundredth of a volt it is a rapid and accurate method. FIG. 75 78 ELECTRICITY EXPERIMENT 60. (d) A modification of (c). Apparatus. The cell, resistance box, and the voltmeter used in Experiment 59; and two switches. Manipulation. Couple the apparatus so that the voltmeter may be thrown into the circuit alone or in parallel with the resistance box. Throw the voltmeter into the circuit and call the reading V- Throw the resistance in, in parallel with the voltmeter, and take a second reading immediately after the drop that takes place on throw- ing the switch. Call this reading V". Measure the resistance of the switch and connecting wires, add this to the reading of the resistance box, and call it R'. Then C = ~ Call the resistance of the cell \rr T/// f* R. Then R = l v . C NOTE. When the voltmeter switch is closed, the reading must be taken immediately on account of the polarization of the cell. The effect of this polarization will be shown by a gradual decrease in the reading. 68. Variation of Resistance with Temperature. Makers of resistance boxes to be used where a high degree of accuracy is necessary always state the temperature at which the box will give the rated resistance, as well as the temperature coefficient. In order to determine this varia- tion some method of taking the resistance at different temperatures must be used. EXPERIMENT 61. To determine the temperature coefficient. Apparatus. (a) German silver. A coil of fine German silver wire ; a number of battery cells; a -thermometer ; beaker; and a Bunsen burner. Manipulation. Fill the beaker with cold water and take its tem- perature. Insert the coil in the beaker and measure its resistance. Heat the water to a temperature of 60 and again measure the resist- ance of the coil. Bring the water to the boiling point and measure again. From the results obtained determine the temperature coefficient, i.e. the change of the resistance per degree of temperature, for German silver. The determination of this coefficient is important, since- the use of a large current heats a conductor and hence changes its resistance. VARIATION OF RESISTANCE WITH TEMPERATURE 79 (b) Copper. Repeat the experiment with a copper wire of the same resistance. EXPERIMENT 62. The effect of raising the temperature of carbon, upon its resistance. Apparatus. A small carbon pencil, such as is sometimes used in projection lanterns ; a number of storage cells, or a dynamo ; ammeter, voltmeter, and Wheatstone bridge. Manipulation. Measure the cold resistance of the carbon by the Wheatstone bridge method. Send enough current through the pencil to raise it to a high temperature, and measure the resistance by the fall of potential method. How does carbon compare with German silver in regard to the relation between temperature and resistance? How does it compare with copper ? EXPERIMENT 63. To compare the hot resistance of incandescent lamps with their resistance when cold. Apparatus. Dynamo or storage cells; incandescent lamps of the proper voltage for the circuits used ; ammeter ; voltmeter ; and Wheatstone bridge. Manipulation. Measure the cold resistance of one, five, and ten lamps by the Wheatstone bridge. Bring the lamps up to their proper voltage and measure their hot resistance by the fall of potential method. Compare the results of these experiments and state the importance of these results. EXPERIMENT 64. To measure the resistance of an arc light. Apparatus. A dynamo; hand-regulated arc lamp ; ammeter; and voltmeter. Manipulation. () Run the lamp with a nine, a ten, and a twelve ampere current, keeping the distance between the carbon points con- stant, and not over a quarter of an inch. Measure the resistance for each by the fall of potential method. (b) Repeat the measurements with a long arc, keeping the length constant. (c) Start the lamp with a short arc and let it burn until the arc breaks. Measure the resistance at different times. Measure the final length of the arc and determine the rate of consumption of the carbons. How does the resistance of the arc vary with its length? Does its resistance vary with the current used? 80 ELECTRICITY 69. Insulation Resistance. It is frequently necessary to have a rapid method of finding the resistance of a certain insulation. The following method fulfills the requirements. EXPERIMENT 65. To measure insulation resistance with volt- meters. Apparatus. Two high-resistance voltmeters; a dynamo or storage battery; and the insulation to be measured. Manipulation. Let the points A and B be the terminals of the electric generator. Couple one voltmeter directly to these terminals. Couple one binding post of the other voltmeter to one of these terminals, as A, and the other to one Oside of the insulation. B Couple B to the other side of the insulation and take simultaneous readings of the two voltmeters. Let V represent the reading of the first volt- meter, V" that of the second, r the resistance of the second voltmeter, and R the resistance of Hence S FIG. 76 the insulation ; then V" : V - V" = r : R. 70. The Resistance of Electrolytes. An electrolyte is any solution that is a conductor for an electric current. When a current passes through such a conductor, a decom- position, called electrolysis, takes place in the solution. The plate by which the current enters the solution is called the positive electrode, or anode, and that by which the cur- rent leaves the solution is called the negative electrode, THE RESISTANCE OF ELECTROLYTES 81 or cathode. The determination of the resistance of an electrolyte is complicated by the counter electro-motive force that is set up whenever a current is sent through it. This difficulty is overcome in the following method : EXPERIMENT 66. To measure the resistance of an electrolyte. Apparatus. A glass tube an inch in diameter and a foot long; two pieces of platinum wire 6 in. long; cells; a galvanometer; resist- ance box ; switch ; and a solution of copper sulphate. Manipulation. Wind each platinum wire into a flat spiral that will nearly fill the tube. Close the end of the tube in a Bunsen flame, sealing in one of the platinum spirals as shown. Solder the other spiral to an insulated copper wire and paraffin the latter for a foot from the joint. Couple the apparatus as shown in Fig. 77, and send a current through the circuit when the upper spiral is in the position P', regulating the resistance in the box until a suitable deflection is obtained in the galvanometer. Lower the upper spiral to a second position P", sending a current through the circuit a second time, changing the resistance in the box until the deflection of the galvanometer is the same as before. When this condition is secured, the resistance added in the box will be the resistance of the liquid column P'P". Since this measurement gives the resistance of the column P'P", the resistance of the column per unit length is readily found. It is well in every measurement to leave the current on only long enough to take the readings. Notes should be made of the per cent of the solution and of the temperature at the time of the experiment, as both of these conditions modify the results. EXPERIMENT 67. To measure the resistance of an electrolyte with the alternating current. Apparatus. The electrolytic tube used in Experiment 66; a Wheatstone bridge; resistance box; induction coil; telephone re- ceiver; and cells. ELEC. AND MAG. 6 FIG. 77 82 ELECTRICITY Manipulation. Couple the apparatus as in Fig. 78, placing the induction coil at such a distance (in another room if necessary) that the noise of the contact breaker can not be heard. Find by trial a point D in the bridge wire that will give the least sound in the receiver. C I 1 o o o o 1 1 -hi 19 ? 9 xL 1 1 L i ib (. 1 Ol IO J J FIG. 78 When this point is determined, the resistance may be computed by applying the law of the bridge. If the point D is in the middle of the bridge wire, the resistance of the electrolyte is the same as that in the box. 71. The Unit of Resistance, the Ohm. Mention has been made, in Section 37, of the ohm as the unit of elec- trical resistance. The unit in use at the present time is the international ohm. This was recommended at the meeting of the British Association in 1892, was adopted by the International Electrical Congress held in Chicago in 1893, and was legalized for use in the United States by Act of Congress in 1894. It is defined as the resistance of 14.4521 g. of mercury in the form of a column of uniform cross section, 106.3cm. in length, at a temperature of C. This is equivalent to a THE UNIT OF RESISTANCE 83 column 106.3 cm. long, having a uniform cross section of 1 sq. mm. Previous to this there had been three more or less generally accepted values of the ohm. First : The Siemens Unit. This was the resistance of a column of mercury 100 cm. long and 1 sq. mm. in cross section, at C. Second : The B. A. (British Association) Unit. In this the mercury column was 1 sq. mm. in cross section and approximately 104.9 cm. long. Third: The unit adopted by the Paris Conference of 1884, which was defined in the same terms, except that the length was given as 106 cm. This was called the Legal Ohm. The comparative values of these units are as follows : UNIT VALUE DATE International Ohm 1.000 1893 Legal Ohm 9972 1884 B. A. Ohm ...... . . 9866 1864 Siemens Unit 9407 72. Rheostats. A rheostat is a device for regulating the resistance in an electric circuit. There are many forms, that vary with the requirements of the circuit in which they are used. Examples of the most useful types are as follows : (a) The Lamp Resistance Board. A serviceable rheostat can be made by fixing a number of lamp bases to a board and connecting them in parallel between the wires that lead out from two binding posts. Figure 79 shows a form of high-resistance lamp made especially for this use. Lamps that have been in use so 84 ELECTRICITY long that they are practically useless for lighting purposes are still of use as resistances in a board of this kind. FIG. 80 FIG. 79 () The Coiled Wire Rheostat. The principle of this rheostat is shown in Fig. 80. Jt consists of a coil of uncovered resistance wire wound spirally on an insulated cylinder AB that is supported at the ends. One end of the coil is fastened to a binding post on the base of the support at E, and the other end to a sliding contact H which is con- nected to the binding post at F. This contact can be moved to any position along the rod (7J9, the part of the coil in the circuit being only that between the end E and the sliding contact H. (c) The Ironclad Rheostat. One of the commercial forms of this rheostat is shown in Fig. 81. It consists of an iron plate, over the face of which moves a brass arm (7Z>, pivoted at C. The end D of this arm makes electrical contact with the ends of brass plugs that pass through the iron plate and are in- sulated from it. The resistances are made of thin strips RHEOSTATS 85 of iron bent back and forth upon themselves. These are upon the back side of the plate and are connected to the brass plugs as shown. The binding post A is con- nected to the brass arm at (7, while the second binding post is con- nected directly to the last plug. Tracing the path of the current will show the part of the resistance that is in use with any position of the arm. FlG 81 EXPERIMENT 68. The study of a rheostat. Apparatus. An ironclad rheostat with from 20 to 40 plugs; appa- ratus for the measurement of its resistance. Manipulation. Measure the resistance of the rheostat with the arm resting on each plug in turn. Make a curve of the resistance, laying off resistances along the verti- cal axis and the number of sections along the horizontal. The Water Rheostat. A resistance that can carry a heavy current and that allows a rapid adjustment is frequently needed in prac- tical work. Figure 82 shows a simple form of rheostat that meets the requirement. A barrel or keg is fitted with a cover through the middle of which passes a rod carrying an iron plate A. This rod can be clamped in any position and FlG> 82 is fitted with a binding post. A second iron plate is connected, by means of a heavy rubber-covered wire, with the binding post C. The solution is usually water to which a small quantity of salt has been added. 86 ELECTRICITY This form of rheostat is sometimes called an " absorption rheostat," since it is frequently used in testing a dynamo, in which case the current is not put to any useful purpose. (e) The Mercury Rheostat. This device is adapted to the case which requires a small resistance that can be changed a very little at a time. A row of holes are bored along each of two opposite sides of a well-seasoned oak plank. These are connected by channels cut out of the plank, as xy. An elevated edge is then put around the board, and it is thoroughly paraffined arid placed upon a level support. Mercury is then poured into the channels (a) J/9 JL to any desired depth, and they are connected by a series of copper straps shaped as in figure (a). By coupling the board into the circuit by FlG 83 ~B ' the binding posts A and B, any resistance from a maxi- mum to a short circuit can be obtained by the proper arrangement of the connecting straps. QUESTIONS AND PROBLEMS 1. If L in the formula for the resistance of a wire, Section 56, is in feet, and D in thousandths of an inch, the value of k for copper is 10.39. Find the resistance of a spool containing 100 ft. of No. 30 copper wire. 2. What is the resistance of a spool of 100 ft. of No. 30 German silver wire, if the value of k for German silver is 136.00? 3. On sending a current of 25 amperes through a copper strap, the difference of potential at its ends was found to be 1.82 volts. What was the resistance of the strap ? 4. Three wires having resistances of 3, 6, and 9 ohms respectively are coupled in parallel. What is their combined resistance? THE UNIT OF CURRENT 87 5. What must be the resistance of a tenth shunt of a galvanom- eter, the resistance of which is 40 ohms? What must it be for a fifth shunt? 6. A voltmeter coupled to the terminals of five cells in series reads 6.86 volts. On sending the current from the cells through a resistance of 5 ohms, the voltmeter reading drops to 3.8. Find the resistance per cell. 7. Devise a lamp board that will give a wide range of resistances, and state some of the advantages of such a resistance board. 8. What is the practical value of the difference between the cold and the hot resistance of incandescent lamps? 9. An inclosed arc lamp requires a current of 4.5 amperes when on a 110-volt circuit. What is the resistance of the lamp? The fall of potential across the arc is 80 volts. What is the resistance of the coil in series with it? 10. If a voltmeter, the resistance of which is 20,000 ohms, is put in series with an insulation resistance on a 110-volt circuit and gives a reading of 6.52 volts, what is the resistance of the insulation? What resistance will give a reading of 1.42 volts? 11. A certain resistance was measured in 1890 as 236 ohms, using a resistance box made in 1870. What was its resistance in legal ohms? What would it be in international ohms if measured to-day? CURRENT, ETC. 73. The Unit of Current ; the Ampere. The electric current can be measured by its magnetic effect, or by its chemical effect, or by its heating effect. As a matter of fact, the unit of current is defined and measured by the chemical effect, while most of the practical measuring instruments make use of the magnetic effect. The unit of current is the international ampere. This is a current of unvarying strength that will deposit .001118 g. (.01725 grain) of silver per second from a certain solution of silver nitrate. The same current will deposit .00032959 g. (.005086 gram) of copper per second from a certain solution of copper sulphate. 88 ELECTRICITY 74. The Measurement of Current ; the Electrolytic Method. EXPERIMENT 69. To measure a current by the copper voltameter. Apparatus. A copper voltameter; galvanometer; cells; switch; a mercury rheostat ; and a timepiece. Manipulation. Make the copper sulphate solution by dissolving crystals of copper sulphate in distilled water to which one per cent of sulphuric acid has been added. The density of the solution should be about 1.15. Place this solution in a large beaker or battery jar, and for electrodes use either flat coils of uncovered copper wire or copper plates. These must be thoroughly cleaned and washed before use. If plates are used, the cathode upon which the copper will be deposited should be of thin copper, so that any increase in its weight can be more accu- rately determined. After the plates have been weighed the apparatus should be coupled in series, and the time noted when the current is turned on. Keep the current constant by regulating the rheostat so that the reading of the galvanometer shall be uni- form, and take the time when the current is turned off. Wash and dry the cathode thoroughly and weigh it. From the difference in the weight of the cathode before and after the experiment determine the current used. Does this experiment suggest a method of calibrating the galvanometer, i.e. determining the galvanometer constant? 75. The Measurement of Current ; the Fall of Potential Method. In order to apply the fall of potential method to the measurement of the current, it is necessary to have a known resistance that will not change in amount on hav- ing a current sent through it. This method makes it possible to use any low-reading voltmeter as a direct-read- ing ammeter for small currents. EXPERIMENT 70. To measure a current by the fall of potential method. THE UNIT OF ELECTRO-MOTIVE FORCE 89 Apparatus. Large size resistance wire ; a direct-reading voltmeter giving full scale deflection for five or ten volts ; an ammeter ; rheostat ; cells ; and a switch. Manipulation. Cut from the resistance wire a sufficient length to measure one tenth of an ohm, and wind it into a non-inductive coil of large diameter. Couple this coil in series with the cells, rheostat, switch, and ammeter. Couple the voltmeter as a shunt to the coil and send a current through the circuit. Take simultaneous readings of the voltmeter and ammeter and compare the results. Send a number of different currents through the circuit, regulating the amount of current by the rheostat, and find whether the accuracy of the voltmeter readings is affected by the change of the temperature of the coil due to the heating effect of the larger currents sent through it. A study of this kind will show the limitations of the method and the necessity of having a small resistance in the coil and a low-reading voltmeter. A resistance wire with a small temperature coefficient will give the most satisfactory results. An accurate form of ammeter is made on this principle. The coil, or shunt box, is of very small resistance, and in- stead of a voltmeter .._,._ a millivoltmeter is used. The shunt box is frequently arranged so that the millivolt- meter will read five amperes, say, for the full scale, when at- tached to the binding posts A and C, and fifty amperes when attached to A and B. LINE WIRE 13 c ho LINE WIRE p 6| [5 "1 r VM FIG. 85 76. The Unit of Electro-motive Force ; the Volt. The present unit of electro-motive force is the international volt, which is the E. M. F. that steadily applied to a con- ductor, the resistance of which is one international ohm, will produce a current of one international ampere. There 90 ELECTRICITY is no standard cell that gives an E.M.F. of one volt, but the Clark cell, at a temperature of 15 centigrade, gives a uniform E. M. F. of 1.434 volts, and is taken as a standard at that rating. The gravity cell gives an E. M. F. of nearly one volt and makes a fairly good unit. 77. The Measurement of Electro-motive Force ; the Poten- tiometer Method. A potentiometer is, in principle, a high- resistance wire of uniform diameter stretched between two binding posts in such a way that contact can be made at its ends and along its length. The wire of a Wheatstone bridge can be used for the purpose. EXPERIMENT 71. To measure the E. M. F. of a cell with a poten- tiometer. Apparatus. A potentiometer; gravity cells; switch; galvanom- eter; voltmeter; standard cell; and the cell to be measured. Manipulation. Couple the apparatus as in the figure. Close the switch S and read the ^ fall of potential from B to A. Having the switch S closed, touch the wire with the key K, and find such a posi- tion for it that there will be no deflection of the galvanometer f7, in series with the stand- ard cell E. Read the distance AK and call it Z', the distance AB being L. Find a point K' such that the cell to be measured, E', will give no deflection to the galvanometer, and call the distance AK', L". The reading of the voltmeter will give the fall of potential from B to A, and since the galvanometer shows that there is no current when the key is depressed, the fall of potential from K to A must be the same as the E. M. F. of the cell. Hence the following propor- G ' E' G E >*' 1; FIG. 86 ELECTRO-MOTIVE FORCE 91 tion holds : V:E = L:L f . The E. M. F. of the cell E' is found from ( L"\ the proportion E : E' = L' : L", from which E' = E (JT}' If the resistance of the switch S and the connections from the battery to the terminals A and B is small, the potential difference of the battery = V -= E~- j j 78. The Measurement of Potential Difference by Ohm's Law. A modification of the fall of potential method of measuring resistances can be used to determine the difference of potential at the terminals of a cell as follows : EXPERIMENT 72. Ohm's law applied to the measurement of potential difference. Apparatus. A coil of known resistance; an ammeter; cells; and a switch. Manipulation. Couple the apparatus as in Fig. 87. Send the current through the circuit and take a reading of the ammeter. The product obtained by multiplying the sum of the resistances of the coil and ammeter by the ammeter reading will give the fall of potential between the points B and C. By knowing the resistances of the connecting wires and switch, as well as that of the ammeter and coil, the potential difference at the terminals of the battery can be determined. 79. The Calibration of Instruments. Early forms of ammeters and voltmeters were made with the scale divided in degrees, so that it became necessary to calibrate them in order to know the value of a given deflection. This was sometimes done by finding the reduction fac- tor by means of which the deflection could be changed to 92 ELECTRICITY the required units ; and sometimes by taking a series of readings, and from these making the curve that would show the relation of the deflection to the required units. The first method was not very satisfactory, since the value of the reduction factor in one part of the scale was often different from its value in another part ; while the second method made it necessary to refer constantly to the curve of the instrument. In order to obviate these difficulties instruments are now made direct-reading, i.e. they are so calibrated that the divisions of the scale are given in amperes or volts. EXPERIMENT 73. To calibrate a voltmeter by comparison with a standard voltmeter. Apparatus. A standard voltmeter ; two similar rheostats; cells; the voltmeter to be calibrated; and a switch. Manipulation. Couple the voltmeters in parallel to the terminals of one of the rheostats, and put both the rheostats in series with the cells and switch. There should be a sufficient number of cells to give a full deflection of the voltmeter to be calibrated. A dynamo can be substituted if it is more convenient. The rheostats should have a wide range of resistance and a large number of steps. Beginning with the rheostat arm of R in the position of maxi- mum resistance, and the arm of R' in that of minimum, send a current through the circuit and take a simultaneous reading of the two instruments. Increase the resistance in one rheostat and FIG. 88 THE CALIBRATION OF INSTRUMENTS 93 diminish it in the other, by one point each, and take 'a second reading. Do the same for every point until you reach the full deflection of the voltmeter to be calibrated. This experiment gives the direct method of comparison that would be used in the case of an instrument that had been repaired and needed to be recalibrated. If the instrument is a voltmeter the scale of which is in degrees, or is a high-resistance galvanometer with a similar scale, a curve should be made showing the relation between the two instruments and the reduction factor found for the different parts of the scale. EXPERIMENT 74. To calibrate a high-resistance galvanometer by Ohm's law. Apparatus. An ammeter; switch; two similar rheostats; the galvanometer to be calibrated ; and a battery capable of sending a current of five amperes through the entire resistance of one rheostat. Manipulation. Couple the apparatus as in Fig. 89, with the gal- vanometer placed as a shunt to the rheostat /?, the resistance of which is known for each step. Let the rheostat R' be an exact duplicate of R if possible. Take a set of simultaneous readings of the ammeter and galvanometer, beginning with the maximum resistance in R and the minimum resistance in R'. Move the arms of the rheostats one point each be- tween consecutive readings. This will give a nearly constant current and a diminishing fall of potential in R, with a corresponding change in the reading of the galvanometer. Compute the values of the potential difference at the different points from the expression E = CR, and make the calibration curve of the galvanometer. EXPERIMENT 75. To calibrate an ammeter by comparison with a standard ammeter. Apparatus. A standard ammeter; switch; battery; rheostat; and the ammeter to be calibrated. FIG. 94 ELECTRICITY Manipulation. Couple the apparatus as in Fig. 90 and send a current through the circuit when the rheostat arm is in such a posi- tion that it gives the minimum S A i I current. Take simultaneous readings of the two ammeters. Move the rheostat arm one step and repeat the readings. Do the same for every step of the rheostat. Make the curve for the in- strument and find the reduc- FIG. 90 tion factor. EXPERIMENT 76. To calibrate a low-resistance galvanometer by Ohm's law. Apparatus. Cells ; rheostat ; a low-reading voltmeter ; switch ; and the galvanometer to be calibrated. Manipulation. Couple the apparatus as in Fig. 91, and with the resistance of the rheostat all in, take a reading of the two instruments. Move the arm of the rheostat one step at a time and take a set of simultaneous readings. Make the curve of the gal- vanometer, computing the cur- rents from the expression 77* C ' In this expression, J is the reading of the voltmeter, and R is the resistance of the galvanometer. QUESTIONS AND PROBLEMS 1. A uniform current passing for 12 min. through a silver vol- tameter increased the weight of the negative plate by 6.84 g. What was the current in amperes ? 2. The same current was sent through a copper voltameter for 20 min. How much copper was deposited? 3. A potentiometer wire, 1 m. long, has 5 cells attached at its terminals. There is no deflection of the galvanometer when the key FIG. 91 ELECTRICAL INDUCTION 95 connected to a Clark standard cell touches the wire at 292.6 mm. from one end. What is the potential difference of the battery pej cell? 4. On substituting another cell for the standard, the new position of the key reads 387.7 cm. What is the E. M. F. of the cell ? 5. A high-resistance galvanometer coupled to the terminals of a coil and ammeter placed in series gave a deflection of 55. The resistance of the coil being 12 ohms, and that of the ammeter being .2 ohm, what potential difference does the reading indicate? What is the reduction factor of the galvanometer if the current was .5 ampere ? 80. Electrical Induction. The setting up of a current in an electrical conductor through the action of a current in a neighboring conductor is what is called electrical in- duction. The physical cause for the production of this current is the cutting of lines of magnetic force by a con- ductor. The phenomena have various forms, but they can all be traced to this one cause. It is immaterial whether the lines of force are cut by a moving conductor, or whether the conductor is stationary and is itself cut by the moving of the lines of force. With a given field of force, i.e. one with a certain number of lines per unit area, the maximum current is induced when the directions of the lines of force and the conductor are perpendicular to each other. Since a current is induced by the cutting of the lines of force alone, it is evident that a constant current flowing X^^-zr^v in a circuit will not induce a secondary current in a stationary conductor near it. If, however, we consider that current is increasing from zero to maximum and coming toward the ob- FIG. 92 server, as indicated in A, Fig. 92, lines of force will be sent out from it, will cut conductor 96 ELECTRICITY and will set up in it a current in the opposite direction. The amount of the induction will depend upon the inten- sity of the primary current in A, the time taken by the current to rise from zero to a maximum, and the distance between the conductors. If now the current in A' is conceived to dimmish to zero, the lines of force will contract upon A', cutting B' in the other direction, and the induced current will be in the same direction as the primary. The origin of the lines of force does not in any way affect the resulting induction, hence induced currents can be obtained from a permanent magnet. EXPERIMENT 77. Induction from a permanent magnet. Apparatus. A cylindrical permanent magnet about 18 in. long; copper wire No. 30 ; a ballistic galvanometer or millivoltmeter. Manipulation. Wind a test coil of fifty or a hundred turns so that it will slide easily over the magnet, and connect its terminals to the galvanometer. Make two wooden collars that will fit over the magnet, and arrange brass screws so that the collars can be fixed at any place along the magnet. Slide the test coil over the magnet and fix the collars 2 in. or 3 in. apart so that the coil can be dropped from one collar to the other. Observe and make a record of the throw of the galvanometer needle. Move the collars a half inch and repeat. Do this for every half inch over the entire length of the magnet. This experiment should bring out the facts that the amount of the induction depends upon the number of lines of force cut in a given time, i.e. upon the rate of cutting the lines of force, and that the direc- tion of the current induced is determined by the direction of cutting of the lines of force. Make a curve in which the distance of the middle of the coil from one end shall be laid off along the vertical axis, and the throw of the needle along the horizontal. EXPERIMENT 78. The induction of a current in a coil. Apparatus. Copper wire Nos. 18 and 24; spools of some insu- lating material with an inch hole in them; ballistic galvanometer; ammeter ; rheostat ; cells ; and a switch. ELECTRICAL INDUCTION 97 Manipulation. Wind one spool with wire No. 18, counting the number of turns. Wind a spool with the No. 24 wire, putting on the same number of turns as on the first spool. Couple the spool of No. 18 wire (the primary) in series with the cells, rheostat, ammeter, and switch, and the secondary to the gal- vanometer, as in Fig. 93. Send a current through the primary circuit with all the rheostat resistance in, and read the throw of the galvanometer. Read the throw on breaking the circuit also, and keep a record. Re- peat the experiment for each step of the rheostat until its resistance is all out, keeping the record on both the " make " and the " break " of the circuit. Make a curve having for horizontal distances the current in the primary and for vertical distances the throw of the needle. It will be well to make the experiment in the reverse order; i.e. beginning with the last reading of the experiment, go over each step, increasing the resistance until the maximum is reached. Does this curve coin- cide with the first? FIG. S3 EXPERIMENT 79. The induction of a current in a coil with an iron core. Apparatus. The same as that used in Experiment 78, with the addition of a soft iron rod an inch in diameter and an inch longer than the combined length of the coils used. Manipulation. Thrust the iron rod through the coils so that it will extend a half inch on each side. Repeat the experiment in the same order as before and keep a record. Repeat the experiment, sub- stituting a bundle of soft iron wires for the iron rod. Make curves of the results on the same sheet that the curve for the previous experiment was made on, using a different colored ink. Do the curves coincide? In what respects do they differ? What is the significance of these differences? ELEC. AND MAG. 7 98' ELECTEICITY Tf Fig. 94 represents a cross section through the axis of the coils and the core, it will be seen that since the coil P is the origin of the lines of force, in order to pass through the core and take the position indicated they must cut each turn of the coil S. Hence the total E. M. F. of the induction will depend upon the number of turns in S, as well as upon the number of lines of force. EXPERIMENT 80. The effect of increasing the turns in the sec- ondary. Apparatus. The same as that used in the preceding experiment, with the addition of another coil, S', of No. 24 wire of double the number of turns. Manipulation. Repeat Experiment 79, substituting coil S' for coil S. Make the curve for this experiment and compare it with those previously obtained. The above arrangement is practically a transformer, and shows that if V represents the voltage of an alternating current applied to the terminals of a primary coil, and V the voltage of the current obtained from the secondary, the relation between them will be expressed by the proportion V: V = T:T f , in which T and T' are the number of turns in the primary coil and in the secondary, respectively. EXPERIMENT 81. The effect of increasing the amount of iron in the magnetic circuit. Apparatus. The same as that used in Experiment 78, with the addition of a quantity of soft iron wire. Manipulation. Cut the wire into such lengths that on thrusting it through the coils the ends can be brought over the outside and lapped over each other. When the coils have been entirely filled with the wire so arranged, repeat Experiment 78. Make the curve for the results obtained and compare it with the SELF-INDUCTION 99 others. This arrangement provides a nearly complete iron circuit for the magnetic lines and reduces the magnetic reluctance of the circuit. Would you use the Wheatstone bridge to measure the resistance of a coil with an iron core ? 81. Self-induction. We have seen, in Fig. 92, that an increasing current in a primary wire induces a current in the opposite direction in a secondary, and that a diminish- ing current in a primary induces a current in the same direction in the secondary. The same phenomena will take place between any two wires of a coil, one of which may be considered the primary and the other the secondary. This means that the influence of a coil upon an increasing current passing through it is to oppose or delay its passage, while the effect upon a diminishing current is to aid or prolong its passage. This is called self-induction^ and its amount in any case depends upon the number of turns in the coil and the character of the magnetic circuit. EXPERIMENT 82. The effect of self-induction in a coil. Apparatus. A spark coil ; cells ; ammeter; lamp board or water rheostat ; and a knife switch. Manipulation. Measure the resist- ance of the spark coil and arrange the rheostat so that its resistance shall be the same. Couple the apparatus as in the figure, close the switch, and observe the action of the ammeter. Open the switch and observe both the action of the ammeter and the sparking at the switch. Substitute the rheostat for the spark coil and repeat the experiment. The gradual creeping up of the cur- rent when it is sent through the spark Fio. 95 coil, and the increase, giving a spark, when the current is broken, show conclusively the effect of self- induction in a coil. 100 ELECTEICITT This effect need not be taken into account in work with direct currents, but is of great importance in alternating work. A coil can be wound non-inductively by doubling the wire and winding from the middle, thus causing the self-induction of one half to neutralize that of the other. A suitable spark coil for the experiment can be made by winding a pound or two of No. 24 magnet wire on a spool having a bundle of iron wire for a core. 82. Electrical Testing. Testing may be broadly di- vided into two classes : first, the testing of manufactured apparatus to see that the requirements of its operation have been met ; and, second, the testing for faults that have developed in use, or what is generally known as "hunting trouble." The principles brought out in the measurements that have been considered will usually apply in these tests. Only a few of the simpler tests that may be made in the laboratory will be taken up. EXPERIMENT 83. To test the resistance of a switch contact. It has been shown in Experiment 48 that a good contact is of great importance in an electrical circuit. With large currents a poor contact results in a loss of power and a heating of the switch ; with small currents, in a lack of uniformity in the current. This test is simply the measurement of a small resistance. Apparatus. Ammeter ; millivoltmeter ; cells ; and the switch to be tested. Manipulation. Couple the cells, ammeter, and switch in series, and the millivoltmeter as a shunt to the switch. Compute the resist- ance by the fall of potential method, using different currents. Compare the resistances of different kinds of switches. EXPERIMENT 84. To test the resistance of the body. Apparatus. A source of current giving from 50 to 150 volts; a high-resistance voltmeter; a pair of tubular brass handles an inch in diameter; and a switch. ELECTRICAL 101 Manipulation. Couple one terminal of the voltmeter to one side of the generator and the other terminal to one of the brass handles. Connect the second handle to the other side of the generator, with the switch in the circuit, and let the person whose resistance is to be measured take a firm hold of both handles. Close the circuit and take a reading of the voltmeter. Then, as in Section 69, the resist- ance will be given by the expression R = I - 1 )r, in which V' is the voltage of the generator, V" is the reading of the voltmeter, and r is the resistance of the voltmeter. The character of the contact between the hands and the brass handles has a great influence upon the amount of the resistance. Make the experiment first with the hands dry, and then after wetting them with salt water or any other electrolytic solution. EXPERIMENT 85. To test a lighting circuit for a ground. In many lighting stations it is the custom to connect two incan- descent lamps across the terminals of the dynamo and permanently to connect some point between them to the earth, as shown in the figure. These lamps must each require half the potential of the circuit, e.g. on a 110-volt circuit the lamps must be 55 volt. If a leak develops at some point on the line, as at C, the current that escapes through it will be shunted around lamp A, which will become dim. If the ground is on the negative side of the line, lamp B will grow dim. The resistance of the ground can be determined as follows : 102 ELECTRICITY Apparatus. The line to be tested ; a high-resistance voltmeter. Manipulation. If the ground is on the positive side, couple the voltmeter between the negative terminal and the water pipes of the building. Read the voltmeter and compute the resistance as in the preceding experiment. If the line is not supplied with the ground-test lamps, both sides of the circuit should be tested. The insulation of the dynamo can be tested in the same way, by cutting out the line current and coupling the voltmeter between one terminal of the dynamo and the earth, or any part of the frame or the foundation. A convenient form of contact point for the voltmeter is shown in Fig. 97. This consists of a wooden or vulcanite handle with a brass rod set in the end and pointed like a scratch awl. A nut, running on the rod near the handle, connects a flexible cord to one terminal of the voltmeter. . By means of a pair of these points, contact can be made where only a small part of the surface is exposed. EXPERIMENT 86. To test for faults in commutator and arma- ture. Apparatus. A low-reading voltmeter or millivolt meter; a source of current; and the armature to be tested. Manipulation. Couple the millivoltmeter to the contact points that have just been described and the commutator brushes to the source of the current. Send a heavy current through the armature and touch any two opposite bars of the commutator with the points. Read the millivoltmeter. Pass around the commutator, taking the opposite pairs in order. If the readings are not practically all alike, it is evidence that there is a fault in either the armature or the commutator. The location of the fault can easily be made by taking the readings with the contact points placed on adjacent commutator bars all around the commutator. EXPERIMENT 87. To test the leakage of lines of force around a dynamo. Apparatus. Storage cells ; ammeter ; rheostat ; insulated copper wire; a millivoltmeter ; switch; and the dynamo to be tested. ELECTRICAL TESTING 103 Manipulation. Couple the storage cells to the terminals of the field winding of the dynamo to be tested, with the switch, rheostat, and ammeter in the circuit. Wind from the wire a test coil of several turns around the middle of the field coil, at B in the figure. Connect this coil to the millivoltmeter and throw the switch. Read the throw FIG. 98 of the needle, and if it is not great enough, either increase the current in the field coil, or increase the number of turns in the test coil. Wind a coil of the same number of turns around the armature at C and repeat. Make this experiment with different currents, taking the read- ing on both the " make " and the "break," and from the results obtained compute the ratio v between the number of lines of force generated in the field core and the number sent through the core of the armature. The ratio, w, determined in this test is of great importance in the designing of a dynamo. In the study of a dynamo already built it is also of importance to know where the losses occur. For this purpose the test can be extended by winding test coils of the same number of turns at different places, as at D, E, F, etc., and repeating the experi- ment. As a large number of storage cells would be required to give the requisite voltage for the terminals of the field coil, a second dynamo of the same voltage as the first is frequently used to excite the field coils. 104 ELECTRICITY EXPERIMENT 88. To test the carrying capacity of fuse wire. Apparatus. Ordinary fuse wire of which the commercial rating is known ; storage cells ; ammeter ; rheostat ; fuse block ; and a switch. Manipulation. Couple the cells, which should be capable of giving a current of at least double the rated capacity of the fuse wire, in series with the fuse block, ammeter, rheostat, and switch. Arrange the rheostat so that the current shall be the same as the rating of the fuse. Turn on the current for 30 sec. and observe the effect upon the fuse. Increase the current by moving the arm of the rheostat one step and again send the current through the circuit for 30 sec. Keep in- creasing the current and sending it through the circuit until the fuse blows within the 30 sec. The results obtained will show that the rating of fuses must be con- sidered as only approximate. If the experiment is extended by intro- ducing a circuit breaker into the circuit, the relative value of the two methods of protecting the line in different classes of work can be con- clusively shown. EXPERIMENT 89. To test the influence of the length of a fuse wire upon its carrying capacity. Apparatus. Fuse blocks of different sizes and the apparatus used in the preceding experiment. Manipulation. Find the fusing load of the shortest wire, then of the next, and so on, using all the blocks. Make a curve showing the relation between the fusing current and the length of the fuse. The character of the contact pieces by which the fuse is held, whether heavy or light, as well as the position of the fuse, i.e. whether lying directly upon the block or free from it, has a great effect upon the current that the fuse will carry. This test will be more satisfactory if made by using a set of fuses mounted as in Fig. 99. The ends of the fuses are clamped in the same sized terminals taken from fuse blocks and mounted on strips of wood fastened to a base board as shown. In this method of support the differences of length are easily arranged and the conditions of conduction and radiation are the same in all. APPENDIX TABLE NO. 1 DIMENSIONS AND RESISTANCE OF PURE COPPER WIRE Matthieson's Standard at 75 F. Sp. Gr. 8.9. SIZE DIAMETER IN MILS AREA IN CIRCULAR MILS OHMS PER 1000 FEET FEET PER POUND 000 409.64 167805.0 .062 1.97 00 364.80 133079.4 .078 2.49 324.95 105592.5 .098 3.13 1 289.30 83694.2 .124 3.95 2 257.63 66373.0 .156 4.99 3 229.42 52634.0 .197 6.29 4 204.31 41742.0 .249 7.93 5 181.94 33102.0 .314 10.00 6 162.02 26250.0 .395 12.61 7 144.28 20816.0 .499 15.90 8 128.49 16509.0 .629 20.05 9 114.43 13094.0 .793 25.28 10 101.89 10381.0 1.000 31.38 11 90.74 8234.0 1.261 40.20 12 80.81 6529.9 1.590 50.69 13 71.96 5178.4 2.005 63.91 14 64.08 4106.8 2.591 80.59 15 57.07 3256.7 3.115 101.63 16 50.82 2582.9 4.019 128.14 17 45.26 2048.2 5.068 161.59 18 40.30 1624.3 6.391 203.76 105 106 APPENDIX TABLE NO. 1 (Continued} SIZE DIAMETER IN MILS AREA IN CIRCULAR MILS OHMS PER 1000 FEET FEET PER POUND 19 35.39 1252.4 8.289 264.26 20 31.96 1021.5 10.163 324.00 21 28.46 810.1 12.815 408.56 22 25.35 642.7 16.152 515.15 23 22.57 509.5 20.377 649.66 24 20.10 404.0 25.695 819.21 25 17.90 320.4 32.400 1032.96 26 15.94 254.0 40.468 1302.61 27 14.20 201.5 51.519 1642.55 28 12.64 159.8 64.966 2071.22 29 11.26 126.7 81.921 2611.82 30 10.03 100.5 103.300 3293.97 It will be observed in the above table that the ohms per 1000 ft. and the feet per pound double with every third size, that the area in circular mils is divided by two with every third size, and that the diameter in mils is divided by two with every sixth size. A mil is one one-thousandth of an inch. A circular mil is the area of a circle one mil in diameter = .7854 sq. mil. TABLE NO. 2 THE RELATIVE RESISTANCE OF CHEMICALLY PURE SUBSTANCES FOR THE SAME LENGTH AND CROSS SECTION AT CENTIGRADE Silver, annealed Copper, annealed . Silver, hard drawn . Copper, hard drawn Aluminum, annealed Platinum, annealed Iron, annealed German silver Mercury . 1.000 1.063 1.086 1.086 1.935 6.022 6.460 13.92 62.73 APPENDIX 107 TABLE NO. 3 RELATIVE PROPERTIES OF COPPER AND ALUMINUM COPPER ALUMINUM Specific gravity . ... ... 8.93 2.68 Conductivity ... . . . '* 100.00 63.00 Weight for equal conductivity 100.00 48.00 Area for equal conductivity .... 100.00 160.00 Diameter for equal conductivity . 100.00 126.04 TABLE NO. 4 EQUIVALENTS 1 horse-power = 33,000 foot-pounds per minute. 1 kilowatt = 44,236 foot-pounds per minute. 1 horse-power = 746 watts. 1 kilowatt = 1.34 horse-power. 1 B. T. U. (British Thermal Unit) = 772 foot-pounds. 1 watt = 44.236 foot-pounds per minute. 1 horse-power = 42.746 B. T. U. per minute. 1 kilowatt = 57.3 B. T. U. per minute. ANSWERS TO PROBLEMS Page 34. 3. .192. 7. 4.29. 8. H: H' :: 259.21 : 324. Page 60. 6. 15 42'. 7. .000345 volts. 9. 7.32 Ib. if the sulphate is in the dry form, but if it is in the usual form of crystals or "blue stone," the chemical symbol of which is CuS0 4 (5H 2 0), the amount required will be 11.5 Ib. Page 86. 1. 10.33 ohms. 2. 135.19 ohms. 3. .0728 ohms. 4. 1.63 ohms. 5. (a) 4.44 ohms, (6) 10 ohms. 6. .805 ohms. 9. (a) 24.4 ohms, (6) 6.66 ohms. 10. (a) 317423.3 ohms, (6) 1529295.77 ohms. 11. 233.5 legal ohms, 232.84 international ohms. Page 94. 1. 8.497 amp. 2. 3.36 g. 3. .98 volt per cell. 4. 1.9 volts. 5. (a) 61 volts, (6) 1.109. 108 INDEX A tangent position, 30. Ammeter, denned, 53. calibration of, 91-94. Ampere, 87, 46. Angle of dip, 20, 21. Anode, 80. Armature, of electro-magnet, 40. of horseshoe magnet, 7. Astatic galvanometer, 48, 49. Ballistic galvanometer, 52. Batteries, 54-60. internal resistance of, 76-78. B. A. Unit, 83. Calibration of instruments, 91-94. Cathode, 81. Cells, 54-60. electro-motive force of, 59, 60, 90. internal resistance of, 76-78. Clark cell, 90. Closed-circuit cell, 57. Crowfoot cell, 56. Current, 87-89, 46. unit of, 87. See Electric Current. Curve, 22. D'Arsonval galvanometer, 50, 51. Deadbeat, 51. Declination, 24. Deflection, law of, 36. Demagnetization, 10-12, 9. Differential galvanometer, 51, 52. method of measuring .resistance, 72, 73. Dipping needle, 20, 23, 24. Direct-reading, 92. Distribution of magnetism, along 2 bar magnet, 27. Dry battery, 58. Dynamo, tests of, 102, 103. Earth's magnetic force, 8-10. components of, 19, 20, 33. Edelmann galvanometer, 49. Electric bell, 41, 42. Electric current, 46, 35, 36, 39. magnetic effects of, 35-39, 44, 45. measurement of, 87-89. representation of, 45. Electrical contacts, 60, 61. Electrical induction, 95-100. Electrical resistance, see Resistance. Electrical testing, 100-104. Electrode, 80. Electrolysis, 80. Electrolyte, 80. resistance of, 80-82. Electrolytic method of measuring cur- rent, 88. Electro-magnets, 40. polarity of, 39. uses of, 40-43. Electro-motive force, 46, 90, 91. unit of, 89, 90. Fall of potential, along a wire, 64, 65. method of measuringcurrent, 88, 89. method of measuring resistance, 65-S7. Figure of merit, of galvanometers, 52, 53. Fuse wire, tests of, 104. Galvanic cell, 54. Galvanometers, 46-54. calibration of, 93, 94. classes of, 46, 47. 109 110 INDEX Galvanometers, controlling force of, 47. figure of merit of, 52, 53. principles of, 37, 38, 46. Graphical method, 22. Gravity cell, 55, 56, 90. Horizontal component of earth's mag- netism, 19, 20, 33. Horseshoe magnet, 7. See Magnets. Inclination, of earth's magnetic force, 20, 21. Induction, electrical, 95-100. Induction, magnetic, 8. explanation of, 16. 17. of the earth, 8-10. Insulation resistance, 80. Internal resistance of batteries, 76-78. Lamp resistance board, 85. Law of deflection, 36. Law of mutual action, 7, 14. Law of polarity, caused by current in coil, 39, 44. Leclanche cell, 56, 57. Lines of magnetic force, 12-15. around a conductor, 44, 45. construction of direction, 14, 15. induction caused by cutting of, 95- 99. Magnet. See Magnets. Magnetic couple, of earth, 19. Magnetic declination, 24-26. Magnetic effects of electric current, 35-39, 44, 45, 95-99. Magnetic field, 12. intensity of, 27. Magnetic induction, 8-10. explanation of, 16, 17. Magnetic lines of force, 12-15, 44, 45, 95-99. Magnetic meridian, 7, 8. Magnetic moment, of needle, 19. of magnet, 30, 33, 34. Magnetic needle, 6. action of a magnet upon, 27-31. action of earth upon, 18, 19. deflected by current near, 36, 37. Magnetic needle, how to make, 6, 10. magnetic moment of, 19. vibration of, 27, 28, 31-33. See Magnets. Magnetic poles, of earth, 8. Magnetic substances, 5. Magneto, 43. Magnetometer, 31. Magnets, 5-7. action on a needle, 27-31. bar, 6. demagnetized by heat, 11, 12. distribution of magnetism, 27, 28. effect of breaking, 15, 1G. effect on a needle, 27-31. horseshoe, 7. how to make, 9, 10. lifting power of, 17, 18. lines of force of, 12-15. magnetic moment of, 30, 33, 34. moment of inertia of, 31, 32. mutual action of, 7, 14. poles of, 6, 7, 23. vibration of, 31-33. See Magnetic Needle. Mance's method of measuring inter- nal resistance, 76, 77. Measurement, of current, 88, 89. of electro-motive force, 90, 91. of inclination of earth's magnetic force, 20, 21. of magnetic declination, 24-26. of magnetic intensity, 27. of magnetic moment, 19, 30, 33. of potential difference, 91. of resistance, 64-83, 100-102. Moment of inertia, of magnet, 31, 32. Nil method, 48. Non-inductive coil, 76, 100. North pole, 7. North star, 24-26. Oersted's experiment, 35, 36. Ohm, unit of resistance, 82, 83, 46. Ohm's law, 62, 63. in measurement of potential differ- ence, 91. Open-circuit cell, 57. INDEX 111 Parallel circuits, resistance of, 73-75. Parallel coupling of cells, 37. Plunge battery, 58. Polaris, 24-26. Polarity, test of, 9. law of, in electro-magnets, 39. Polarized bell, 42-44. Poles of a magnet, 6, 7. found by dipping needle, 23, 24. found by method of vibrations.27,28. Portable testing set, 70-72. Potassium bichromate cell, 57, 58. Potential difference, measurement of, 91. Potentiometer, 90. Primary, 96, 97. Reflecting galvanometer, 49. Relay, 40. Resistance, 60-86, 46. affected by temperature, 78, 79. battery, internal, 76-78. boxes, 63. formula for, 62. measurement of, 64-83. of electric lights, 79. of electrolytes, 80-82. of a ground, 101, 102. of human body, 100, 101. of insulation, 80. of parallel circuits, 73-75. of switch contact, 100. specific, 62. Resistance, tables of, 105, 106. unit of, 82, 83. Rheostats, 83-86. Secondary, 95, 97. Self-induction, 99, 100. Series coupling of cells, 37. Shunts, 75, 76. Siemens unit, 83. Solenoid galvanometer, 37, 38. Sounder, 40. South pole, 7. Specific resistance, 62. Substitution method of measuring re- sistance, 64. Tangent galvanometer, 47, 48. Telegraph, 40, 41. Temperature coefficient, 78. Testing set, portable, 70-72. Thomson galvanometer, 49. Throw of galvanometer needle, 52. Transformer, 98. Volt, 46, 89, 90. Voltaic cell, 54. Voltameter, 88. Voltmeters, 53, 54. calibration of, 91-93. Wheatstone bridge, 67-71. Zero method, 49. A Brief Course in General Physics Experimental and Applied BY GEORGE A. HOADLEY, A.M., C.E. Professor of Physics in Swarthmore College. Cloth, 12mo, 463 pages. Fully illustrated . '.- . $1.20 This Brief Course in General Physics is designed to provide a text-book for High Schools and other Second- ary Schools that can be completed, with a reasonable amount of work, within an academic year. In its prepara- tion the author's aim has been to present the essential facts and phenomena of physics in a clear and concise manner, and in such a way as to awaken the interest of the student in the subjects treated, and by awakening this interest to secure familiarity with the action of physical forces, and the laws which govern those forces. The book is constructed on the principle that to in- sure the greatest benefit from the study of Physics, there should be a coordination of (i) a reliable text, (2) class demonstrations of stated laws, (3) practical questions and problems on the application of these laws, and (4) per- sonal experimentation in the laboratory. Copies of the book -will be sent, prepaid, on receipt of tht price. American Book Company New York Cincinnati Chicago (159) LOWER DIVISION 328841 LOWER DIVISION UNIVERSITY OF CALIFORNIA LIBRARY