meter is connected to the armature terminals. Set up a large wheel and crank so as to drive the armature by means of a belt. Excite the field-magnet by sending a small current through the coil, and rotate the armature. Note the effect of increasing the speed of rotation, and of reversing the direction of rotation. Do this last carefully to avoid damaging the voltmeter. What is the effect of changing the magnitude and direction of the magnetizing current in the field-coil?

Diagram the connections.

In commercial direct-current generators, the field is excited by sending some or all of the current generated by the dynamo through the field-coils. It is sometimes necessary to start them, however, with outside excitation, as in this experiment.

EXPERIMENT NO. 414

THE EARTH'S MAGNETIC FIELD.

References: Stewart, Physics, Sect. 349-353; Kimball, College Physics, Sect. 490-493, 711; Duff, College Physics, Sect. 299, 300; Spinney, Text-Book of Physics, Sect. 251-254, 357, 358.

The purpose of this experiment is to determine the relative magnitudes of the horizontal and vertical components of the earth's magnetic field, and from these values to compute the angle of dip. The student should be able to tell what is meant by these two components of the earth's field.

The earth inductor is simply a coil of wire in which a current can be induced by turning it in a magnetic field. It is connected in series with a resistance-box and a galvanometer.

If a coil is moved in a magnetic field so that the total change in the number of magnetic lines passing through it is N, the quantity of electricity traversing the coil is Q=N/R, where R is the resistance of the circuit. If the coil lies in a horizontal plane the number of lines of force passing through each turn of the coil is AV, where A is the area of the coil and V is the vertical component of the earth's field. Therefore if n is the number of turns in the coil, the total number of lines of force threading it is nAV, since each turn must be counted separately. If the coil

be suddenly turned over, through 180°, the same number of lines thread it, but in the opposite direction. Therefore, the change in the number of lines, N is 2nAV, and Q=2nAV/R.

We know that, if this change occurs quickly, and, if the galvanometer has a slow period, the throw of the galvanometer is proportional to Q. Therefore the deflection of the galvanometer is given by:

2knAV

R

where k is some constant of proportionality. Take about ten throws in this way, turning the coil very quickly and recording each throw.

Now hold the coil against an east and west wall, or against a board set up for the purpose. If the coil is then turned suddenly around, the same thing occurs as before, except that instead of V, the vertical component of the earth's field, we must now use H, the horizontal component. Therefore,

The resistance must be the same in each case. Make two trials, one without any resistance in the resistance box, another with a very low resistance.

The tangent of the angle of dip is given by

Look up in a table of trigonometric functions the angle corresponding to this tangent. This will be the angle of dip for the place where the experiment is made. Compare the result with values given in reports of the Geodetic Survey for the locality in question.

EXPERIMENT NO. 415

CONDENSERS, THE BALLISTIC GALVANOMETER.

References: Stewart, Physics, Sect. 508-515; Kimball, College Physics, Sect. 568-577; Duff, College Physics, Sect. 272

275; Spinney, Text-Book of Physics, Sect. 285-288, 290, 291, 293, 294.

Many of the condensers in elementary laboratories are telephone condensers of one or two microfarads capacitance. These condensers are built up of numerous layers of tinfoil ribbon separated by paper strips, the odd numbered strips of tinfoil being connected to one terminal of the condenser, the even numbered ones to the other terminal. The assembled strips are rolled up and mounted in a small metal box from which the terminals project.

The purpose of this experiment is to show (a) how the capacitances of condensers may be compared, (b) the effects on capacitance of connecting condensers in parallel and in series, and (c) how the electromotive forces of cells may be compared.

If (+Q) is the total charge on one set of sheets and (—Q) that on the other set, and V the difference in potential between them, the ratio Q/V is a constant, known as the capacity or capacitance of the condenser.

C = Q/V.

We can charge several condensers to the same potential by connecting them successively to a given cell. Now, if we can measure. the quantities or charges in the condensers, we can compare the capacitances, since then:

By the same method, we can compare the capacitance of a combination of condensers with the separate capacitances of the individual condensers. If we charge the same condenser suc

cessively from different cells, we can compare the electromotive forces by the relation:

This is a real comparison of the electromotive forces because. there is no internal potential drop in the cell under test, as no current is flowing through it.

A galvanometer, as ordinarily used, measures current, not quantity, by means of its steady deflection. However, if the period of vibration of the galvanometer is fairly large, and if a given quantity of electricity is suddenly discharged through it, the throw of the galvanometer is proportional to the quantity passing through it. Under these conditions the galvanometer is used ballistically. If d, and de represent the maximum swings of the galvanometer when quantities Q, and Q2 are discharged through it, then

1

2

2

Fig. 14.

(a) To compare the capacitances of different condensers. Connect up the apparatus as shown in the figure. B is a battery, C, one of the condensers to be compared, G, a galvanometer, K1 and K2 tapping keys. First adjust the galvanometer-telescope so that the zero of the scale comes on the cross-wires. Now close the key, K1, and record the throw of the galvanometer. Then release K1, and when the galvanometer has come to rest, close K2, releasing it again immediately, and record the new throw in the

opposite direction. The two throws should be equal but probably will not, owing to imperfections in the condenser. Take four such pairs of deflections and find the average. Replace C by another condenser, leaving B the same, and repeat. Do this with three condensers in all. From the observed data, calculate the ratio of the capacitance of the first condenser to that of each of the others.

(b) Condensers in parallel and in series. Connect the three condensers in parallel and insert the combination in place of C in the set-up of part (a). Repeat the charge and discharge tests. Since the capacitance of a group of condensers in parallel is equal to the sum of their separate capacitances, the throw resulting in this case should equal the sum of the throws obtained with the three separately.

Finally connect the three in series, charge with the same cell, and obtain the charge and discharge throws of the galvanometer. A much smaller throw will be obtained, for the capacitance of a group of condensers in series is less than that of any one of them alone. In fact, if C is the capacitance of the combination, and C1, C2, and C, the capacitances of the individual condensers:

3

(c) E. M. F.'s of cells. Proceed exactly as before, but keep the condenser the same throughout, and change the cell. Use three cells of different types and calculate the ratio of the e. m. f's. to that of a gravity cell or to that of some cell used as a standard.

(d) Residual Charges in a Condenser. In any imperfect condenser, the whole charge is not given up at once, but on the contrary a second, third, etc., discharge can be obtained if the condenser is left insulated for a few seconds after the previous discharge.

With the apparatus as above, get the second, third, etc., discharges, allowing the condenser to stand about 30 seconds between discharges.