Ex. 5. The resistance of the wire of a galvanometer is 4,000 ohms; it is required to find the resistance of a wire, which, acting as a shunt, will reduce ten-fold the sensitiveness of the galvan

ometer.

Let it bez ohms. The conductivity of the galvanometer is 1/4000 ampere per volt, of the shunt 1/2 ampere per volt; therefore of the two together 1/4000 + 1/2 ampere per volt. Hence the ratio of the current through the galvanometer to the total current will be

1. Compare the currents which the same electromotive force is capable of producing in two wires of the same material, whose lengths are as 5 to 1, and crosssections as 3 to 2.

2. The resistance of a piece of platinum wire, 41 metres long, and 5 millimetres in diameter, is found to be '19 ohms. What is the resistance of a bar of the same inaterial 1 decimetre long and 1 square centimetre in section?

3. Compare the resistances of two copper wires, one of them 8 feet long and weighing 1/4 ounce, the other 14 feet long and weighing 6/7 ounce.

4. A piece of copper wire 100 yards long weighs 1 lb.; another piece of copper wire 500 yards long weighs 1/4 lb. Find the relative resistance of the latter piece to the former.

5. Find the resistance of 485 m. of copper wire, one mm. in diameter, at 0° C. 6. Find the resistance per mile of iron wire, 24 inch in diameter.

7. What length of German silver wire one mm. in diameter will give a resistance of one ohm?

8. What is the resistance of 2000 yards of German silver wire, '0108 inch in diameter?

9. Find the length of a copper wire 1 mm. in diameter which has

of one C.G.S. electromagnetic unit.

10. The resistance of a column of silver 100 cm. long and 1 gm. in ` •1687 ohms. Find the resistance of silver in terms of the C.G.S. unit.

11. Two brass plates, 10 inches square, are separated from one another b plate of gutta-percha 1/4 inch in thickness. How many miles of copper wire, 056 inch in diameter, will have a resistance equal to that between the plates. The relative resistance of guttapercha to copper is 2.8 × 1020 ?

12. An electrical current may pass from A to B by either of the wires ACB and ADB, the resistances of which are 3 ohms and 7 ohms respectively. What is the resistance of a single wire, which can replace ACB and ADB in such a way as not to produce any alteration in the current in the rest of the circuit?

13. With the shunts 1/999, 1/99, 1/9, compare the currents in the galvanometer, when any two of the shunts, and when all three are in circuit together.

14. In a submarine cable 1000 knots in length, the electrical resistance of the conductor is 5 ohms per knot, and the whole insulation resistance of the guttapercha sheath is 115,000 ohms. Determine the total resistance of the cable exclusive of batteries.

15. Three incandescent lamps having a resistance of 50 ohms each, are joined in multiple arc. What is the resulting resistance?

16. Two wires, whose conductivities, lengths, and cross-sections are as 7 to 6, 5 to 3, 2 to 1 respectively, are in the same circuit. Compare the rate at which heat is developed in the former to the rate at which heat is developed in the latter.

17. A galvanometer of 500 ohms is shunted by a shunt of 50 ohms. Compare the amounts of heat generated in the galvanometer and shunt.

18. Show how to arrange 12 similar galvanic cells, each of which has a resistance of 1.2 units, so as to give the current of greatest strength through a wire whose resistance is 2.5 units.

19. A battery of 12 similar cells is connected in series; each cell has an electromotive force of 1.1 volt, and a resistance of 3 ohms; and the resistance of the external circuit is 240 ohms. What is the strength of the current?

20. If there are 20 cells in a battery, each having a resistance of 2 ohms, and if the external resistance is 1 ohm, what arrangement of cells will give the strongest current?

21. Find the condition which must hold, when the current given by the arrangement in series is equal to the current given by the arrangement in multiple arc. 22. Find the current when a battery of 12 cells, each having a resistance of 100 ohms and an electromotive force of 1.5 volts, is joined to an external circuit of 1000 ohms; first, when the cells are arranged in multiple arc; second, in series; third, in two series joined in multiple arc.

med of seven Daniell's cells in series are iding screw of a galvanometer is joined by reckoning from the copper end. With other screw of the galvanometer be conflected?

s expressed in terms of the millimetre, Find the multiplier for changing to the C.G. S. unit.

CHAPTER SEVENTH.

ACOUSTICAL.

SECTION L.-MUSICAL SOUND.

ART. 233.-Period and Frequency. It is a property of a vibrating body that it vibrates always in the same amount of time, whether the amplitude of its vibration is large or small, provided that the amplitude does not exceed certain limits, which differ for different bodies. For instance, if an iron bar be held in a vice, and the upper end be displaced from the perpendicular, the bar, when let go, will vibrate on either side of the perpendicular, each point in the bar performing a simple harmonic motion (Art. 123). Each succeeding vibration has a less amplitude than its predecessor, but the time occupied in making the vibration remains the same. This constant time is called the period of the body, and is expressed in terms of

T per vibration.

The vibration may be defined in one or other of two ways; either as the movement from one side to the other, or the movement from one side to the other and back again. The latter is the more appropriate definition; for distinction it is sometimes called a complete vibration.

The reciprocal idea is the frequency; it is expressed in terms of vibrations per T.

ART. 234.-Wave-length. A disturbance initiated at any part

of a material medium is propagated outwards in all directions and with a constant velocity, provided the medium is uniform.

Let the velocity of propagation be

This gives us the idea of wave-length. The wave-length is the distance-period, that is the uniform distance from one point of greatest condensation to the next point of greatest condensation. The reciprocal is

ART. 235.-Pitch.

n/v vibrations per L.

The pitch of a sound depends on the number of vibrations received by the ear per unit of time. It is the same as the frequency, when the spectator and the source of sound are at rest relatively to one another.

If the spectator and the vibrating body move towards one another with a velocity v L per T, the velocity with which the vibrations will arrive will be v+ L per T; and as there are n/v vibrations per L, he will receive n(v + v1)/v vibrations per T.

If they move from one another with a velocity v1 L per T, the velocity with which the vibrations will arrive will be v-v1 L per T, and the spectator will receive n(v – v1)/v vibrations per T.

ART. 236.-Intensity. By the objective intensity of a source of sound is meant the amount of energy transformed per unit of time. It is expressed in the form

μ W per T.

Its amount at any time is proportional to the square of the amplitude of the vibrations.

By the intensity of the sound at a given position in the medium is meant the amount of energy received per unit of time per unit of cross-section; it is expressed in terms of

W per T per S cross-section.