diameter, and have 100 convolutions of wire on it, while the two small coils are each 15 centimetres in diameter, and have respectively 100 and 50 convolutions on them.

By means of compass needles (Figs. 38 and 40) the fields of the three coils can be explored, both as regards the direction of the, lines of force, and the strength of the field at different points, and, from the results so obtained conclusions can be drawn as to change of the force at the centre of a coil produced by varying the size of the coil or the number of windings and the rate of variation of the force as we depart from the centre for each of the two sizes of coils.

The three coils must, of course, be placed far enough apart that the fields do not act on one another, and to save time the fields for the different coils may be mapped out simultaneously by different explorers.

If

Example 13.--A tangent galvanometer is made with two coils of equal diameter, the first consisting of 500 convolutions of wire, the second of one convolution. a current of 0.25 ampere sent through the first cause a deflection of 45°, what current sent through the second in the opposite direction, while the same current was still flowing through the first, would cause the deflection to become one of 10° ?

Let x be the unknown number of

amperes :

Example 14.-A galvanometer is about to be constructed of two coils: the first, 6 inches in diameter, consists of 350 convolutions of wire; the second has two convolutions only. A current of 04 ampere sent through the first causes a deflection of 30°. What must be the diameter of the second coil, in order that a current

of 80 amperes in the opposite direction, sent through it, while 04 ampere is still flowing through the first, may cause the deflection to become 5° ?

Let x be the diameter of the second coil.

Since the effect of the current is directly proportional to the number of convolutions, and inversely proportional to the diameter

Example 15.-A tangent galvanometer is about to be constructed of two coils: the first, 7 inches in diameter, consists of 600 convolutions of wire; the second is to be 5.5 inches in diameter. A current of 0.1656 ampere sent through the first causes a deflection of 40°. Of how many convolutions of wire must the second coil consist, in order that while 0.1656 ampere is still flowing through the first, a current of 65 amperes flowing through the second may cause the deflection to become 8° ?

Answer. One convolution.

27. Values in Amperes of the Deflections of a Tangent Galvanometer controlled only by the Earth's Magnetism. The sensibility of any galvanometer depends not merely on the bobbin, but also on the strength of the controlling field. If this controlling field be altered by bringing up a magnet, then even if the magnet be so placed that the position of rest of the needle for no current be unchanged, still the force and therefore the current required to turn the needle through a given angle will be altered. For let the controlling force N P be increased to NP' (Fig. 54) so that the zero position of the needle is the same, but the needle is held in that position with a greater force, then in order

that the angle P'N R' may remain of the same value as before, the deflecting force PR must be increased to P' R', that is, in the same proportion as the controlling force. If the current has the same value as before, so that P' R" is equal to P R, then the angular deflection of the needle instead of being PN R' will be reduced to P'N R′′. Even if the controlling field be merely that due to the earth, this will alter from place to place, and from year to year; so that a tangent galvanometer requiring a current equal to 1 ampere to produce a deflection of 45 degrees in some particular town, will generally need a somewhat different current to produce the same deflection if moved to another town, and even if kept in the same position the calibration will be found to gradually alter with time.

When the needle of a tangent galvanometer is sup

Fig. 54.

ported in such a way that it turns in a horizontal plane, and when the controlling force is entirely produced by the "horizontal component of the earth's magnetic force," the following formula connects the current A in amperes, passing through the coil, with the deflection d in degrees, the radius r of the coil in inches, and the number of convolutions N of wire on the bobbin

where K is a constant which depends on the place where the galvanometer is situated, and on the year. The

The horizontal component of the earth's magnetic force is that component of the earth's force which exerts a directive action on a compass needle, or needle turning in a horizontal plane.

following table gives the values of K, for London, for the middle of the years 1891 to 1900:-

When the controlling force acting on the needle of a tangent galvanometer is due to the presence of a distant magnet, placed so that the needle is parallel to the plane of the coil when no current passes, the preceding formula holds true, but the constant, K, must be determined experimentally.

If the value of K for the earth's field alone be accurately known for the particular place and the particular year, then the value of K for any other controlling field may be ascertained by employing the principle described in § 21, page 79. Remove all magnets, pieces of iron, &c., so that the needle of the tangent galvanometer is acted on by the earth's field alone, and count the number of oscillations, n1, say, that the needle makes in any convenient time. Replace the controlling magnet, or magnets, as desired, and again count the number of oscillations, no say, that the needle makes in the same time, then the K for the earth's field alone must be multiplied by n2/n,2 to obtain the K to be used in the preceding formula for the particular combination of controlling magnets in question.

Example 16.-How many amperes would deflect the needle of a tangent galvanometer 60° in the year 1891, the controlling force being the horizontal component of the earth's magnetism at London, and the galvanometer

having a bobbin 5 inches in radius, wound with six convolutions of wire?

0-7378 × 5 × /3
1

The number of amperes is

6

Answer.-1.065 ampere.

Example 17.-Through what angle would 0-598 ampere deflect the needle of a tangent galvanometer with a bobbin 7 inches in radius, wound with five convolutions of wire, in the year 1898, the controlling force being the horizontal component of the earth's magnetism at London? 0.7437 x 7 x tan, d

0.598

=

5

5 × 0.598

... tan. d =

0.7437.x 7

Having found tan. d, d may be found either by looking in a table of tangents or in the following way :

Take a sheet of squared paper, and on it select two axes, or lines of reference, o x, o Y, at right angles to one another. Choose any number of the divisions on your paper to represent unity, taking care that there are more than 100 of these larger divisions along o x, and at least 58 along o Y. These numbers are chosen because the tangent of the angle required is approximately given by

the ratio

57.4

100

Along o x mark off o A, equal to 100 of

the divisions, then on the line through A, parallel to o Y, mark off A B as nearly as possible equal to 57·4 of the divisions. Join 0 B. Then B O A is the angle d.