Page images
PDF
EPUB

given the following values for the electrochemical equivalent of copper.

[blocks in formation]

The results of this Table may be expressed by the equation

0003288-0000003

A 50
50

-'0000002

t-12
11

where A is the area of the cathode surface per ampère, and t the temperature. The value of A is found by calculating the current in the first instance approximately, using the equivalent.

as

Measure the total area of the two sides of the cathode, and obtain an approximate value of the area per ampère. From this and the temperature during the experiment find from the table the equivalent which applies to your experiment. Record and reduce the observations as follows:

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small]
[blocks in formation]

Thus currents measured by the instrument using the constant 05 would agree to within one part in a thousand with their value as determined by copper electrolysis. The constant supplied by the maker of the Kelvin balance is equal to the mean current divided by twice the square root of the reading; i.e. 025 in the case of the above instrument. A table of doubled squared roots is provided with the instrument, and the last column in the above Table may be replaced by one in which the double square roots are entered. But the method here adopted is applicable to all instruments of the dynamometer type and the square roots are easily found in Barlow's Tables*. If the instrument to be tested is a direct reading one, the last column is unnecessary, and if it is of the tangent galvanometer type it must be replaced by the tangents of the angles of deflection.

* If the square root of e.g. 408·4 is taken from Barlow's tables, interpolation would seem necessary between the values of the roots given for 408 and 409, but this may be avoided by finding that number in the neighbourhood of 2000, the square of which has for its first four significant figures 4084. The position of the decimal point is obvious.

SECTION LVII.

ON MIRROR GALVANOMETERS AND THEIR

ADJUSTMENT.

Apparatus required: Mirror galvanometer and scale, watch, uniform wire.

IN Section LI. it has been explained that the sensitiveness of a tangent galvanometer may be increased by diminishing the radius of the coil through which the current is passing; but that if the tangent law is to hold good the length of the needle must also be diminished. In many experiments it is of greater importance to have the galvanometer as sensitive as possible, than that the tangent law should hold accurately. We use in such cases a galvanometer the coils of which have as small a radius as possible, with only just sufficient room inside for the magnet to move. Any movement of the magnet is rendered apparent, and measured if necessary, by the help of a mirror attached to it, in the way explained in Section XXXIV. Several small magnets are often used instead of a single one in order to increase the magnetic moment and so decrease the time of oscillation, and these are either attached directly to the back of the mirror by means of a little shellac, or the mirror is placed outside the coil and attached to a thin wire which passes through the coils and carries the magnets at its end. The suspended system must be free to move round a vertical axis, and is for this purpose attached to a fibre just strong enough to carry its weight and as free from torsion as possible.

The deflection of a galvanometer for a given current being increased by a diminution of the intensity of the magnetic field at the centre of the coil, we have a further means at our disposal of rendering a galvanometer more sensitive, or of adjusting its sensitiveness to any desired value within certain limits. For this purpose a permanent magnet is placed near the instrument in such a position that it produces together with the

earth's field a resultant field of the desired strength. Such a magnet is also necessary when the galvanometer has to be set up with the plane of the coil not in the magnetic meridian. The strength and direction of the earth's field being given, it is theoretically always possible to produce a resultant field of any desired strength and direction by placing a permanent magnet with a sufficiently great magnetic moment in a proper position. When great sensitiveness is required, and at the same time the direction of the field is to be altered, it is generally advisable to proceed by two steps. With a magnet of known magnetic moment, it will not be difficult to find by calculation a position for it such that it will nearly neutralise the earth's field. A second weaker magnet may then be used to regulate the strength and direction of the field within the coil of the galvanometer. A galvanometer made sensitive by counterbalancing in this way the greater part of the earth's force by means of external magnets, has the disadvantage of being very sensitive to slight magnetic disturbances either caused by actual changes of the terrestrial forces, or to disturbing currents (electric trams) or to the accidental displacements of magnetic material (keys, spectacles, corset steels) which are almost unavoidable in a laboratory. To get rid of that portion of these effects which is nearly uniform throughout the space occupied by the galvanometer needles, so called astatic magnetic systems are often used. These consist of two magnets or two sets of magnets with nearly equal magnetic moments, rigidly connected together, so that the similar poles of the two sets point in opposite directions. One of the sets is placed in the centre of the galvanometer coil, the other above or below it, and in some instruments the second set will be placed in the centre of a second galvanometer coil in all respects similar to the first, but with the current passing round it in the opposite direction. The whole of the combination of magnets, called an astatic system, will behave like a very weak magnet towards the earth's force, and may set in a direction which it is impossible to predict.

To make this latter point clear, let H represent the earth's field, m1, m, the magnetic moments and a1, α, the angles between

the magnetic meridian and the magnetic axes of the two sets. The mechanical couples exerted by the earth's field will be

Hm, sin a, and Hm, sin ag

and in the position of equilibrium

m1 sin a1 + m2 sin a2 = 0.

If the angle between the two magnetic axes is very nearly equal to two right angles we may write

[ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][ocr errors][merged small][merged small][ocr errors]

hence the astatic system will set at right angles to the magnetic meridian; if on the other hand 80 but m, differs from ma, a1 = 0 and the system will set in the meridian. As in practice neither & nor m1 — m, vanish, but will be small, a, depends on the ratio between two unknown small quantities.

Directing magnets have therefore to be used with an astatic system to bring it into its proper position with respect to the galvanometer coils and to regulate the strength of the field.

The increased sensitiveness of an astatic galvanometer depends on the fact that while the two sets of magnets oppose each other in so far as the earth's directing force is concerned, the electric current acts on both in the same direction. If there are two galvanometer coils, the current is led through them in opposite directions, so that the couples exerted by the currents in both coils have the same direction. A galvanometer with two coils can also be used as a "differential galvanometer," when it is required to test the equality of two currents or to measure very small differences between them. The two

« PreviousContinue »