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(c) The formula for calculating the inductance is simple, and comparatively few quantities have to be measured. There is, however, a sufficient number of variables to permit measuring inductances of a very wide range of values with the same bridge, using comparatively few values of the capacity.
(d) The method is particularly well adapted to measure inductance by the substitution method, where the inductance to be determined is replaced by a standard of nearly equal value. The difference between them can then be measured with very great precision, the residual errors of the bridge being nearly if not entirely eliminated.
There are no disadvantages of the method that are not shared by other methods, except so far as the use of a condenser may be deemed a disadvantage. There are, however, some sources of error to be guarded against which we shall discuss later.
3. ADVANTAGES AND DISADVANTAGES OF A VIBRATION GALVANOMETER.
When the bridge is completely balanced (the conditions for a resistance balance and an inductance balance being simultaneously satisfied) the current will be zero in the galvanometer at every instant. If, however, the steady current balance is slightly disturbed by the heating of the resistances, especially that of the inductance coil to be measured, no adjustment of the variable resistance r will make the current in the galvanometer zero. The result is that the needle of the galvanometer will have a certain minimum amplitude of vibration when r is correctly set. If now one of the resistances (say Q) is slightly altered, a complete balance may be attained and the needle will be perfectly still. This will be seen to be a distinct advantage, for one is always certain, when the needle is quiet, that both of the conditions of the bridge are satisfied; namely, the condition of the simple Wheatstone bridge (P S=RQ), and the condition imposed by the presence of the inductance which requires a particular value for the resistance r. But the vibration galvanometer does more than merely save the trouble of going back to the use of a direct current and a direct current galvanometer to see whether the balance still holds; for, when an appreciable current is used, the resistance may be changing sufficiently to render such a test insufficient. The vibration galvanometer, on the other hand, insures that at the very moment when the inductive balance is attained the resistance balance also holds, and thus no error from this cause can enter.
Still further, if the resistance of the inductive coil, or of the arms of the bridge, is different when carrying alternating current from its resistance when carrying direct current (as it always is, although the difference is very small for tine wires and low frequencies), the vibra
tion galvanometer takes account of the true resistance under the conditions of the experiment as a direct current galvanometer could not do. This is of considerable importance in measuring the inductance of coils of large wire. Neither a telephone nor an alternating current d'Arsonval galvanometer possesses this advantage.
In practice it is not necessary to make a close adjustment of the direct-current balance at all, as this can be determined just as well by the vibration galvanometer. In our work a graduated scale is viewed in a telescope by reflection from the mirror of the vibration galvanometer, the filament of an incandescent lamp used to illuminate the scale being also seen in the telescope. When an approximate adjustment of r and Q is secured, the filament will appear somewhat broad
ened by the slight vibration of the needle of the galvanometer. Small changes in rand Q are then made successively until the filament appears as a fine line and the lines on the scale are perfectly distinct". This adjustment can be made so delicately that a change in r or Q of one part in a hundred thousand can be detected, when measuring inductances of large values.
The chief disadvantage of the vibration galvanometer lies in the fact that its sensibility decreases rapidly when the frequency of the current varies from the natural period of the galvanometer. The sensibility is nearly constant for a range of about one-half per cent in the frequency but falls off rapidly when the frequency goes beyond this range.
a Wien: Ann. d. Phys., 309, p. 441; 1901.
In order to maintain the frequency at the point of maximum sensibility a Maxwell bridge is employed, as when measuring the capacity of a condenser. The condenser capacity and resistances of the bridge remaining constant, any change in speed causes a deflection of the galvanometer. An adjustable carbon resistance in the armature circuit of the driving motor permits the speed to be adjusted so that the deflection is reduced to zero. The motor is driven by current from a storage battery, and hence the changes in speed are relatively small. A glance at the galvanometer scale at any time shows whether the speed is correct, and if not, it is quickly adjusted by means of the rheostat.
Fig. 5 gives the sensibility curve of the vibration galvanometer, showing two peaks of high sensibility at 110.6 and 120 vibrations per second, respectively. At a frequency of 115 the sensibility is very low-much less than it is at frequencies outside the peaks of maximum sensibility. The curve is affected by changes of temperature, and can be altered at pleasure by varying the length and tension of the suspension wire.
4. THE APPARATUS.
A Rubens vibration galvanometer, having a resistance of 200 ohms, is used. Its frequency may be varied between 100 and 200 per second, but has been used chiefly at about 110.
The several resistances are of manganin, and are all submerged in oil, to prevent heating and to enable their temperatures to be more accurately determined. The values of these resistances bave been carefully measured every day that measurements of inductance have been made, when results of the highest accuracy have been sought. In series with the resistances r and Q, and forming part of them, are two slide wires which enable these resistances to be adjusted to 0.001 ohm, or even less, when necessary.
In order to eliminate as far as possible the errors due to slight changes in the arms Pand R of the bridge, as well as any difference in their residual inductance and capacity, these resistances are always made equal and a commutator is employed to reverse them; a pair of readings is taken in every case, the mean of which is used in the calculation. The resistances Q and S were taken from two resistance boxes, in which the higher coils are subdivided to reduce the electrostatic capacity of the coil. We found in some of our early work that the residual capacity or inductance of noninductive resistances may be considerable; in the lower resistance coils the inductance predominates, and in the higher coils the capacity predominates. The connecting
a W. Oehmke, maker, Berlin.
Table 1.- RESULTS OF MEASUREMENTS OF Two INDUCTANCE COILS OF 1 HENRY EACH; Coils MEASURED SINGLY AND IN SERIES,
MARCH 23, 1905.