place and then at another nearer place closer by a distance cms., then the difference of the inductances measured in the two cases has a value L such that;

This formula is easily derived from one given by Maxwell. It is a simple matter to obtain in this manner an inductance having a value say of 30,000 cms., and by its aid to test methods of measurement.

By the use of a long solenoid having an inductance predetermined by the rule given above, the method can be used for the determination of small capacities of the order of a thousandth of a microfarad. It is to be hoped, therefore, that in future those who describe experiments or appliances such as wireless telegraphy arrangements in which such small capacities or inductances are used, will cease from the practicə of speaking of jars with so many "square inches or square centimetres of coated surface," and take the slight trouble to measure and record the capacity and inductances, and in this way afford the means of testing theories of the operation of the appliances.

It can hardly be said that the practical problem of measuring with great accuracy very small inductances of the order of 1 microhenry or less has been satisfactorily solved.

Probably in the case of inductances of very low resistance the best method to adopt would be to measure the fall of potential down the conductor first, with a continuous current, and then with a high-frequency sine form alternating current. Professor W. Stroud and Mr. J. H. Oates recently described a bridge method employing alternating currents, which they stated could be employed for the measurement of very small

inductances *.

LXV. On a Hot-Wire Ammeter for the Measurement of very small Alternating Currents. By J. A. FLEMING, D.Sc., F.R.S., Professor of Electrical Engineering in University College, London†.

THERE

HERE are many occasions on which it becomes necessary to measure a small alternating current of the order of one-hundredth of an ampere.

In taking the magnetizing currents of small transformers *See Prof. W. Stroud and Mr. J. H. Oates on the "Application of Alternating Currents to the Calibration of Capacities and Inductances," Phil. Mag. ser. 6, vol. vi. P. 707 (1903).

+ Communicated by the Physical Society: read March 25, 1904.

of one kilowatt size or less for the determination of the power-factor on the high-tension side, say, at 2000 volts, the magnetizing current to be measured may be at most about 002 of an ampere, or less in proportion to the size of the transformer.

The capacity of a small condenser or short length of cable or wireless telegraph aerial can be measured by means of a simple harmonic electromotive force, if we have the means of measuring a small alternating current and a high voltage. For if a simple harmonic electromotive force of frequency n=2π/p, and R.M.S. value V, is applied to a condenser of capacity C microfarads, then the alternating current (R.M.S. value) flowing into it has a value of CpV/106 amperes, provided there is no sensible resonance.

If the frequency is about 80 so that p = 500 and if V=2000 volts, then a capacity as small as 1/500 of a microfarad can be measured in this manner, provided we have the means of measuring the voltage V and an alternating current of the above-named magnitude. This can of course be done by any form of electro-dynamometer adapted for measuring very small currents, but the hot-wire ammeter here described is much simpler to construct.

The following form of hot-wire ammeter can be so made as to measure currents as small as two milliamperes, and is easily calibrated at the time of using it.

The ammeter consists of a wooden box (A B, see fig. 1) 104 cms. in length, 8 cms. in height, and 6 cms. in width.

The top of this box opens on hinges, and in the centre is fixed an achromatic convex lens 7 having a focal length of 10 cms. The front of the box is cut down to form a window, W, which is glazed with a sheet of thin transparent mica (see fig. 1). In the box is fixed a square rod of well-seasoned pine, a metre in length and 2.5 cms. in width and breadth. To each end

of this rod are fixed two small brass uprights to which terminal screws are attached and also small spring pieces of brass, PP, which are pressed in by screws passing through the uprights (see figs. 1 and 2).

To these springs at each end of the rod are attached fine. wires, either of pure silver or of some high resistance alloy, such as constantan, platinoid, &c., according to the use to which the instrument is to be placed.

In the instrument I have already constructed, these wires are of platinoid, the length of the wires being one metre and the diameter 005 of a millimetre. The distance apart of these wires is about 5 millimetres. The extremities of these wires are soldered to the two spring pieces at the ends of the wooden rod, and the tension of these wires can be adjusted by means of the screws passing through the small uprights and pressing against the spring pieces.

To the centre of the wooden rod carrying the abovementioned fine wires are fastened two very delicate spiral springs, s, which have their other ends looped over the long straight wires. These spiral springs are made of extremely fine platinoid wire, and they serve to keep the ammeter wires tight (see fig. 2).

If one of the wires is heated by passing a current through it, it sags down slightly. This sag is indicated in the following manner :-The two wires are embraced by an exceedingly small loop of paper m made from a strip of paper a couple of millimetres in width and about 12 or 15 millimetres in length.

To this loop of paper is attached with a touch of shellac a fragment of silvered microscopic glass about a couple of millimetres in width and 5 millimetres in length.

The tension of one of the wires is so adjusted that when no current is passing through either of them one wire sags more than the other, and this little loop of paper and its attached mirror sets itself at an angle of about 45 degrees to the horizontal. This is attained by slightly relaxing the tension on one of the wires. Upon the lid of the containing box is carried an incandescent lamp, having a straight or horseshoeshaped filament, and in front of the box is placed (see fig. 1)

a vertical strip of ground glass S, carried in a brass grooved frame which can be adjusted to any height on a vertical metal rod. The height of the incandescent lamp is so adjusted that the lens forms a clear image of the filament or of one leg of the filament upon the ground glass in the form of a horizontal line of light. With a good lens this image can be made very sharp. The lens actually used was the objective of an old opera-glass. A hood of metal or asbestos placed over the lamp prevents the direct rays of the lamp falling on the ground-glass screen. The screen can be conveniently placed about a metre from the wire box.

If, then, a small current is passed through the slacker of the two measuring wires, its sag will increase and the small mirror attached to the two wires will be tilted, and the image of the filament on the ground glass will move down, but return again to its original zero, as soon as the current is removed.

As a preliminary step, both the wires must be aged by sending intermittently a small current through them for a considerable time, this current being continually interrupted.

In the instrument actually made, the platinoid wires have a resistance of about 168 ohms each; hence, if an electromotive force of 2 volts is applied to the ends of the wires, a current of about 1/84 of an ampere passes through them.

The instrument is calibrated in the following manner:A secondary cell having a measured electromotive force, say, of about 2 volts, is connected in series with one of the working wires through a resistance-box of the usual plug pattern. By varying this resistance, different currents are passed through the wire and the position of the spot of light on the screen corresponding to the different currents is noted.

If the wire employed is of platinoid or of constantan, its resistance will not be altered appreciably by different small currents passed through it, and hence the resistance of the wire can be determined once for all, with a sufficient degree of approximation for practical purposes, by means of a potentiometer. When this has once been done, a few observations taken with a cell of known electromotive force and a plug resistance-box used as above, enable the observer to mark off on the ground-glass strip with a pencil the position of the line of light for various known currents lying within a certain range. The strip of ground glass may then be removed and applied to a sheet of squared paper, and a curve plotted down showing the deflexions in terms of the actual currents. This curve proves to le a parabola (see fig. 3) because, if we plot the logarithms of the deflexions and the

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logarithms of the currents, we have a straight line delineated, making an angle with the horizontal, the tangent of which is equal to 2. If, then, we replace the ground-glass screen in its original position and pass through the ammeter

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O

wire any current, continuous or alternating, lying within the range of the graduation, the resulting deflexion of the line of light on the screen can be at once marked off on the ground glass, and from the curve of calibration obtained as above described the ampere value of this current becomes at once known.

In the instrument actually used the deflexion of the line