(2) To find the small change in the capacity a when cd has been moved into its second position.

In first position :

where

we get

2 log

12

1=8.01 cms.,

r1=3.95 cms.,

12= 97 cm.,

a=2.85 electrostatic units

=3.16 micro-microfarads.

We get, therefore, 3.16 by calculation,

and

3.05 by experiment.

The method is therefore quite capable of detecting and measuring with considerable accuracy a capacity of 1 micromicrofarad or even less.

Discussion of the Advantages of the Method.

It is not necessary to compare this method in detail with the many other methods used in comparing capacities; it will be sufficient to point out a few leading facts.

Capacities may, of course, be compared by the electrometer without any use of radioactive substances by charging the unknown capacity to a potential which is measured by the electrometer, and then sharing the charge with a known capacity, and again measuring the potential. The method of working is not, however, as accurate as that described above, especially when the capacities are small.

Capacities are often compared by charging them to the same potential, and discharging them through a ballistic galvanometer. The galvanometer-deflexion must be accurately read, and a correction applied for damping, observations which cannot be made with the accuracy with which we can compare two intervals of time. Again, when the capacities are small, they must be charged or discharged through the galvanometer a great number of times per second, which requires carefully constructed apparatus to enable the number of charges to be accurately known. In addition it is somewhat difficult to be certain that the apparatus is working properly; for example, an error might arise through faulty insulation, and escape detection.

The method of De Sauty is free from many of the objections mentioned above; but others might be urged against it, and especially that it can be of little use when the capacities are very small.

One of the chief advantages of the method described in this paper is that, from the nature of the apparatus used, it is scarcely possible for any serious source of error to come in without detection; a faulty insulation, for example, can easily be guarded against. The only quantity requiring to be measured is an interval of time, which can be done with great accuracy. The ionization produced by the uranium keeps very constant throughout the time required to make a determination, and there is no other quantity that requires to be kept very constant. The potential of the battery joined to one of the plates between which the uranium is placed may vary considerably between the observations and produce no effect, provided the potential is sufficiently great.

The only objection that seems likely to be made to the method is the fact that it employs a quadrant-electrometer, the use of which in ordinary laboratory work has hitherto been discouraged. As stated above, the writer sees no reason for the reluctance to use electrometers when their use can be

avoided by means of galvanometers and other, sometimes complicated, apparatus. Some of the lines of research in recent years have necessitated an extensive use of quadrant electrometers, with the natural result that they have been greatly improved; and whatever reasons there may formerly have been for avoiding the use of electrometers, these reasons have now entirely disappeared.

XLIV. On a New Form of Sensitive Hot-Wire Voltmeter. By R. THRELFALL, F.R.S.*

HE practical need for a sensitive alternate-current voltmeter arises in connexion with the measurement of large alternating currents. The instruments at present employed for the purpose of measuring alternating currents are substantially of two types, the ampere gauge of Lord Kelvin forming the standard and almost only representative of one class; and instruments based on transformers forming the other. Both classes of instruments require calibration in manufacture, and from time to time, and it is then that the want of a sensitive voltmeter is felt; for the obviously most direct method is to measure the potential drop across a standard resistance traversed by the whole current in question. It may seem curious that the larger the current to be measured, the more sensitive must be the voltmeter employed; but a little consideration will show that this is the case because it is not practicable to go on increasing the weight of a standard resistance without limit. In the other alternative the heating becomes excessive, and there is a risk of damaging the standard. For instance, suppose that it is a question of measuring 2000 amperes by means of a resistance of 0002 ohm, the P.D. drop is 4 volt, and the power expended in heat is 8 kilowatt-quite a consideration. The practical standard alternating-current voltmeter must therefore be sensitive and adjusted to work across an external resistance which may be considered negligible in comparison with its own resistance. If the hot-wire form be adopted, it is seen that the electrical considerations point to the wire being as short as possible, and also as fine as possible; for it has often been shown that the rise of temperature for a given current-density increases as the diameter of the wire decreases.

Taking everything into account, the most suitable material appears to be pure silver. As this can be obtained commercially nicely gilded and of such a thickness that two miles

* Communicated by the Physical Society: read November 27, 1903.

go to the troy ounce, it was not worth while trying to improve upon it in the laboratory, though no doubt finer stuff could be produced by special artifice. For instance, by making a silver wire or strip the anode in a dilute solution of potassium iodide, it can be very materially reduced in thickness, but the mechanical properties are impaired to some extent in spite of the equalizing action of the coating of silver iodide which is formed.

In order to make use of the gilt silver wire as a hot-wire voltmeter, it is necessary to be certain that the wire is always stretched by the same force, and then the small changes in length consequent on the passing of a current can be measured.

The chief peculiarity of the instrument in question is in regard to the means adopted for securing uniformity of tension of the fine wire.

Referring to fig. 1. The fine wire is seen stretched between two supports, and pulled downwards at the centre by a microscopic hook and spiral spring insulated from the base; a small

Fig. 1.

mirror hinged on a wire stretched alongside rests on the head of the hook. The deflexion of the wire is exaggerated in the diagram, in reality the interior angle is about 175°, or from that to 178°.

In order to get an idea of the relation of the sag of the wire to its increment of length, suppose that it is stretched quite straight to begin with; that its length is 27, and that we require to find the contraction of the spiral spring for a given increment of length a in the wire. This is seen to be given by 2-la, when a is small.

To form an idea of the multiplication obtainable in practice, suppose that the distance between supports =5 cms., and that the wire is heated through 1o C., the initial interior angle being 175°, and the coefficient of expansion of the wire per degree 00002. Calculation shows that in this case the magnification is about 22; and of course it increases rapidly the more nearly the initial angle approaches 180°. The condition as to the length of wire which it is best to employ, is easily obtained from the following considerations.

The resistance of the instrument-circuit is practically the same as the resistance of the fine wire. The diameter of this being fixed at the minimum available, the resistance is simply proportional to the length. The rate of heat evolution is therefore inversely as the length at constant P.D. If the length of wire be increased n-fold, the rate at which heat is supplied is of its former value, and the cooling surface is increased n-fold; therefore, for small rises of temperature the rise of temperature of the wire is of its former value.

1

n

1

n2

The total increase of length of the wire which is the subject of measurement is proportional both to the length of the wire and to the temperature difference; so that it finally becomes

The sensitiveness of the instrument, in so far as the limit is set by the difficulty of measuring small changes of length, is therefore inversely as the length of the wire. If the sensitiveness be regarded as limited by the least amount of sag that can be perceived due to heating, we have to consider what further condition is imposed. The practical condition is that enough sag must be allowed initially to prevent the wire getting broken if the current is accidentally taken off while the measuring apparatus is in the position necessary to make the sag constant in spite of the heating. In this case the magnification is constant, and a depends only on the length-giving the same condition for sensitiveness as obtains when we consider the measuring apparatus as imposing the limit.