should act simultaneously all over a circle of latitude, for that would imply considerable currents across the earth's surface. It is more likely that the principal action takes place along a geographical meridian; and if that is the case, the horizontal force should shew stronger evidence of these lunar periodicities than the declination. There is also the possibility that what is observed in the daily average of declination is only a remnant of a variation having the lunar day for its period. In that case the periodicity should disappear when the average position of the needle in a lunar day is subjected to calculation. If this is the correct explanation it should not be difficult to prove it, for it would require a much greater amplitude within the lunar day to account for the 0''06 amplitude found in the daily averages. How much greater may be seen from the following consideration. If from a periodic function cost another is formed by taking averages over a period 27 we obtain

KT 28.53
П 29.53

day, ; hence т equals 174° and the amplitude of the curve obtained by taking averages is only about the 29th part of that of the original curve. The comparison of averages of successive days will therefore produce an apparent period having the lunar month as periodic time and, if the period found above is due to this cause, the amplitude of the original lunar variation should be 1'74. Such an amplitude ought to be traceable without much difficulty.

A thorough enquiry into the nature of lunar periodicities of magnetic records seems to me to be of special importance, but requires considerable arithmetical labour; for, to be conclusive it must be complete. I have been assisted in the numerical calculations which were necessary in the present investigation by Mr J. R. Ashworth, to whom I desire to tender my thanks. The expense connected with the numerical work was partially covered by a small contribution from the Government Grant Fund of the Royal Society.

VII. Experiments on the Oscillatory Discharge of an Air Condenser, with a Determination of "v." By OLIVER J. LODGE, D.Sc., F.R.S., and R. T. GLAZEBROOK, M.A., F.R.S.

[Received 9 August, 1899.]

PART I.

GENERAL DESCRIPTION OF THE METHOD.

AFTER a considerable number of experiments on the discharge of Leyden jars, and a qualitative study of the electric oscillations accompanying such discharge, it seemed desirable to make an exact determination of the frequency of alternation given by a standard condenser through a circuit of known self-induction, in order to ascertain whether the well-known theory of the case was accurate or only an approximation.

The absolute determinations necessary were three, viz.:

(1) The capacity of a condenser, which is K times a length ;

(2) The self-induction of a coil, which is coil, which is μ times a length; though it would be natural to measure it indirectly by comparison with the already carefully determined standard of electrical resistance;

(3) The period of one oscillation of the discharge, under circumstances when the damping influences are not appreciably disturbing.

The resistance of the circuit might possibly enter as a correction into the result, and many other minor determinations might have to be made, but these three are the main quantities involved, and the relation between them is

T= 2π √(μl1. Kl2),

and the formula would be verified if the resulting value for the product of the as yet entirely unknown constants, μ the permeability and K the inductive capacity of the medium, agreed at all closely with the already otherwise determined value, viz. the square of the reciprocal of the velocity of light.

It was hoped indeed that the method might turn out sufficiently accurate to give a useful re-determination of this important quantity. It was with this idea in mind

that the following research was undertaken, and much care was accordingly bestowed upon it.

It may be here noted that Lord Kelvin himself, in one of his popular lectures* suggests this method of electric oscillation as just conceivably one of the methods by which could be practically determined; and he puts the matter in a geometrical way, which it may be interesting freely to paraphrase thus:

Take a wheel of radius equal to the geometric mean of the following two lengths, the electrostatic measure of the capacity of a condenser, and the electromagnetic measure of the self-induction of its discharge circuit; make this wheel rotate in the time of one complete electric oscillation of the said condenser (as if it were being driven by an electrically oscillating piston and crank), then it will roll itself along a railway with the velocity v.

And indeed (as Maxwell discovered) ethereal waves excited by the discharge are actually transmitted through space at this very speed.

sions.

GENERAL REQUIREMENTS OF THE METHOD.

The first essential is a condenser of capacity directly measurable from its dimenIts dielectric must accordingly be air, its plates must be a reasonable distance apart, and they should be either spherical or have a guard-ring. The necessary smallness of capacity of a condenser satisfying these requirements is a difficulty, especially when a quantity so large as the velocity of light is the subject of measurement. A difficulty of the same sort is, however, common to all methods, and is what makes “v” a quantity so much more difficult to determine than for instance "the ohm."

To compensate for the smallness of practicable electrostatic capacity a discharge circuit of very great inductance must be employed, or else the time-determination will be difficult from its excessive minuteness.

The inductance must be secured in combination with as much conductance as possible, or the discharge will fail in being oscillatory. To this end Messrs W. T. Glover and Co. were requested to supply a regularly wound hank or coil of No. 22 (s. w. G.) high conductivity copper, very thinly india-rubber covered, of shape such as to give maximum self-induction, and of size estimated to give between 5 and 6 secohms, i.e., in magnetic measure, a length of 5 or 6 earth quadrants.

This would be afforded by a coil of 4 inches cross-sectional area and mean diameter 15 inches, with three or four thousand turns of wire. But to guard against the danger of sparking or leaking between layers it was decided to reduce the dangerous tension to one-quarter by having the coil in two halves. Accordingly it was made as follows (to quote Messrs Glover's statement):

* Sir W. Thomson's Lectures and Addresses, Vol. 1. p. 119. Lecture on Electrical Units to the Inst. C. E. VOL. XVIII.

18

4

4,330 yards of No. 22 tinned copper wire covered with 2 coats of pure indiarubber to the diameter of 035 inch. This was the only covering. In two parallel coils, internal diameter 102 inches, 4 inches deep, and 2 inches wide." See Figure 1. This pair of coils were then packed carefully and permanently in a round walnut box or drum, with a thin sheet of glass between them, and the terminals of each coil were led to the outside and finished off on four ebonite pillars.

2"

They could, therefore, be connected up in series, or parallel, or used separately; but in practice they were usually joined in simple series. With this coil many preliminary experiments were made at Liverpool.

The self-induction of the double coil was estimated as about 5 secohms or quadrants," but no attempt was made to measure it with any care at this time, because it was better to do it when all the apparatus was in position in the basement room set aside for the experiments described in Part II.

FIG. 1.

The chief part of the whole business consisted in taking clear images of a spark on a moving sensitive plate, getting every detail of the oscillation clearly recorded on the negatives, so that they could be subsequently analysed under a microscope and the time of an oscillation accordingly determined.

The sparks used were extremely feeble, and each was drawn out by motion into a band, so that in order to get every detail clear the plates had to be super-sensitive. For such plates we were indebted to the kindness of Mr J. W. Swan, who sent on several occasions a special packet of Messrs Mawson and Swan's most highly sensitized plates, which answered admirably.

The next principal part consisted in the micrometric reading of the records on the photographic plates. The reading is rather a tedious process as a great many numbers. have to be recorded for each plate, and care is necessary to disentangle the several sparks, which to economise time and labour at the experimental end were usually taken during a single spin.

The details of the method of obtaining the record will now be described.

TIME OF ONE OSCILLATION.

The long-established method of observing spark oscillation by means of a revolving mirror was at first used; but this plan, though easy for observation, does not readily lend itself to precise measurement. It is desirable to obtain a photographic record which can be studied at leisure, and it seemed therefore best to form an image of the spark on a plate moving so rapidly that its constituent oscillations were clearly visible.

For metrical purposes there are many advantages in thus moving only the sensitive plate, though for mere display Mr Boys's more recent plan of spinning a succession of lenses is able to give more striking results.

Accordingly an old packing case was made light-tight, and used as the camera. In it were contained: first the spark-gap, a pair of adjustable brass knobs about half-aninch in diameter, clamped to a glass pillar, one vertically over the other and with a clear space, on the average about 2 millimetres, between them; next the lens, an ordinary camera lens on a special stand; and lastly the sensitive plate in its conjugate focus, arranged so that the image was not very much smaller than the object. The photographic plate is supported firmly in a revolving wooden carrier or frame fixed to the horizontal axle of a whirling machine (one of Weinhold's) which was firmly clamped to a stone pillar outside the camera and was driven by a long carefully spliced whipcord belt by means of one of Bailey's "Thirlmere" turbines standing on a distant sink, and having a large grooved pulley to give the necessary "gearing up." One end of the whirling machine axle passed through into the box in a light-tight manner, and it was supplied with a self-oiling syphon wick. The ordinary speed at which it was driven was 64 revolutions per second; occasionally it rose as high as 85, but the water pressure was not often enough for this.

The turbine could have been fed from a cistern in the roof, but greater pressure was attainable in the mains, and though liable to fluctuation this was found at certain times in the day or evening regular enough for good observation.

MODE OF CONTROLLING AND DETERMINING THE SPEED.

Uniformity of rotation was essential, and to secure it the method employed by Lord Rayleigh in his determination of the ohm was imitated. A small cardboard stroboscopic disk was painted with several circles of radial markings, or "teeth," the ones chiefly used being 3, 4, 5, 6, 8 teeth respectively in a circumference, especially the pattern 4.

This disk was watched through a pair of slits carried by the prongs of a large electromagnetically maintained Koenig fork, whose loads were adjusted to give 128 vibrations per second precisely. The slits permitted vision at the middle of each swing, consequently 256 glimpses a second. Hence whenever the 4 pattern on the stroboscopic disk was distinct and stationary as seen through the slits, it meant that the sensitive plate on the same axle was spinning 64 times in a second.

Photographs of sparks were taken only when the pattern was stationary and the speed thus known to be regular.

To determine the speed absolutely it was necessary to calibrate or specially observe the period of the fork. To this end two methods were employed: one the ordinary method devised by Lord Rayleigh, for comparing an electromagnetically maintained fork