Page:EB1911 - Volume 02.djvu/911

At the temperate stations the maximum occurs near midwinter; in the Arctic it seems deferred towards spring.

6. Diurnal Variation.—Table II. gives the mean diurnal variation for the whole year at a number of stations arranged in order of latitude, the mean from the 24 hourly values being taken as 100. The data are some from “all” days, some from “quiet,” “fine” or “dry” days. The height, h, and the distance from the wall, l, were the potential is measured are given in metres when known. In most cases two distinct maxima and minima occur in the 24 hours. The principal maximum is usually found in the evening between 8 and 10 p.m., the principal minimum in the morning from 3 to 5 a.m. At some stations the minimum in the afternoon is indistinctly shown, but at Tokyo and Batavia it is much more conspicuous than the morning minimum.

7. In Table III. the diurnal inequality is shown for “winter” and “summer” respectively. In all cases the mean value for the 24 hours is taken as 100. By “summer” is meant April to September at Sodankylä, Greenwich and Batavia; May to August at Kew, Bureau Central (Paris), Eiffel Tower and Perpignan; and May to July at Karasjok. “Winter” includes October to March at Sodankylä, Greenwich and Batavia; November to February at Kew and Bureau Central; November to January at Karasjok, and December and January at Perpignan. Mean results from March, April, September and October at Kew are assigned to “Equinox.”

At Batavia the difference between winter and summer is comparatively small. Elsewhere there is a tendency for the double period, usually so prominent in summer, to become less pronounced in winter, the afternoon minimum tending to disappear. Even in summer the double period is not prominent in the arctic climate of Karasjok or on the top of the Eiffel Tower. The diurnal variation in summer at the latter station is shown graphically in the top curve of fig. 1. It presents a remarkable resemblance to the adjacent curve, which gives the diurnal variation at mid-winter at the Bureau Central. The resemblance between these curves is much closer than that between the Bureau Central’s own winter and summer curves. All three Paris curves show three peaks, the first and third representing the ordinary forenoon and afternoon maxima. In summer at the Bureau Central the intermediate peak nearly disappears in the profound afternoon depression, but it is still recognizable. This three-peaked curve is not wholly peculiar to Paris, being seen, for instance, at Lisbon in summer. The December and June curves for Kew are good examples of the ordinary nature of the difference between midwinter and midsummer. The afternoon minimum at Kew gradually deepens as midsummer approaches. Simultaneously the forenoon maximum occurs earlier and the afternoon maximum later in the day. The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole. The somewhat remarkable resemblance between the diurnal variation for the two elements, first remarked on by J. D. Everett (19), is of interest in connexion with recent theoretical conclusions by J. P. Elster and H. F. K. Geitel and by H. Ebert.

In the potential curves of the diagram the ordinates represent the hourly values expressed—as in Tables II. and III.—as percentages of the mean value for the day. If this be overlooked, a wrong impression may be derived as to the absolute amplitudes of the changes. The Kew curves, for instance, might suggest that the range (maximum less minimum hourly value) was larger in June than in December. In reality the December range was 82, the June only 57 volts; but the mean value of the potential was 243 in December as against 111 in June. So again, in the case of the Paris curves, the absolute value of the diurnal range in summer was much greater for the Eiffel Tower than for the Bureau Central, but the mean voltage was 2150 at the former station and only 134 at the latter.

8. Fourier Coefficients.—Diurnal inequalities such as those of Tables II. and III. and intended to eliminate irregular changes, but they also to some extent eliminate regular changes if the hours of maxima and minima or the character of the diurnal variation alter throughout the year. The alteration that takes place in the regular diurnal inequality throughout the year is best seen by analysing it into a Fourier series of the type

c₁ sin(t + a₁) + c₂ sin(2t + a₂) + c₃ sin(3t + a₃) + c₄ sin(4t + a₄) + ...

where t denotes time counted from (local) midnight, c₁, c₂, c₃, c₄, ... are the amplitudes of the component harmonic waves of periods 24, 12, 8 and 6 hours; a₁, a₂, a₃, a₄, are the corresponding phase angles. One hour of time t is counted as 15°, and a delay of one hour in the time of maximum answers to a diminution of 15° in a₁, of 30° in a₂, and so on. If a₁, say, varies much throughput the year, or if the ratios of c₂, c₃, c₄, ... to c₁, vary much, then a diurnal inequality derived from a whole year, or from a season composed of several months, represents a mean curve arising from the superposition of a number of curves, which differ in shape and in the positions of their maxima and minima. The result, if considered alone, inevitably leads to an underestimate of the average amplitude of the regular diurnal variation.

It is also desirable to have an idea of the size of the irregular changes which vary from one day to the next. On stormy days, as already mentioned, the irregular changes hardly admit of satisfactory treatment. Even on the quietest days irregular changes are always numerous and often large.

Table IV. aims at giving a summary of the several phenomena for a single station, Kew, on electrically quiet days. The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days. The hourly values are derived from smoothed curves, the object being to get the mean ordinate for a 60-minute period. If the actual crests of the excursions had been measured the figures in the second line would have been even larger. The third line gives the range of the regular diurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed. These mean values, ranges and amplitudes are all measured in volts per metre (in the open). The last four lines of Table IV. give the phase angles of the first four Fourier waves.

Table IV.—Absolute Potential Data at Kew (12).

		Jan.	Feb.	March.	April.	May.	June.	July.	Aug.	Sept.	Oct.	Nov.	Dec.
Mean Potential Gradient		201	224	180	138	123	111	98	114	121	153	200	243
Mean of individual daily ranges		203	218	210	164	143	143	117	129	141	196	186	213
Range in Diurnal inequality		73	94	83	74	71	57	55	60	54	63	52	82
Amplitudes of Fourier waves $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	c1	22	22	17	13	18	9	6	6	9	7	14	30
	c2	21	33	34	31	22	23	24	26	23	30	17	21
	c3	7	10	5	5	3	1	3	2	3	6	5	7
	c4	2	3	5	6	4	1	4	3	4	3	2	3
		°	°	°	°	°	°	°	°	°	°	°	°
Phase angles of Fourier waves$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	a1	206	204	123	72	86	79	48	142	154	192	202	208
	a2	170	171	186	193	188	183	185	182	199	206	212	175
	a3	11	9	36	96	100	125	124	107	16	18	38	36
	a4	235	225	307	314	314	277	293	313	330	288	238	249

It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2·0 in May to 3·6 in November.

At midwinter the 24-hour term is the largest, but near midsummer it is small compared to the 12-hour term. The 24-hour term is very variable both as regards its amplitude and its phase angle (and so