Table XXII.—Mean Absolute Daily Ranges (Units 1′ for Declination, 1γ for H and V).Jan.Feb.Mar.April.May.June.July.Aug.Sept.Oct.Nov.Dec.Year.Declination.Pavlovsk13.4217.2018.2217.2517.7615.9116.8916.5716.7515.7013.8712.3715.99Ekatarinburg7.339.5411.9012.8913.6313.0312.7812.2111.239.447.866.8510.72Kew. All days11.1613.6915.9315.0014.9013.6514.1314.2214.5714.0711.719.8013.57Kew. Ordinary days10.1411.8714.1914.2413.8513.2613.4713.6713.7113.1010.409.0012.58Kew. Quiet days6.127.5710.5911.8412.0911.9511.6011.9310.869.166.545.089.61Zi-ka-wei3.883.256.227.047.157.407.778.066.734.682.912.525.63Mauritius6.937.797.115.754.874.034.366.006.286.716.996.786.13Horizontal force.Pavlovsk52.474.579.180.186.279.086.777.676.767.355.745.971.8Ekatarinburg33.243.148.451.756.254.156.751.749.344.134.129.346.0Mauritius37.935.036.237.635.034.133.834.536.637.437.835.335.9Vertical force.Pavlovsk27.050.454.743.245.334.842.135.542.537.533.525.539.3Ekatarinburg17.426.629.230.129.627.629.626.125.222.119.616.424.9Mauritius17.119.520.117.316.515.517.122.022.719.416.715.218.2A comparison of the absolute ranges in Table XXII. with the inequality ranges for the same stations derivable from Tables VIII. to X. is most instructive. At Mauritius the ratio of the absolute to the inequality range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and 2.05 for V. The declination data for Kew in Table XXII. illustrate other points. The first set of data are derived from all days of the year. The second omit the highly disturbed days. The third answer to the 5 days a month selected as typically quiet. The yearly mean absolute range from ordinary days at Kew in Table XXII. is 1.49 times the mean inequality range in Table VIII.; comparing individual months the ratio of the absolute to the inequality range varies from 2.06 in January to 1.21 in June. Even confining ourselves to the quiet days at Kew, which are free from any but the most trifling disturbances, we find that the mean absolute range for the year is 1.20 times the arithmetic mean of the inequality ranges for the individual months of the year, and 1.22 times the range from the mean diurnal inequality for the year. In this case the ratio of the absolute to the inequality range varies from 1.55 in December to only 1.09 in May.§ 25. The variability of the absolute daily range of declination is illustrated by Table XXIII., which contains data for Kew24derived from all days of the 11-year period 1890-1900. It gives the total number of times during the 11 years when the absolute range lay within the limits specified at the heads of the first nine columns of figures. The two remaining columns give the arithmetic means of the five largest and the five least absolute ranges encountered each month. The mean of the twelve monthly diurnal inequality ranges from ordinary days was only 8′.44, but the absolute range during the 11 years exceeded 20′ on 492 days, 15′ on 1196 days, and 10′ on 2784 days,i.e.on 69 days out of every 100.Table XXIII.—Absolute Daily Range of Declination at Kew.Number of occasions during 11 years when absolute range was:—Means from the 5 largestand 5 least ranges of themonth on the average of11 years.0′ to 5′.5′ to 10′.10′ to 15′.15′ to 20′.20′ to 25′.25′ to 30′.30′ to 35′.35′ to 40′.over 40′.5 largest.5 least.′′January51145693724743122.905.07February26998451261042827.216.55March17213861322181729.878.93April04316773271063123.6910.31May05715785201230725.369.50June0561856715131219.929.89July0591857014522422.499.96August0372027522120221.2710.05September1681537119545424.559.52October3103111673410112023.928.01November42140812814985323.585.64December64166562914711320.434.36Totals1881045158871426198562542§ 26. Magnetic phenomena, both regular and irregular, at any station vary from year to year. The extent of this variation is illustrated in Tables XXIV. and XXV., both relating to the period 1890 to 1900.25Table XXIV. gives the amplitudes ofRelations to Sun-spot Frequency.the regular diurnal inequality in the elements stated at the head of the columns. The ordinary day declination data (D0) for Kew represent arithmetic means from the twelve months of the year; the other data all answer to the mean diurnal inequality for the whole year. Table XXV. gives the arithmetic means for each year of the absolute daily range, of the monthly range (or difference between the highest and lowest values in the month), and of the yearly range (or difference between the highest and lowest values of the year). The numerals attached to the years in these tables indicate their order as regards sun-spot frequency according to Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest frequency, and 1890 that of least. The difference in sun-spot frequency between 1897 and 1898 was microscopic; the differences between 1890, 1900 and 1899 were small, and those between 1893, 1894 and 1892 were not very large.The years 1892-1895 represent high sun-spot frequency, while 1890, 1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to 1895 were in all cases distinguished by the large size of the inequality ranges, and 1890, 1899 and 1900 by the small size. The range in 1893 is usually the largest, and though the H and Vranges at Ekaterinburg are larger in 1892 than in 1893, the excess is trifling. The phenomena apparent in Table XXIV. are fairly representative; other stations and other periods associate large inequality ranges with high sun-spot frequency. The diurnal inequality range it should be noticed is comparatively little influenced by irregular disturbances. Coming to Table XXV., we have ranges of a different character. The absolute range at Kew on quiet days is almost as little influenced by irregularities as is the range of the diurnal inequality, and in its case the phenomena are very similar to those observed in Table XXIV. As we pass from left to right in Table XXV., the influence of disturbance increases. Simultaneously with this, the parallelism with sun-spot frequency is less close. The entries relating to 1892 and 1894 become more and more prominent compared to those for 1893. The yearly range may depend on but a single magnetic storm, the largest disturbance of the year possibly far outstripping any other. But taking even the monthly ranges the values for 1893 are, speaking roughly, only half those for 1892 and 1894, and very similar to those of 1898, though the sun-spot frequency in the latter year was less than a third of that in 1893. Ekatarinburg data exactly analogous to those for Pavlovsk show a similar prominence in 1892 and 1894 as compared to 1893. The retirement of 1893 from first place, seen in the absolute ranges at Kew, Pavlovsk and Ekatarinburg, is not confined to the northern hemisphere. It is visible, for instance, in the amplitudes of the Batavia disturbance results. Thus though the variation from year to year in the amplitude of the absolute ranges is relatively not less but greater than that of the inequality ranges, and though the general tendency is for all ranges to be larger in years of many than in years of few sun-spots, still the parallelism between the changes in sun-spot frequency and in magnetic range is not so close for the absolute ranges and for disturbances as for the inequality ranges.Table XXIV.—Ranges of Diurnal Inequalities.Pavlovsk.Ekatarinburg.Kew.D.I.H.D.I.H.V.Dq.Iq.Hq.Do.′′γ′′γγ′′γ′1890116.321.33225.831.051896.90207.32189167.311.79306.851.3825148.041.52288.48189238.752.21377.741.7232199.501.66319.85189319.642.24388.831.80311710.061.963510.74189428.582.17387.801.7330179.321.94349.80189548.222.08337.291.6428158.591.66309.54189657.391.77296.501.3825157.771.31258.50189766.791.59266.011.1621126.711.14227.76189876.251.56265.761.1921116.851.07217.59189996.021.44245.331.1220116.691.01217.301900106.201.28225.880.931786.521.06216.83Table XXV.—Absolute Ranges.Kew Declination.Daily.Pavlovsk.Daily.Monthly.Yearly.q.o.a.D.H.V.D.H.V.D.H.V.′′′′γγ′γγ′γγ1890118.310.510.712.1492128.21188042.11691791891610.012.813.716.0703946.321823392.35506141892312.315.417.721.01117393.6698575194.0241613851893111.815.215.617.8794148.324121087.15144571894211.314.716.520.4976284.1493493145.612278781895410.614.815.618.1804647.422022373.9395534189659.512.914.517.5744352.423223688.7574608189788.211.512.114.6613043.8201170101.1449480189878.211.212.314.7673546.6276242118.91136888189997.910.511.313.1582738.317815063.83825271900107.48.99.210.5441632.81348994.2457365Means9.612.613.616.0723951.1274246100.2752629§ 27. The relationship between magnetic ranges and sun-spot frequency has been investigated in several ways. W. Ellis26has employed a graphical method which has advantages, especially for tracing the general features of the resemblance, and is besides independent of any theoretical hypothesis. Taking time for the axis of abscissae, Ellis drew two curves, one having for its ordinates the sun-spot frequency, the other the inequality range of declination or of horizontal force at Greenwich. The value assigned in the magnetic curve to the ordinate for any particular month represents a mean from 12 months of which it forms a central month, the object being to eliminate the regular annual variation in the diurnal inequality. The sun-spot data derived from Wolf and Wolfer were similarly treated. Ellis originally dealt with the period 1841 to 1877, but subsequently with the period 1878 to 1896, and his second paper gives curves representing the phenomena over the whole 56 years. This period covered five complete sun-spot periods, and the approximate synchronism of the maxima and minima, and the general parallelism of the magnetic and sun-spot changes is patent to the eye. Ellis27has also applied an analogous method to investigate the relationship between sun-spot frequency and the number of days of magnetic disturbance at Greenwich. A decline in the number of the larger magnetic storms near sun-spot minimum is recognizable, but the application of the method is less successful than in the case of the inequality range. Another method, initiated by Professor Wolf of Zurich, lends itself more readily to the investigation of numerical relationships. He started by supposing an exact proportionality between corresponding changes in sun-spot frequency and magnetic range. This is expressed mathematically by the formulaR = a + bS ≡ a {1 + (b/a) S },where R denotes the magnetic range, S the corresponding sun-spot frequency, while a and b are constants. The constant a represents the range for zero sun-spot frequency, while b/a is the proportional increase in the range accompanying unit rise in sun-spot frequency. Assuming the formula to be true, one obtains from the observed values of R and S numerical values for a and b, and can thus investigate whether or not the sun-spot influence is the same for the different magnetic elements and for different places. Of course, the usefulness of Wolf’s formula depends largely on the accuracy with which it represents the facts. That it must be at least a rough approximation to the truth in the case of the diurnal inequality at Greenwich might be inferred from Ellis’s curves. Several possibilities should be noticed. The formula may apply with high accuracy, a and b having assigned values, for one or two sun-spot cycles, and yet not be applicable to more remote periods. There are only three or four stations which have continuous magnetic records extending even 50 years back, and, owing to temperature correction uncertainties, there is perhaps no single one of these whose earlier records of horizontal and vertical force are above criticism. Declination is less exposed to uncertainty, and there are results of eye observations of declination before the era of photographic curves. A change, however, of 1′ in declination has a significance which alters with the intensity of the horizontal force. During the period 1850-1900 horizontal force in England increased about 5%, so that the force requisite to produce a declination change of 19′ in 1900 would in 1850 have produced a deflection of 20′. It must also be remembered that secular changes of declination must alter the angle between the needle and any disturbing force acting in a fixed direction. Thus secular alteration in a and b is rather to be anticipated, especially in the case of the declination. Wolf’s formula has been applied by Rajna28to the yearly mean diurnal declination ranges at Milan based on readings taken twice daily from 1836 to 1894, treating the whole period together, and then the period 1871 to 1894 separately. During two sub-periods, 1837-1850 and 1854-1867, Rajna’s calculated values for the range differ very persistently in one direction from those observed; Wolf’s formula was applied by C. Chree25to these two periods separately. He also applied it to Greenwich inequality ranges for the years 1841 to 1896 as published by Ellis, treating the whole period and the last 32 years of it separately, and finally to all (a) and quiet (q) day Greenwich ranges from 1889 to 1896. The results of these applications of Wolf’s formula appear in Table XXVI.The Milan results are suggestive rather of heterogeneity in the material than of any decided secular change inaorb. The Greenwich data are suggestive of a gradual fall ina, and rise inb, at least in the case of the declination.Table XXVII. gives values ofa,bandb/ain Wolf’s formula calculated by Chree25for a number of stations. There are two sets of data, the first set relating to the range from the mean diurnal inequality for the year, the second to the arithmetic mean of the ranges in the mean diurnal inequalities for the twelve months. It is specified whether the results were derived from all or from quiet days.Table XXVI.—Values ofaandbin Wolf’s Formula.Milan.Greenwich.Epoch.Declination(unit 1′).Epoch.Declination(unit 1′).Horizontal Force(unit 1γ).a.b.a.b.a.b.1836-945.31.0471841-967.29.037726.4.1901871-945.39.0471865-967.07.039623.6.2151837-506.43.0411889-96(a)6.71.041823.7.2181854-674.62.0471889-96(q)6.36.041525.0.213As explained above,awould represent the range in a year of no sun-spots, while 100bwould represent the excess over this shown by the range in a year whenWolf’ssun-spot frequency is 100. Thusb/aseems the most natural measure of sun-spot influence. Accepting it, we see that sun-spot influence appears larger at most places for inclination and horizontal force than for declination. In the case of vertical force there is at Pavlovsk, and probably in a less measure at other northern stations, a large difference between all and quiet days, which is not shown in the other elements. The difference between the values ofb/aat different stations is also exceptionally large for vertical force. Whether this last result is wholly free from observational uncertainties is, however, open to some doubt, as the agreement between Wolf’s formula and observation is in general somewhat inferior for vertical force. In the case of the declination, the mean numerical difference between the observed values and those derived from Wolf’s formula, employing the values ofaandbgiven in Table XXVII., represented on the average about 4% of the mean value of the element for the period considered, the probable error representing about 6% of the difference between the highest and lowest values observed. The agreement was nearly, if not quite, as good as this for inclination and horizontal force, but for vertical force the corresponding percentages were nearly twice as large.Table XXVII.—Values ofaandbin Wolf’s Formula.Declination(unit 1′).Inclination(unit 1′).Horizontal Force(unit 1γ).Vertical Force(unit 1γ).Diurnal Inequality for the Year.a.b.100b/a.a.b.100b/a.a.b.100b/a.a.b.100b/a.Pavlovsk, 1890-1900all5.74.0400.701.24.01261.0120.7.2111.028.1.2653.26Pavlovsk, 1890-1900quiet6.17.0424.69· ·· ·· ·20.6.1950.955.9.0270.46Ekatarinburg, 1890-1900all5.29.0342.650.93.01051.1316.8.1821.098.6.1171.37Irkutsk , 1890-1900all4.82.0358.740.97.00870.9018.2.1901.046.5.0711.09Kew, 1890-1900quiet6.10.0433.710.87.01251.4518.1.1941.0714.3.0810.56Falmouth, 1891-1902quiet5.90.0451.76· ·· ·· ·20.1.2331.16· ·· ·· ·Kolaba, 1894-1901quiet2.37.0066.28· ·· ·· ·31.6.2810.8919.4.0720.37Batavia, 1887-1898all2.47.0179.723.60.02180.6138.7.2740.7130.1.1560.52Mauritius1875-18801883-1890all4.06.0164.40· ·· ·· ·15.0.0960.6411.9.0690.58Mean from individual months:—Pavlovsk, 1890-1900all6.81.0446.661.44.01511.0522.8.2431.079.7.2872.97Pavlovsk, 1890-1900quiet6.52.0442.68· ·· ·· ·22.2.2080.947.0.0440.63Ekatarinburg, 1890-1900all6.18.0355.581.12.01201.0619.2.1951.019.2.1561.70Greenwich, 1865-1896all7.07.0396.56· ·· ·· ·23.6.2150.91· ·· ·· ·Kew, 1890-1900all6.65.0428.64· ·· ·· ·· ·· ·· ·· ·· ·· ·Kew, 1890-1900quiet6.49.0410.631.17.01301.1121.5.1910.8916.0.0720.45Falmouth, 1891-1902quiet6.16.0450.73· ·· ·· ·20.9.2361.13· ·· ·· ·Applying Wolf’s formula to the diurnal ranges for different months of the year, Chree found, as was to be anticipated, that the constantahad an annual period, with a conspicuous minimum at midwinter; but whilstbalso varied, it did so to a much less extent, the consequence being thatb/ashowed a minimum at midsummer. The annual variation inb/aalters with the place, with the element, and with the type of day from which the magnetic data are derived. Thus, in the case of Pavlovsk declination, whilst the mean value of 100b/afor the 12 months is, as shown in Table XXVII., 0.66 for all and 0.68 for quiet days—values practically identical—if we take the four midwinter and the four midsummer months separately, we have 100b/a, varying from 0.81 in winter to 0.52 in summer on all days, but from 1.39 in winter to 0.52 in summer on quiet days. In the case of horizontal force at Pavlovsk the corresponding figures to these are for all days—winter 1.77, summer 0.98, but for quiet days—winter 1.83, summer 0.71.Wolf’s formula has also been applied to the absolute daily ranges, to monthly ranges, and to various measures of disturbance. In these cases the values found forb/aare usually larger than those found for diurnal inequality ranges, but the accordance between observed values and those calculated from Wolf’s formula is less good. If instead of the range of the diurnal inequality we take the sum of the 24-hourly differences from the mean for the day—or, what comes to the same thing, the average departure throughout the 24 hours from the mean value for the day—we find that the resulting Wolf’s formula gives at least as good an agreement with observation as in the case of the inequality range itself. The formulae obtained in the case of the 24 differences, at places as wide apart as Kew and Batavia, agreed in giving a decidedly larger value forb/athan that obtained from the ranges. This indicates that the inequality curve is relatively less peaked in years of many than in years of few sun-spots.§ 28. The applications of Ellis’s and Wolf’s methods relate directly only to the amplitude of the diurnal changes. There is, however, a change not merely in amplitude but in type. This is clearly seen when we compare the values found in years of many and of few sun-spots for the Fourier coefficients in the diurnal inequality. Such a comparison is carried out in Table XXVIII. for the declination on ordinary days at Kew. Local mean time is used. The heading S max. (sun-spot maximum) denotes mean average results from the four years 1892-1895, having a mean sun-spot frequency of 75.0, whilst S min. (sun-spot minimum) applies similarly to the years 1890, 1899 and 1900, having a mean sun-spot frequency of only 9.6. The data relate to the mean diurnal inequality for the whole year or for the season stated. It will be seen that the difference between the c, or amplitude, coefficients in the S max. and S min. years is greater for the 24-hour term than for the 12-hour term, greater for the 12-hour than for the 8-hour term, and hardly apparent in the 6-hour term. Also,relatively considered, the difference between the amplitudes in S max. and S min. years is greatest in winter and least in summer. Except in the case of the 6-hour term, where the differences are uncertain, the phase angle is larger,i.e.maxima and minima occur earlier in the day, in years of S min. than in years of S max. Taking the results for the whole year in Table XXVIII., this advance of phase in the S min. years represents in time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour term, and 14.7 minutes for the 8-hour term. The difference in the phase angles, as in the amplitudes, is greatest in winter. Similar phenomena are shown by the horizontal force, and at Falmouth24as well as Kew.Table XXVIII.—Fourier Coefficients in Years of many and few Sun-spots.Year.Winter.Equinox.Summer.S max.S min.S max.S min.S max.S min.S max.S min.′′′′′′′′c13.472.212.411.433.762.414.382.98c22.041.511.150.782.331.712.732.06c30.890.720.550.421.160.970.970.77c40.280.270.300.270.420.420.110.11°°°°°°°°α1228.5232.4243.0256.0231.3233.7218.2220.3α241.746.623.536.940.643.950.652.5α3232.6243.6234.0257.6228.4236.2236.8245.4α458.057.352.360.862.058.257.445.2§ 29. There have already been references toquietdays, for instance in the tables of diurnal inequalities. It seems to have been originally supposed that quiet days differed from other days onlyQuiet Day Phenomena.in the absence of irregular disturbances, and that mean annual values, or secular change data, or diurnal inequalities, derived from them might be regarded as truly normal or representative of the station. It was found, however, by P. A. Müller29that mean annual values of the magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885 derived from quiet days alone differed in a systematic fashion from those derived from all days, and analogous results were obtained by Ellis30at Greenwich for the period 1889-1896. The average excesses for the quiet-day over the all-day means in these two cases were as follows:—WesterlyDeclination.Inclination.HorizontalForce.VerticalForce.St Petersburg+0.24−0.23+3.2γ−0.8γGreenwich+0.08+3.2γ−0.9γThe sign of the difference in the case of D, I and H was the same in each year examined by Müller, and the same was true of H at Greenwich. In the case of V, and of D at Greenwich, the differences aresmall and might be accidental. In the case of D at Greenwich 1891 differed from the other years, and of two more recent years examined by Ellis31one, 1904, agreed with 1891. At Kew, on the average of the 11 years 1890 to 1900, the quiet-day mean annual value of declination exceeded the ordinary day value, but the apparent excess 0′.02 is too small to possess much significance.Another property more recently discovered in quiet days is the non-cyclic change. The nature of this phenomenon will be readilyNon-cyclic Change.understood from the following data from the 11-year period 1890 to 1900 at Kew32. The mean daily change for all days is calculated from the observed annual change.D.I.H.V.′′Mean annual change−5.79−2.38+25.9γ−22.6γMean daily change, all days−0.016−0.007+0.07γ−0.06γMean daily change, quiet days+0.044−0.245+3.34γ−0.84γThus the changes during the representative quiet day differed from those of the average day. Before accepting such a phenomenon as natural, instrumental peculiarities must be carefully considered. The secular change is really based on the absolute instruments, the diurnal changes on the magnetographs, and the first idea likely to occur to a critical mind is that the apparent abnormal change on quiet days represents in reality change of zero in the magnetographs. If, however, the phenomenon were instrumental, it should appear equally on days other than quiet days, and we should thus have a shift of zero amounting in a year to over 1,200γ in H, and to about 90′ in I. Under such circumstances the curve would be continually drifting off the sheet. In the case of the Kew magnetographs, a careful investigation showed that if any instrumental change occurred in the declination magnetograph during the 11 years it did not exceed a few tenths of a minute. In the case of the H and V magnetographs at Kew there is a slight drift, of instrumental origin, due to weakening of the magnets, but it is exceedingly small, and in the case of H is in the opposite direction to the non-cyclic change on quiet days. It only remains to add that the hypothesis of instrumental origin was positively disproved by measurement of the curves on ordinary days.It must not be supposed that every quiet day agrees with the average quiet day in the order of magnitude, or even in the sign, of the non-cyclic change. In fact, in not a few months the sign of the non-cyclic change on the mean of the quiet days differs from that obtained for the average quiet day of a period of years. At Kew, between 1890 and 1900, the number of months during which the mean non-cyclic change for the five quiet days selected by the astronomer royal (Sir W. H. M. Christie) was plus, zero, or minus, was as follows:—Element.D.I.H.V.Number +631311247Number 01416119Number −55101974The + sign denotes westerly movement in the declination, and increasing dip of the north end of the needle. In the case of I and H the excess in the number of months showing the normal sign is overwhelming. The following mean non-cyclic changes on quiet days are from other sources:—Element.Greenwich(1890-1895).Falmouth(1898-1902).Kolaba(1894-1901).′′′D+ 0.03+ 0.05+ 0.07H+ 4.3γ+ 3.0γ+ 3.9γThe results are in the same direction as at Kew, + meaning in the case of D movement to the west. At Falmouth32, as at Kew, the non-cyclic change showed a tendency to be small in years of few sun-spots.§ 30. In calculating diurnal inequalities from quiet days the non-cyclic effect must be eliminated, otherwise the result would depend on the hour at which the “day” is supposed to commence. If the value recorded at the second midnight of the average day exceeds that at the first midnight by N, the elimination is effected by applying to each hourly value the correction N(12 − n)/24, where n is the hour counted from the first midnight (0 hours). This assumes the change to progress uniformly throughout the 24 hours. Unless this is practically the case—a matter difficult either to prove or disprove—the correction may not secure exactly what is aimed at. This method has been employed in the previous tables. The fact that differences do exist between diurnal inequalities derived from quiet days and all ordinary days was stated explicitly in § 4, and is obvious in Tables VIII. to XI. An extreme case is represented by the data for Jan Mayen in these tables. Figs. 9 and 10 are vector diagrams for this station, for all and for quiet days during May, June and July 1883, according to data got out by Lüdeling. As shown by the arrows, fig. 10 (quiet days) is in the main described in the normal or clockwise direction, but fig. 9 (all days) is described in the opposite direction. Lüdeling found this peculiar difference between all and quiet days at all the north polar stations occupied in 1882-1883 except Kingua Fjord, where both diagrams were described clockwise.Fig. 9.Fig. 10.In temperate latitudes the differences of type are much less, but still they exist. A good idea of their ordinary size and character in the case of declination may be derived from Table XXIX., containing data for Kew, Greenwich and Parc St Maur.The data for Greenwich are due to W. Ellis30, those for Parc St Maur to T. Moureaux33. The quantity tabulated is the algebraic excess of the all or ordinary day mean hourly value over the corresponding quiet day value in the mean diurnal inequality for the year. At Greenwich and Kew days of extreme disturbance have been excluded from the ordinary days, but apparently not at Parc St Maur. The number of highly disturbed days at the three stations is, however, small, and their influence is not great. The differences disclosed by Table XXIX. are obviously of a systematic character, which would not tend to disappear however long a period was utilized. In short, while the diurnal inequality from quiet days may be that most truly representative of undisturbed conditions, it does not represent the average state of conditions at the station. To go into full details respecting the differences between all and quiet days would occupy undue space, so the following brief summary of the differences observed in declination at Kew must suffice. While the inequality range is but little different for the two types of days, the mean of the hourly differences from the mean for the day is considerably reduced in the quiet days. The 24-hour term in the Fourier analysis is of smaller amplitude in the quiet days, and its phase angle is on the average about 6°.75 smaller than on ordinary days, implying a retardation of about 27 minutes in the time of maximum. The diurnal inequality range is more variable throughout the year in quiet days than on ordinary days, and the same is true of the absolute ranges. The tendency to a secondary minimum in the range at midsummer is considerably more decided on ordinary than on quiet days. When the variation throughout the year in the diurnal inequality range is expressed in Fourier series, whose periods are the year and its submultiples, the 6-month term is notably larger for ordinary than for quiet days. Also the date of the maximum in the 12-month term is about three days earlier for ordinary than for quiet days. The exact size of the differences between ordinary and quiet day phenomena must depend to some extent on the criteria employed in selecting quiet days and in excluding disturbed days. This raises difficulties when it comes to comparing results at different stations. For stations near together the difficulty is trifling. The astronomer royal’s quiet days have been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew, as well as at Greenwich. But when stations are wide apart there are two obvious difficulties: first, the difference of local time; secondly, the fact that a day may be typically quiet at one station but appreciably disturbed at the other.If the typical quiet day were simply the antithesis of a disturbed day, it would be natural to regard the non-cyclic change on quiet days as a species of recoil from some effect of disturbance. This view derives support from the fact, pointed out long ago by Sabine34, that the horizontal force usually, though by no means always, is lowered by magnetic disturbances. Dr van Bemmelen35who has examined non-cyclic phenomena at a number of stations, seems disposed to regard this as a sufficient explanation. There are, however, difficulties in accepting this view. Thus, whilst the non-cyclic effect in horizontal force and inclination at Kew and Falmouth appeared on the whole enhanced in years of sun-spot maximum, the difference between years such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other, was by no means proportional to the excess of disturbance in the former years. Again, when the average non-cyclic change of declination was calculated at Kew for 207 days, selected as those of most marked irregular disturbance between 1890 and 1900, the sign actually proved to be the same as for the average quiet day of the period.Table XXIX.—All or Ordinary, less Quiet Day Hourly Values (+ to the West).Hour.Forenoon.Afternoon.Kew1890-1900.Greenwich1890-1894.Parc St Maur1883-1897.Kew1890-1900.Greenwich1890-1894.Parc St Maur1893-1897.′′′′′′1−0.58−0.59−0.63+0.42+0.44+0.402−0.54−0.47−0.47+0.52+0.45+0.503−0.51−0.31−0.32+0.57+0.52+0.594−0.41−0.23−0.16+0.60+0.51+0.555−0.28−0.10−0.01+0.46+0.34+0.386−0.08+0.12+0.18+0.21+0.04+0.077+0.13+0.30+0.34−0.06−0.24−0.258+0.29+0.48+0.47−0.27−0.50−0.549+0.40+0.56+0.53−0.47−0.68−0.7410+0.44+0.58+0.51−0.61−0.78−0.7911+0.48+0.50+0.44−0.62−0.77−0.7912+0.45+0.44+0.38−0.54−0.61−0.67§ 31. A satisfactory definition of magnetic disturbance is about as difficult to lay down as one of heterodoxy. The idea in its generality seems to present no difficulty, but it is a very different matter when one comes to details. AmongstMagnetic Disturbances.the chief disturbances recorded since 1890 are those of February 13-14 and August 12, 1892; July 20 and August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903; February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On such days as these the oscillations shown by the magnetic curves are large and rapid, aurora is nearly always visible in temperate latitudes, earth currents are prominent, and there is interruption—sometimes very serious—in the transmission of telegraph messages both in overhead and underground wires. At the other end of the scale are days on which the magnetic curves show practically no movement beyond the slow regular progression of the regular diurnal inequality. But between these two extremes there are an infinite variety of intermediate cases. The first serious attempt at a precise definition of disturbance seems due to General Sabine35a. His method had once an extensive vogue, and still continues to be applied at some important observatories. Sabine regarded a particular observation as disturbed when it differed from the mean of the observations at that hour for the whole month by not less than a certain limiting value. His definition takes account only of the extent of the departure from the mean, whether the curve is smooth at the time or violently oscillating makes no difference. In dealing with a particular station Sabine laid down separate limiting values for each element. These limits were the same, irrespective of the season of the year or of the sun-spot frequency. A departure, for example, of 3′.3 at Kew from the mean value of declination for the hour constituted a disturbance, whether it occurred in December in a year of sun-spot minimum, or in June in a year of sun-spot maximum, though the regular diurnal inequality range might be four times as large in the second case as in the first. The limiting values varied from station to station, the size depending apparently on several considerations not very clearly defined. Sabine subdivided the disturbances in each element into two classes: the one tending to increase the element, the other tending to diminish it. He investigated how the numbers of the two classes varied throughout the day and from month to month. He also took account of the aggregate value of the disturbances of one sign, and traced the diurnal and annual variations in these aggregate values. He thus got two sets of diurnal variations and two sets of annual variations of disturbance, the one set depending only on the number of the disturbed hours, the other set considering only the aggregate value of the disturbances. Generally the two species of disturbance variations were on the whole fairly similar. The aggregates of the + and − disturbances for a particular hour of the day were seldom equal, and thus after the removal of the disturbed values the mean value of the element for that hour was generally altered. Sabine’s complete scheme supposed that after the criterion was first applied, the hourly means would be recalculated from the undisturbed values and the criterion applied again, and that this process would be repeated until the disturbed observations all differed by not less than the accepted limiting value from the final mean based on undisturbed values alone. If the disturbance limit were so small that the disturbed readings formed a considerable fraction of the whole number, the complete execution of Sabine’s scheme would be exceedingly laborious. As a matter of fact, his disturbed readings were usually of the order of 5% of the total number, and unless in the case of exceptionally large magnetic storms it is of little consequence whether the first choice of disturbed readings is accepted as final or is reconsidered in the light of the recalculated hourly means.
Table XXII.—Mean Absolute Daily Ranges (Units 1′ for Declination, 1γ for H and V).
A comparison of the absolute ranges in Table XXII. with the inequality ranges for the same stations derivable from Tables VIII. to X. is most instructive. At Mauritius the ratio of the absolute to the inequality range is for D 1.38, for H 1.76, and for V 1.19. At Pavlovsk the corresponding ratios are much larger, viz. 2.16 for D, 2.43 for H, and 2.05 for V. The declination data for Kew in Table XXII. illustrate other points. The first set of data are derived from all days of the year. The second omit the highly disturbed days. The third answer to the 5 days a month selected as typically quiet. The yearly mean absolute range from ordinary days at Kew in Table XXII. is 1.49 times the mean inequality range in Table VIII.; comparing individual months the ratio of the absolute to the inequality range varies from 2.06 in January to 1.21 in June. Even confining ourselves to the quiet days at Kew, which are free from any but the most trifling disturbances, we find that the mean absolute range for the year is 1.20 times the arithmetic mean of the inequality ranges for the individual months of the year, and 1.22 times the range from the mean diurnal inequality for the year. In this case the ratio of the absolute to the inequality range varies from 1.55 in December to only 1.09 in May.
§ 25. The variability of the absolute daily range of declination is illustrated by Table XXIII., which contains data for Kew24derived from all days of the 11-year period 1890-1900. It gives the total number of times during the 11 years when the absolute range lay within the limits specified at the heads of the first nine columns of figures. The two remaining columns give the arithmetic means of the five largest and the five least absolute ranges encountered each month. The mean of the twelve monthly diurnal inequality ranges from ordinary days was only 8′.44, but the absolute range during the 11 years exceeded 20′ on 492 days, 15′ on 1196 days, and 10′ on 2784 days,i.e.on 69 days out of every 100.
Table XXIII.—Absolute Daily Range of Declination at Kew.
§ 26. Magnetic phenomena, both regular and irregular, at any station vary from year to year. The extent of this variation is illustrated in Tables XXIV. and XXV., both relating to the period 1890 to 1900.25Table XXIV. gives the amplitudes ofRelations to Sun-spot Frequency.the regular diurnal inequality in the elements stated at the head of the columns. The ordinary day declination data (D0) for Kew represent arithmetic means from the twelve months of the year; the other data all answer to the mean diurnal inequality for the whole year. Table XXV. gives the arithmetic means for each year of the absolute daily range, of the monthly range (or difference between the highest and lowest values in the month), and of the yearly range (or difference between the highest and lowest values of the year). The numerals attached to the years in these tables indicate their order as regards sun-spot frequency according to Wolf and Wolfer (see Aurora Polaris), 1893 being the year of largest frequency, and 1890 that of least. The difference in sun-spot frequency between 1897 and 1898 was microscopic; the differences between 1890, 1900 and 1899 were small, and those between 1893, 1894 and 1892 were not very large.
The years 1892-1895 represent high sun-spot frequency, while 1890, 1899 and 1900 represent low frequency. Table XXIV. shows that 1892 to 1895 were in all cases distinguished by the large size of the inequality ranges, and 1890, 1899 and 1900 by the small size. The range in 1893 is usually the largest, and though the H and Vranges at Ekaterinburg are larger in 1892 than in 1893, the excess is trifling. The phenomena apparent in Table XXIV. are fairly representative; other stations and other periods associate large inequality ranges with high sun-spot frequency. The diurnal inequality range it should be noticed is comparatively little influenced by irregular disturbances. Coming to Table XXV., we have ranges of a different character. The absolute range at Kew on quiet days is almost as little influenced by irregularities as is the range of the diurnal inequality, and in its case the phenomena are very similar to those observed in Table XXIV. As we pass from left to right in Table XXV., the influence of disturbance increases. Simultaneously with this, the parallelism with sun-spot frequency is less close. The entries relating to 1892 and 1894 become more and more prominent compared to those for 1893. The yearly range may depend on but a single magnetic storm, the largest disturbance of the year possibly far outstripping any other. But taking even the monthly ranges the values for 1893 are, speaking roughly, only half those for 1892 and 1894, and very similar to those of 1898, though the sun-spot frequency in the latter year was less than a third of that in 1893. Ekatarinburg data exactly analogous to those for Pavlovsk show a similar prominence in 1892 and 1894 as compared to 1893. The retirement of 1893 from first place, seen in the absolute ranges at Kew, Pavlovsk and Ekatarinburg, is not confined to the northern hemisphere. It is visible, for instance, in the amplitudes of the Batavia disturbance results. Thus though the variation from year to year in the amplitude of the absolute ranges is relatively not less but greater than that of the inequality ranges, and though the general tendency is for all ranges to be larger in years of many than in years of few sun-spots, still the parallelism between the changes in sun-spot frequency and in magnetic range is not so close for the absolute ranges and for disturbances as for the inequality ranges.
Table XXIV.—Ranges of Diurnal Inequalities.
Table XXV.—Absolute Ranges.
§ 27. The relationship between magnetic ranges and sun-spot frequency has been investigated in several ways. W. Ellis26has employed a graphical method which has advantages, especially for tracing the general features of the resemblance, and is besides independent of any theoretical hypothesis. Taking time for the axis of abscissae, Ellis drew two curves, one having for its ordinates the sun-spot frequency, the other the inequality range of declination or of horizontal force at Greenwich. The value assigned in the magnetic curve to the ordinate for any particular month represents a mean from 12 months of which it forms a central month, the object being to eliminate the regular annual variation in the diurnal inequality. The sun-spot data derived from Wolf and Wolfer were similarly treated. Ellis originally dealt with the period 1841 to 1877, but subsequently with the period 1878 to 1896, and his second paper gives curves representing the phenomena over the whole 56 years. This period covered five complete sun-spot periods, and the approximate synchronism of the maxima and minima, and the general parallelism of the magnetic and sun-spot changes is patent to the eye. Ellis27has also applied an analogous method to investigate the relationship between sun-spot frequency and the number of days of magnetic disturbance at Greenwich. A decline in the number of the larger magnetic storms near sun-spot minimum is recognizable, but the application of the method is less successful than in the case of the inequality range. Another method, initiated by Professor Wolf of Zurich, lends itself more readily to the investigation of numerical relationships. He started by supposing an exact proportionality between corresponding changes in sun-spot frequency and magnetic range. This is expressed mathematically by the formula
R = a + bS ≡ a {1 + (b/a) S },
where R denotes the magnetic range, S the corresponding sun-spot frequency, while a and b are constants. The constant a represents the range for zero sun-spot frequency, while b/a is the proportional increase in the range accompanying unit rise in sun-spot frequency. Assuming the formula to be true, one obtains from the observed values of R and S numerical values for a and b, and can thus investigate whether or not the sun-spot influence is the same for the different magnetic elements and for different places. Of course, the usefulness of Wolf’s formula depends largely on the accuracy with which it represents the facts. That it must be at least a rough approximation to the truth in the case of the diurnal inequality at Greenwich might be inferred from Ellis’s curves. Several possibilities should be noticed. The formula may apply with high accuracy, a and b having assigned values, for one or two sun-spot cycles, and yet not be applicable to more remote periods. There are only three or four stations which have continuous magnetic records extending even 50 years back, and, owing to temperature correction uncertainties, there is perhaps no single one of these whose earlier records of horizontal and vertical force are above criticism. Declination is less exposed to uncertainty, and there are results of eye observations of declination before the era of photographic curves. A change, however, of 1′ in declination has a significance which alters with the intensity of the horizontal force. During the period 1850-1900 horizontal force in England increased about 5%, so that the force requisite to produce a declination change of 19′ in 1900 would in 1850 have produced a deflection of 20′. It must also be remembered that secular changes of declination must alter the angle between the needle and any disturbing force acting in a fixed direction. Thus secular alteration in a and b is rather to be anticipated, especially in the case of the declination. Wolf’s formula has been applied by Rajna28to the yearly mean diurnal declination ranges at Milan based on readings taken twice daily from 1836 to 1894, treating the whole period together, and then the period 1871 to 1894 separately. During two sub-periods, 1837-1850 and 1854-1867, Rajna’s calculated values for the range differ very persistently in one direction from those observed; Wolf’s formula was applied by C. Chree25to these two periods separately. He also applied it to Greenwich inequality ranges for the years 1841 to 1896 as published by Ellis, treating the whole period and the last 32 years of it separately, and finally to all (a) and quiet (q) day Greenwich ranges from 1889 to 1896. The results of these applications of Wolf’s formula appear in Table XXVI.
The Milan results are suggestive rather of heterogeneity in the material than of any decided secular change inaorb. The Greenwich data are suggestive of a gradual fall ina, and rise inb, at least in the case of the declination.
Table XXVII. gives values ofa,bandb/ain Wolf’s formula calculated by Chree25for a number of stations. There are two sets of data, the first set relating to the range from the mean diurnal inequality for the year, the second to the arithmetic mean of the ranges in the mean diurnal inequalities for the twelve months. It is specified whether the results were derived from all or from quiet days.
Table XXVI.—Values ofaandbin Wolf’s Formula.
As explained above,awould represent the range in a year of no sun-spots, while 100bwould represent the excess over this shown by the range in a year whenWolf’ssun-spot frequency is 100. Thusb/aseems the most natural measure of sun-spot influence. Accepting it, we see that sun-spot influence appears larger at most places for inclination and horizontal force than for declination. In the case of vertical force there is at Pavlovsk, and probably in a less measure at other northern stations, a large difference between all and quiet days, which is not shown in the other elements. The difference between the values ofb/aat different stations is also exceptionally large for vertical force. Whether this last result is wholly free from observational uncertainties is, however, open to some doubt, as the agreement between Wolf’s formula and observation is in general somewhat inferior for vertical force. In the case of the declination, the mean numerical difference between the observed values and those derived from Wolf’s formula, employing the values ofaandbgiven in Table XXVII., represented on the average about 4% of the mean value of the element for the period considered, the probable error representing about 6% of the difference between the highest and lowest values observed. The agreement was nearly, if not quite, as good as this for inclination and horizontal force, but for vertical force the corresponding percentages were nearly twice as large.
Table XXVII.—Values ofaandbin Wolf’s Formula.
Applying Wolf’s formula to the diurnal ranges for different months of the year, Chree found, as was to be anticipated, that the constantahad an annual period, with a conspicuous minimum at midwinter; but whilstbalso varied, it did so to a much less extent, the consequence being thatb/ashowed a minimum at midsummer. The annual variation inb/aalters with the place, with the element, and with the type of day from which the magnetic data are derived. Thus, in the case of Pavlovsk declination, whilst the mean value of 100b/afor the 12 months is, as shown in Table XXVII., 0.66 for all and 0.68 for quiet days—values practically identical—if we take the four midwinter and the four midsummer months separately, we have 100b/a, varying from 0.81 in winter to 0.52 in summer on all days, but from 1.39 in winter to 0.52 in summer on quiet days. In the case of horizontal force at Pavlovsk the corresponding figures to these are for all days—winter 1.77, summer 0.98, but for quiet days—winter 1.83, summer 0.71.
Wolf’s formula has also been applied to the absolute daily ranges, to monthly ranges, and to various measures of disturbance. In these cases the values found forb/aare usually larger than those found for diurnal inequality ranges, but the accordance between observed values and those calculated from Wolf’s formula is less good. If instead of the range of the diurnal inequality we take the sum of the 24-hourly differences from the mean for the day—or, what comes to the same thing, the average departure throughout the 24 hours from the mean value for the day—we find that the resulting Wolf’s formula gives at least as good an agreement with observation as in the case of the inequality range itself. The formulae obtained in the case of the 24 differences, at places as wide apart as Kew and Batavia, agreed in giving a decidedly larger value forb/athan that obtained from the ranges. This indicates that the inequality curve is relatively less peaked in years of many than in years of few sun-spots.
§ 28. The applications of Ellis’s and Wolf’s methods relate directly only to the amplitude of the diurnal changes. There is, however, a change not merely in amplitude but in type. This is clearly seen when we compare the values found in years of many and of few sun-spots for the Fourier coefficients in the diurnal inequality. Such a comparison is carried out in Table XXVIII. for the declination on ordinary days at Kew. Local mean time is used. The heading S max. (sun-spot maximum) denotes mean average results from the four years 1892-1895, having a mean sun-spot frequency of 75.0, whilst S min. (sun-spot minimum) applies similarly to the years 1890, 1899 and 1900, having a mean sun-spot frequency of only 9.6. The data relate to the mean diurnal inequality for the whole year or for the season stated. It will be seen that the difference between the c, or amplitude, coefficients in the S max. and S min. years is greater for the 24-hour term than for the 12-hour term, greater for the 12-hour than for the 8-hour term, and hardly apparent in the 6-hour term. Also,relatively considered, the difference between the amplitudes in S max. and S min. years is greatest in winter and least in summer. Except in the case of the 6-hour term, where the differences are uncertain, the phase angle is larger,i.e.maxima and minima occur earlier in the day, in years of S min. than in years of S max. Taking the results for the whole year in Table XXVIII., this advance of phase in the S min. years represents in time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour term, and 14.7 minutes for the 8-hour term. The difference in the phase angles, as in the amplitudes, is greatest in winter. Similar phenomena are shown by the horizontal force, and at Falmouth24as well as Kew.
Table XXVIII.—Fourier Coefficients in Years of many and few Sun-spots.
§ 29. There have already been references toquietdays, for instance in the tables of diurnal inequalities. It seems to have been originally supposed that quiet days differed from other days onlyQuiet Day Phenomena.in the absence of irregular disturbances, and that mean annual values, or secular change data, or diurnal inequalities, derived from them might be regarded as truly normal or representative of the station. It was found, however, by P. A. Müller29that mean annual values of the magnetic elements at St Petersburg and Pavlovsk from 1873 to 1885 derived from quiet days alone differed in a systematic fashion from those derived from all days, and analogous results were obtained by Ellis30at Greenwich for the period 1889-1896. The average excesses for the quiet-day over the all-day means in these two cases were as follows:—
The sign of the difference in the case of D, I and H was the same in each year examined by Müller, and the same was true of H at Greenwich. In the case of V, and of D at Greenwich, the differences aresmall and might be accidental. In the case of D at Greenwich 1891 differed from the other years, and of two more recent years examined by Ellis31one, 1904, agreed with 1891. At Kew, on the average of the 11 years 1890 to 1900, the quiet-day mean annual value of declination exceeded the ordinary day value, but the apparent excess 0′.02 is too small to possess much significance.
Another property more recently discovered in quiet days is the non-cyclic change. The nature of this phenomenon will be readilyNon-cyclic Change.understood from the following data from the 11-year period 1890 to 1900 at Kew32. The mean daily change for all days is calculated from the observed annual change.
Thus the changes during the representative quiet day differed from those of the average day. Before accepting such a phenomenon as natural, instrumental peculiarities must be carefully considered. The secular change is really based on the absolute instruments, the diurnal changes on the magnetographs, and the first idea likely to occur to a critical mind is that the apparent abnormal change on quiet days represents in reality change of zero in the magnetographs. If, however, the phenomenon were instrumental, it should appear equally on days other than quiet days, and we should thus have a shift of zero amounting in a year to over 1,200γ in H, and to about 90′ in I. Under such circumstances the curve would be continually drifting off the sheet. In the case of the Kew magnetographs, a careful investigation showed that if any instrumental change occurred in the declination magnetograph during the 11 years it did not exceed a few tenths of a minute. In the case of the H and V magnetographs at Kew there is a slight drift, of instrumental origin, due to weakening of the magnets, but it is exceedingly small, and in the case of H is in the opposite direction to the non-cyclic change on quiet days. It only remains to add that the hypothesis of instrumental origin was positively disproved by measurement of the curves on ordinary days.
It must not be supposed that every quiet day agrees with the average quiet day in the order of magnitude, or even in the sign, of the non-cyclic change. In fact, in not a few months the sign of the non-cyclic change on the mean of the quiet days differs from that obtained for the average quiet day of a period of years. At Kew, between 1890 and 1900, the number of months during which the mean non-cyclic change for the five quiet days selected by the astronomer royal (Sir W. H. M. Christie) was plus, zero, or minus, was as follows:—
The + sign denotes westerly movement in the declination, and increasing dip of the north end of the needle. In the case of I and H the excess in the number of months showing the normal sign is overwhelming. The following mean non-cyclic changes on quiet days are from other sources:—
The results are in the same direction as at Kew, + meaning in the case of D movement to the west. At Falmouth32, as at Kew, the non-cyclic change showed a tendency to be small in years of few sun-spots.
§ 30. In calculating diurnal inequalities from quiet days the non-cyclic effect must be eliminated, otherwise the result would depend on the hour at which the “day” is supposed to commence. If the value recorded at the second midnight of the average day exceeds that at the first midnight by N, the elimination is effected by applying to each hourly value the correction N(12 − n)/24, where n is the hour counted from the first midnight (0 hours). This assumes the change to progress uniformly throughout the 24 hours. Unless this is practically the case—a matter difficult either to prove or disprove—the correction may not secure exactly what is aimed at. This method has been employed in the previous tables. The fact that differences do exist between diurnal inequalities derived from quiet days and all ordinary days was stated explicitly in § 4, and is obvious in Tables VIII. to XI. An extreme case is represented by the data for Jan Mayen in these tables. Figs. 9 and 10 are vector diagrams for this station, for all and for quiet days during May, June and July 1883, according to data got out by Lüdeling. As shown by the arrows, fig. 10 (quiet days) is in the main described in the normal or clockwise direction, but fig. 9 (all days) is described in the opposite direction. Lüdeling found this peculiar difference between all and quiet days at all the north polar stations occupied in 1882-1883 except Kingua Fjord, where both diagrams were described clockwise.
In temperate latitudes the differences of type are much less, but still they exist. A good idea of their ordinary size and character in the case of declination may be derived from Table XXIX., containing data for Kew, Greenwich and Parc St Maur.
The data for Greenwich are due to W. Ellis30, those for Parc St Maur to T. Moureaux33. The quantity tabulated is the algebraic excess of the all or ordinary day mean hourly value over the corresponding quiet day value in the mean diurnal inequality for the year. At Greenwich and Kew days of extreme disturbance have been excluded from the ordinary days, but apparently not at Parc St Maur. The number of highly disturbed days at the three stations is, however, small, and their influence is not great. The differences disclosed by Table XXIX. are obviously of a systematic character, which would not tend to disappear however long a period was utilized. In short, while the diurnal inequality from quiet days may be that most truly representative of undisturbed conditions, it does not represent the average state of conditions at the station. To go into full details respecting the differences between all and quiet days would occupy undue space, so the following brief summary of the differences observed in declination at Kew must suffice. While the inequality range is but little different for the two types of days, the mean of the hourly differences from the mean for the day is considerably reduced in the quiet days. The 24-hour term in the Fourier analysis is of smaller amplitude in the quiet days, and its phase angle is on the average about 6°.75 smaller than on ordinary days, implying a retardation of about 27 minutes in the time of maximum. The diurnal inequality range is more variable throughout the year in quiet days than on ordinary days, and the same is true of the absolute ranges. The tendency to a secondary minimum in the range at midsummer is considerably more decided on ordinary than on quiet days. When the variation throughout the year in the diurnal inequality range is expressed in Fourier series, whose periods are the year and its submultiples, the 6-month term is notably larger for ordinary than for quiet days. Also the date of the maximum in the 12-month term is about three days earlier for ordinary than for quiet days. The exact size of the differences between ordinary and quiet day phenomena must depend to some extent on the criteria employed in selecting quiet days and in excluding disturbed days. This raises difficulties when it comes to comparing results at different stations. For stations near together the difficulty is trifling. The astronomer royal’s quiet days have been used for instance at Parc St. Maur, Val Joyeux, Falmouth and Kew, as well as at Greenwich. But when stations are wide apart there are two obvious difficulties: first, the difference of local time; secondly, the fact that a day may be typically quiet at one station but appreciably disturbed at the other.
If the typical quiet day were simply the antithesis of a disturbed day, it would be natural to regard the non-cyclic change on quiet days as a species of recoil from some effect of disturbance. This view derives support from the fact, pointed out long ago by Sabine34, that the horizontal force usually, though by no means always, is lowered by magnetic disturbances. Dr van Bemmelen35who has examined non-cyclic phenomena at a number of stations, seems disposed to regard this as a sufficient explanation. There are, however, difficulties in accepting this view. Thus, whilst the non-cyclic effect in horizontal force and inclination at Kew and Falmouth appeared on the whole enhanced in years of sun-spot maximum, the difference between years such as 1892 and 1894 on the one hand, and 1890 and 1900 on the other, was by no means proportional to the excess of disturbance in the former years. Again, when the average non-cyclic change of declination was calculated at Kew for 207 days, selected as those of most marked irregular disturbance between 1890 and 1900, the sign actually proved to be the same as for the average quiet day of the period.
Table XXIX.—All or Ordinary, less Quiet Day Hourly Values (+ to the West).
§ 31. A satisfactory definition of magnetic disturbance is about as difficult to lay down as one of heterodoxy. The idea in its generality seems to present no difficulty, but it is a very different matter when one comes to details. AmongstMagnetic Disturbances.the chief disturbances recorded since 1890 are those of February 13-14 and August 12, 1892; July 20 and August 20, 1894; March 15-16, and September 9, 1898; October 31, 1903; February 9-10, 1907; September 11-12, 1908 and September 25, 1909. On such days as these the oscillations shown by the magnetic curves are large and rapid, aurora is nearly always visible in temperate latitudes, earth currents are prominent, and there is interruption—sometimes very serious—in the transmission of telegraph messages both in overhead and underground wires. At the other end of the scale are days on which the magnetic curves show practically no movement beyond the slow regular progression of the regular diurnal inequality. But between these two extremes there are an infinite variety of intermediate cases. The first serious attempt at a precise definition of disturbance seems due to General Sabine35a. His method had once an extensive vogue, and still continues to be applied at some important observatories. Sabine regarded a particular observation as disturbed when it differed from the mean of the observations at that hour for the whole month by not less than a certain limiting value. His definition takes account only of the extent of the departure from the mean, whether the curve is smooth at the time or violently oscillating makes no difference. In dealing with a particular station Sabine laid down separate limiting values for each element. These limits were the same, irrespective of the season of the year or of the sun-spot frequency. A departure, for example, of 3′.3 at Kew from the mean value of declination for the hour constituted a disturbance, whether it occurred in December in a year of sun-spot minimum, or in June in a year of sun-spot maximum, though the regular diurnal inequality range might be four times as large in the second case as in the first. The limiting values varied from station to station, the size depending apparently on several considerations not very clearly defined. Sabine subdivided the disturbances in each element into two classes: the one tending to increase the element, the other tending to diminish it. He investigated how the numbers of the two classes varied throughout the day and from month to month. He also took account of the aggregate value of the disturbances of one sign, and traced the diurnal and annual variations in these aggregate values. He thus got two sets of diurnal variations and two sets of annual variations of disturbance, the one set depending only on the number of the disturbed hours, the other set considering only the aggregate value of the disturbances. Generally the two species of disturbance variations were on the whole fairly similar. The aggregates of the + and − disturbances for a particular hour of the day were seldom equal, and thus after the removal of the disturbed values the mean value of the element for that hour was generally altered. Sabine’s complete scheme supposed that after the criterion was first applied, the hourly means would be recalculated from the undisturbed values and the criterion applied again, and that this process would be repeated until the disturbed observations all differed by not less than the accepted limiting value from the final mean based on undisturbed values alone. If the disturbance limit were so small that the disturbed readings formed a considerable fraction of the whole number, the complete execution of Sabine’s scheme would be exceedingly laborious. As a matter of fact, his disturbed readings were usually of the order of 5% of the total number, and unless in the case of exceptionally large magnetic storms it is of little consequence whether the first choice of disturbed readings is accepted as final or is reconsidered in the light of the recalculated hourly means.