Sabine applied his method to the data obtained during the decade 1840 to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C. Chambers36applied it to data from Bombay. The yearly publication of the Batavia observatory gives corresponding results for that station, and Th. Moureaux33has published similar data for Parc St Maur. Tables XXX. to XXXII. are based on a selection of these data. Tables XXX. and XXXI. show the annual variation in Sabine’s disturbances, the monthly values being expressed as percentages of the arithmetic mean value for the 12 months. The Parc St Maur and Batavia data, owing to the long periods included, are especially noteworthy. Table XXX. deals with the east (E) and west (W) disturbances of declination separately. Table XXXI., dealing with disturbances in horizontal and vertical force, combines the + and − disturbances, treated numerically. At Parc St Maur the limits required to qualify for disturbance were 3′.0 in D, 20γ in H, and 12γ in V; the corresponding limits for Batavia were 1′.3, 11γ and 11γ. The limits for D at Toronto, Bombay and Hobart were respectively 3′.6, 1′.4 and 2′.4.At Parc St Maur the disturbance data from all three elements give distinct maxima near the equinoxes; a minimum at midwinter is clearly shown, and also one at midsummer, at least in D and H. A decline in disturbance at midwinter is visible at all the stations, but at Batavia the equinoctial values for D and V are inferior to those at midsummer.Table XXX.—Annual Variation of Disturbances (Sabine’s numbers).Parc St Maur1883-97.Toronto1841-48.Bombay1859-65.Batavia1883-99.Hobart1843-48.Month.E.W.E.W.E.W.E.W.E.W.January786055668989180223165182February1169275869467138144121116March12610792941299710287114104April1051131151141061296773110102May101118101101639972716253June77899572788145273237July8210414012612117362465049August8811313713315413169698678September134137163139111108135144135114October1191151011111401289588124123November9994738543431069179111December755851727255124137123130Table XXXII. shows in some cases a most conspicuous diurnal variation in Sabine’s disturbances. The data are percentages of the totals for the whole 24 hours. But whilst at Batavia the easterly and westerly disturbances in D vary similarly, at Parc St Maur they follow opposite laws, the easterly showing a prominent maximum near noon, the westerly a still more prominent maximum near midnight. The figures in the second last line of the table, if divided by 0.24, will give the percentage of hours which show the species of disturbance indicated. For instance, at Parc St Maur, out of 100 hours, 3 show disturbances to the west and 3.7 to the east; or in all 6.7 show disturbances of declination. The last line gives the average size of a disturbance of each type, the unit being 1′ in D and 1γ in H and V.Table XXXI.—Annual Variation of Disturbances.Parc St Maur.Toronto.Batavia.Month.Numbers.Aggregates.Numbers.Aggregates.H.V.H.V.H.V.H.V.January815158569615189154February961339474105123110125March12611894108116105117103April941111501491047610573May108133901121019210595June9085365082697966July99128617190839581August113927510891919891September119122171160113111114115October101941481291148910486November10481987599102100101December70511281008910884110At Batavia disturbances increasing and decreasing the element are about equally numerous, but this is exceptional. Easterly disturbances of declination predominated at Toronto, Point Barrow, Fort Kennedy, Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and Parc St Maur the ratios borne by theeastern to the western disturbances were 1.19 and 1.23 respectively, and so not much in excess of unity; but the preponderance of easterly disturbances at the North American37stations was considerably larger than this.Table XXXII.—Diurnal Variation of Disturbances (Sabine’s numbers).Hour.Parc St Maur.Batavia.D.H.V.D.H.V.E.W.+−+−E.W.+−+−0-310.120.39.08.35.79.21.15.813.16.64.07.43-612.38.28.48.06.410.47.67.314.24.86.310.06-915.73.814.112.57.29.024.916.812.19.921.221.79-noon16.25.118.015.612.915.438.533.08.615.819.816.4noon-319.36.715.316.518.218.318.824.716.821.123.522.13-614.89.712.515.422.921.86.45.413.316.912.612.76-95.721.211.413.218.911.22.33.49.913.67.14.19-125.925.011.210.57.84.70.43.812.011.15.65.4Mean numberper day0.880.721.151.561.040.960.460.441.621.611.191.13Mean size· ·· ·· ·· ·· ·· ·1.721.6918.019.516.715.5§ 32. From the point of view of the surveyor there is a good deal to be said for Sabine’s definition of disturbance, but it is less satisfactory from other standpoints. One objection has been already indicated, viz. the arbitrariness of applying the same limiting value at a station irrespective of the size of the normal diurnal range at the time. Similarly it is arbitrary to apply the same limit between 10 a.m. and noon, when the regular diurnal variation is most rapid, as between 10 p.m. and midnight, when it is hardly appreciable. There seems a distinct difference of phase between the diurnal inequalities on different types of days at the same season; also the phase angles in the Fourier terms vary continuously throughout the year, and much more rapidly at some stations and at some seasons than at others. Thus there may be a variety of phenomena which one would hesitate to regard as disturbances which contribute to the annual and diurnal variations in Tables XXX. to XXXII.Sabine, as we have seen, confined his attention to the departure of the hourly reading from the mean for that hour. Another and equally natural criterion is the apparent character of the magnetograph curve. At Potsdam curves are regarded as “1” quiet, “2” moderately disturbed, or “3” highly disturbed. Any hourly value to which the numeral 3 is attached is treated as disturbed, and the annual Potsdam publication contains tables giving the annual and diurnal variations in the number of such disturbed hours for D, H and V. According to this point of view, the extent to which the hourly value departs from the mean for that hour is immaterial to the results. It is the greater or less sinuosity and irregularity of the curve that counts. Tables XXXIII. and XXXIV. give an abstract of the mean Potsdam results from 1892 to 1901. The data are percentages: in Table XXXIII. of the mean monthly total, in Table XXXIV. of the total for the day. So far as the annual variation is concerned, the results in Table XXXIII. are fairly similar to those in Table XXX. for Parc St Maur. There are pronounced maxima near the equinoxes, especially the spring equinox. The diurnal variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus in the case of H the largest disturbance numbers at Parc St Maur occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur between 4 p.m. and midnight. Considering the comparative proximity of Parc St Maur and Potsdam, one must conclude that the apparent differences between the results for these two stations are due almost entirely to the difference in the definition of disturbance.Table XXXIII.—Annual Variation of Potsdam Disturbances.Element.Jan.Feb.Mar.April.May.June.July.Aug.Sept.Oct.Nov.Dec.D1291701499086576264591189482H109133131102109829491891017584V10617117010812156647493877870Mean115158150100105657376941028279Table XXXIV.—Diurnal Variation of Potsdam Disturbances.Hours.1-3.4-6.7-9.10-noon.1-3.4-6.7-9.10-12.D14.911.18.05.25.713.122.519.5H10.58.48.08.511.317.619.216.5V13.59.75.74.78.517.221.519.2Mean13.09.77.26.18.516.021.118.4Table XXXV.—Disturbed Day less ordinary Day Inequality (Unit 1′, + to West).Hour.123456789101112a.m.−3.4−2.6−2.0−0.3+1.6+1.9+2.3+2.0+2.1+2.0+1.6+1.8p.m.+1.8+2.2+2.1+1.7+1.40.0−1.3−2.8−3.5−2.6−3.5−2.4One difficulty in the Potsdam procedure is the maintenance of a uniform standard. Unless very frequent reference is made to the curves of some standard year there must be a tendency to enter under “3” in quiet years a number of hours which would be entered under “2” in a highly disturbed year. Still, such a source of uncertainty is unlikely to have much influence on the diurnal, or even on the annual, variation.§ 33. A third method of investigating a diurnal period in disturbances is to form a diurnal inequality from disturbed days alone, and compare it with the corresponding inequalities from ordinary or from quiet days. Table XXXV. gives some declination data for Kew, the quantity tabulated being the algebraic excess of the disturbed day hourly value over that for the ordinary day in the mean diurnal inequality for the year, as based on the 11 years 1890 to 1900.Fig. 11.The disturbed day inequality was corrected for non-cyclic change in the usual way. Fig. 11 shows the results of Table XXXV. graphically. The irregularities are presumably due to the limited number, 209, of disturbed days employed; to get a smooth curve would require probably a considerably longer period of years. The differences between disturbed and ordinary days at Kew are of the same general character as those between ordinary and quiet days in Table XXIX.; they are, however, very much larger, the range in Table XXXV. being fully 5½ times that in Table XXIX. If quiet days had replaced ordinary days in Table XXXV., the algebraic excess of the disturbed day would have varied from +2′.7 at 2 p.m. to −4′.1 at 11 p.m., or a range of 6′.8.§ 34. When the mean diurnal inequality in declination for the year at Kew is analysed into Fourier waves, the chief difference, it will be remembered, between ordinary and quiet days was that the amplitude of the 24-hour term was enhanced in the ordinary days, whilst its phase angle indicated an earlier occurrence of the maximum. Similarly, the chief difference between the Fourier waves for the disturbed and ordinary day inequalities at Kew is the increase in the amplitude of the 24-hour term in the former by over 70%, and the earlier occurrence of its maximum by about 1 hour 50 minutes. It is clear from these results for Kew, and it is also a necessary inference from the differences obtained by Sabine’s method between east and west or + and − disturbances, that there is present during disturbances some influence which affects the diurnal inequality in a regular systematic way, tending to make the value of the element higher during some hours and lower during others than it is on days relatively free from disturbance. At Kew the consequence is a notable increase in the range of the regular diurnal inequality on disturbed days; but whether this is the general rule or merely a local peculiarity is a subject for further research.§ 35. There are still other ways of attacking the problem of disturbances. W. Ellis27made a complete list of disturbed days at Greenwich from 1848 onwards, arranging them in classes according to the amplitude of the disturbance shown on the curves. Of the 18,000 days which he considered, Ellis regarded 2,119, or only about 12%, as undisturbed. On 11,898 days, or 66%, the disturbance movement in declination was under 10′; on 3614, or 20%, the disturbance, though exceeding 10′, was under 30′; on 294 days it laybetween 30′ and 60′; while on 75 days it exceeded 60′. Taking each class of disturbances separately, Ellis found, except in the case of his “minor” disturbances—those under 10′—a distinct double annual period, with maxima towards the equinoxes. Subsequently C. W. Maunder,38making use of these same data, and of subsequent data up to 1902, put at his disposal by Ellis, came to similar conclusions. Taking all the days with disturbances of declination over 10′, and dealing with 15-day periods, he found the maxima of frequency to occur the one a little before the spring equinox, the other apparently after the autumnal equinox; the two minima were found to occur early in June and in January. When the year is divided into three seasons—winter (November to February), summer (May to August), and equinox—Maunder’s figures lead to the results assigned to Greenwich disturbed days in Table XXXVI. The frequency in winter, it will be noticed, though less than at equinox, is considerably greater than in summer. This greater frequency in winter is only slightly apparent in the disturbances over 60′, but their number is so small that this may be accidental. The next figures in Table XXXVI. relate to highly disturbed days at Kew. The larger relative frequency at Kew in winter as compared to summer probably indicates no real difference from Greenwich, but is simply a matter of definition. The chief criterion at Kew for classifying the days was not so much the mere amplitude of the largest movement, as the general character of the day’s curve and its departure from the normal form. The data in Table XXXVI. as to magnetic storms at Greenwich are based on the lists given by Maunder39in theMonthly Notices, R.A.S. A storm may last for any time from a few hours to several days, and during part of its duration the disturbance may not be very large; thus it does not necessarily follow that the frequencies of magnetic storms and of disturbed days will follow the same laws. The table shows, however, that so far as Greenwich is concerned the annual variations in the two cases are closely alike. In addition to mean data for the whole 56 years, 1848 to 1903, Table XXXVI. contains separate data for the 14 years of that period which represented the highest sun-spot frequency, and the 15 years which represented lowest sun-spot frequency. It will be seen that relatively considered the seasonal frequencies of disturbance are more nearly equal in the years of many than in those of few sun-spots. Storms are more numerous as a whole in the years of many sun-spots, and this preponderance is especially true of storms of the largest size. This requires to be borne in mind in any comparisons between larger and smaller storms selected promiscuously from a long period. An unduly large proportion of the larger storms will probably come from years of large sun-spot frequency, and there is thus a risk of assigning to differences between the laws obeyed by large and small storms phenomena that are due in whole or in part to differences between the laws followed in years of many and of few sun-spots. The last data in Table XXXVI. are based on statistics for Batavia given by W. van Bemmelen,40who considers separately the storms which commence suddenly and those which do not. These sudden movements are recorded over large areas, sometimes probably all over the earth, if not absolutely simultaneously, at least too nearly so for differences in the time of occurrence to be shown by ordinary magnetographs. It is ordinarily supposed that these sudden movements, and the storms to which they serve as precursors, arise from some source extraneous to the earth, and that the commencement of the movement intimates the arrival, probably in the upper atmosphere, of some form of energy transmitted through space. In the storms which commence gradually the existence of a source external to the earth is not so prominently suggested, and it has been sometimes supposed that there is a fundamental difference between the two classes of storms. Table XXXVI. shows, however, no certain difference in the annual variation at Batavia. At the same time, this possesses much less significance than it would have if Batavia were a station like Greenwich, where the annual variation in magnetic storms is conspicuous.Besides the annual period, there seems to be also a well-marked diurnal period in magnetic disturbances. This is apparent in Tables XXXVII. and XXXVIII., which contain some statistics for Batavia due to van Bemmelen, and some for Greenwich derived from the data in Maunder’s papers referred to above. Table XXXVII. gives the relative frequency of occurrence for two hour intervals, starting with midnight, treating separately the storms of gradual (g) and sudden (s) commencement. In Table XXXVIII. the day is subdivided into three equal parts. Batavia and Greenwich agree in showing maximum frequency of beginnings about the time of minimum frequency of endings and conversely; but the hours at which the respective maxima and minima occur at the two places differ rather notably.§ 36. There are peculiarities in the sudden movements ushering in magnetic storms which deserve fuller mention. According to van Bemmelen the impulse consists usually at some stations of a sudden slight jerk of the magnet in one direction, followed by a larger decided movement in the opposite direction, the former being often indistinctly shown. Often we have at the very commencement but a faint outline, and thereafter a continuous movement which is only sometimes distinctly indicated, resulting after some minutes in the displacement of the trace by a finite amount from the position it occupied on the paper before the disturbance began. This may mean, as van Bemmelen supposes, a small preliminary movement in the opposite direction to the clearly shown displacement; but it may only mean that the magnet is initially set in vibration, swinging on both sides of the position of equilibrium, the real displacement of the equilibrium position being all the time in the direction of the displacement apparent after a few minutes. To prevent misconception, the direction of the displacement apparent after a few minutes has been termed the direction of the firstdecidedmovement in Table XXXIX., which contains some data as to the direction given by Ellis41and van Bemmelen.40The + sign means an increase, the − sign a decrease of the element. The sign is not invariably the same, it will be understood, but there are in all cases a marked preponderance of changes in the direction shown in the table. The fact that all the stations indicated an increase in horizontal force is of special significance.Table XXXVI.—Disturbances, and their Annual Distribution.TotalNumber.Percentages.Winter.Equinox.Summer.Greenwich disturbed days, all, 1848-19024,21433.939.226.9Greenwich disturbed days, range 10′ to 30′, 1848-19023,83033.939.027.1Greenwich disturbed days range 30′ to 60′, 1848-190230734.541.024.4Greenwich disturbed days, range over 60′, 1848-19027729.941.628.6Kew highly disturbed days, 1890-190020938.341.620.1Greenwich magnetic storms, all, 1848-190372632.142.325.6Greenwich magnetic storms, range 20′ to 30′, 1848-190339230.143.626.3Greenwich magnetic storms, range over 30′, 1848-190333434.440.724.9Greenwich magnetic storms, all, 14 years of S. max.25835.338.026.7Greenwich magnetic storms, all, 15 years of S. min.12728.448.023.6Batavia magnetic storms, all, 1883-18991,00832.934.932.2Batavia magnetic storms of gradual commencement67932.434.832.8Batavia magnetic storms of sudden commencement32933.735.331.0Table XXXVII.—Batavia Magnetic Storms, Diurnal Distribution (percentages).Hour.0246810121416182022Beginningg55562016756988s7571010111088987Maximumg1210654996661215s1475229958101316Endall1516191353654545Table XXXVIII.—Greenwich Magnetic Storms, Diurnal Distribution.Epoch.Class.TotalNumber.Percentages.1-8 p.m.9 p.m.-4 a.m.5 a.m.-noon.Beginning1848-1903all72160.121.918.01882-1903”27658.018.823.21882-1903sudden7745.427.327.3End1848-1903all7209.444.646.01882-1903”2767.241.751.11882-1903sudden7711.735.153.2§ 37. That large magnetic disturbances occur simultaneously over large areas was known in the time of Gauss, on whose initiative observations were taken at 5-minute intervals at a number of stationson prearrangedterm days. During March 1879 and August 1880 some large magnetic storms occurred, and the magnetic curves showing these at a number of stations fitted with Kew pattern magnetographs were compared by W. G. Adams.42He found the more characteristic movements to be, so far as could be judged, simultaneous at all the stations. At comparatively near stations such as Stonyhurst and Kew, or Coimbra and Lisbon, the curves were in general almost duplicates. At Kew and St Petersburg there were usually considerable differences in detail, and the movements were occasionally in opposite directions. The differences between Toronto, Melbourne or Zi-ka-wei and the European stations were still more pronounced. In 1896, on the initiative of M. Eschenhagen,43eye observations of declination and horizontal force were taken at 5-second intervals during prearranged hours at Batavia, Manila, Melbourne and nine European stations. The data from one of these occasions when appreciable disturbance prevailed were published by Eschenhagen, and were subsequently analysed by Ad. Schmidt.44Taking the stations in western Europe, Schmidt drew several series of lines, each series representing the disturbing forces at one instant of time as deduced from the departure of the elements at the several stations from their undisturbed value. The lines answering to any one instant had a general sameness of direction with more or less divergence or convergence, but their general trend varied in a way which suggested to Schmidt the passage of a species of vortex with large but finite velocity.Table XXXIX.—Direction of First Decided Movement.Place.Declination.Horizontal Force.Vertical Force.PavlovskWest++PotsdamWest+−GreenwichWest++Zi-ka-weiEast+−KolabaEast+−BataviaWest+−MauritiusEast++Cape HornWest+−The conclusion that magnetic disturbances tend to follow one another at nearly equal intervals of time has been reached by several independent observers. J. A. Broun45pronounced for a period of about 26 days, and expressed a belief that a certain zone, or zones, of the sun’s surface might exert a prepotent influence on the earth’s magnetism during several solar rotations. Very similar views were advanced in 1904 by E. W. Maunder,39who was wholly unaware of Broun’s work. Maunder concluded that the period was 27.28 days, coinciding with the sun’s rotation period relative to an observer on the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he found the interval between the commencement of successive storms to approach closely to the above period in a considerably larger number of instances than one would have expected from mere chance. He found several successions of three or four storms, and in one instance of as many as six storms, showing his interval. In a later paper Maunder reached similar results for magnetic storms at Greenwich from 1848 to 1881. Somewhat earlier than Maunder, Arthur Harvey46deduced a period of 27.246 days from a consideration of magnetic disturbances at Toronto. A. Schuster,47examining Maunder’s data mathematically, concluded that they afforded rather strong evidence of a period of about ½ (27.28) or 13.6 days. Maunder regarded his results asdemonstratingthat magnetic disturbances originate in the sun. He regarded the solar action as arising from active areas of limited extent on the sun’s surface, and as propagated along narrow, well defined streams. The active areas he believed to be also the seats of the formation of sun-spots, but believed that their activity might precede and outlive the visible existence of the sun-spot.Maunder did not discuss the physical nature of the phenomenon, but his views are at least analogous to those propounded somewhat earlier by Svante Arrhenius,48who suggested that small negatively charged particles are driven from the sun by the repulsion of light and reach the earth’s atmosphere, setting up electrical currents, manifest in aurora and magnetic disturbances. Arrhenius’s calculations, for the size of particle which he regarded as most probable, make the time of transmission to the earth slightly under two days. Amongst other theories which ascribe magnetic storms to direct solar action may be mentioned that of Kr. Birkeland,49who believes the vehicle to be cathode rays. Ch. Nordmann50similarly has suggested Röntgen rays. Supposing the sun the ultimate source, it would be easier to discriminate between the theories if the exact time of the originating occurrence could be fixed. For instance, a disturbance that is propagated with the velocity of light may be due to Röntgen rays, but not to Arrhenius’s particles. In support of his theory, Nordmann mentions several cases when conspicuous visual phenomena on the sun have synchronized with magnetic movements on the earth—the best known instance being the apparent coincidence in time of a magnetic disturbance at Kew on the 1st of September 1859 with a remarkable solar outburst seen by R. C. Carrington. Presumably any electrical phenomenon on the sun will set up waves in the aether, so transmission of electric and magnetic disturbances from the sun to the earth with the velocity of light is a certainty rather than a hypothesis; but it by no means follows that the energy thus transmitted can give rise to sensible magnetic disturbances. Also, when considering Nordmann’s coincidences, it must be remembered that magnetic movements are so numerous that it would be singular if no apparent coincidences had been noticed. Another consideration is that the movements shown by ordinary magnetographs are seldom very rapid. During some storms, especially those accompanied by unusually bright and rapidly varying auroral displays, large to and fro movements follow one another in close succession, the changes being sometimes too quick to be registered distinctly on the photographic paper. This, however, is exceptional, even in polar regions where disturbances are largest and most numerous. As a rule, even when the change in the direction of movement in the declination needle seems quite sudden, the movement in one direction usually lasts for several minutes, often for 10, 15 or 30 minutes. Thus the cause to which magnetic disturbances are due seems in many cases to be persistent in one direction for a considerable time.§ 38. Attempts have been made to discriminate between the theories as to magnetic storms by a critical examination of the phenomena. A general connexion between sun-spot frequency and the amplitude of magnetic movements, regular and irregular, is generally admitted. If it is a case of cause and effect, and the interval between the solar and terrestrial phenomena does not exceed a few hours, then there should be a sensible connexion between corresponding daily values of the sun-spot frequency and the magnetic range. Even if only some sun-spots are effective, we should expect when we select from a series of years two groups of days, the one containing the days of most sun-spots, the other the days of least, that a prominent difference will exist between the mean values of the absolute daily magnetic ranges for the two groups. Conversely, if we take out the days of small and the days of large magnetic range, or the days that are conspicuously quiet and those that are highly disturbed, we should expect a prominent difference between the corresponding mean sun-spot areas. An application of this principle was made by Chree23to the five quiet days a month selected by the astronomer royal between 1890 and 1900. These days are very quiet relative to the average day and possess a much smaller absolute range. One would thus have expected on Birkeland’s or Nordmann’s theory the mean sun-spot frequency derived from Wolfer’s provisional values for these days to be much below his mean value, 41.22, for the eleven years. It proved, however, to be 41.28. This practical identity was as visible in 1892 to 1895, the years of sun-spot maximum, as it was in the years of sun-spot minimum. Use was next made of the Greenwichprojectedsun-spot areas, which are the result of exact measurement. The days of each month were divided into three groups, the first and third—each normally of ten days—containing respectively the days of largest and the days of least sun-spot area. The mean sun-spot area from group 1 was on the average about five times that for group 3. It was then investigated how the astronomer royal’s quiet days from 1890 to 1900, and how the most disturbed days of the period selected from the Kew24magnetic records, distributed themselves among the three groups of days. Nineteen months were excluded, as containing more than ten days with no sun-spots. The remaining 113 months contained 565 quiet and 191 highly disturbed days, whose distribution was as follows:Group 1.Group 2.Group 3.Quiet days179195191Disturbed days686558The group of days of largest sun-spot area thus contained slightly under their share of quiet days and slightly over their share of disturbed days. The differences, however, are not large, and in three years, viz. 1895, 1897 and 1899, the largest number of disturbed days actually occurred in group 3, while in 1895, 1896 and 1899 there were fewer quiet days in group 3 than in group 1. Taking the same distribution of days, the mean value of the absolute daily range of declination at Kew was calculated for the group 1 and the group 3 days of each month. The mean range from the group 1 days was the larger in 57% of the individual months as against 43% in which it was the smaller. When the days of each month were divided into groups according to the absolute declination range at Kew, the mean sun-spot area for the group 1 days (those of largest range) exceeded that for the group 3 days (those of least range) in 55% of the individual months, as against 45% of cases in which it was the smaller.Taking next the five days of largest and the five days of least range in each month, sun-spot areas were got out not merely for these days themselves, but also for the next subsequent day and the four immediately preceding days in each case. On Arrhenius’s theory we should expect the magnetic range to vary with the sun-spot area, not on the actual day but two days previously. The following figures give the percentage excess or deficiency of the mean sun-spot area for the respective groups of days, relative to the average value for the whole epoch dealt with. n denotes the day to which the magnetic range belongs, n + 1 the day after, n − 1 the day before, andso on. Results are given for 1894 and 1895, the years which were on the whole the most favourable and the least favourable for Arrhenius’s hypothesis, as well as for the whole eleven years.Table XL.Day.n − 4n − 3n − 2n − 1nn + 1Five days oflargest range1894+12+ 9+11+12+11+ 61895−16−17−15−12−11−1011 yrs.+ 9+ 8+ 8+ 7+ 5+ 0.5Five days ofleast range1894−15−17−19−21−21−191895+17+10+ 1− 2− 2− 411 yrs.− 4− 4− 7− 7− 7− 6Taking the 11-year-means we have the sun-spot area practically normal on the day subsequent to the representative day of large magnetic range, but sensibly above its mean on that day and still more so on the four previous days. This suggests an emission from the sun taking a highly variable time to travel to the earth. The 11-year mean data for the five days of least range seem at first sight to point to the same conclusion, but the fact that the deficiency in sun-spot area is practically as prominent on the day after the representative day of small magnetic range as on that day itself, or the previous days, shows that the phenomenon is probably a secondary one. On the whole, taking into account the extraordinary differences between the results from individual years, we seem unable to come to any very positive conclusion, except that in the present state of our knowledge little if any clue is afforded by the extent of the sun’s spotted area on any particular day as to the magnetic conditions on the earth on that or any individual subsequent day. Possibly some more definite information might be extracted by considering the extent of spotted area on different zones of the sun. On theories such as those of Arrhenius or Maunder, effective bombardment of the earth would be more or less confined to spotted areas in the zones nearest the centre of the visible hemisphere, whilst all spots on this hemisphere contribute to the total spotted area. Still theprojectedarea of a spot rapidly diminishes as it approaches the edge of the visible hemisphere,i.e.as it recedes from the most effective position, so that the method employed above gives a preponderating weight to the central zones. One rather noteworthy feature in Table XL. is the tendency to a sequence in the figures in any one row. This seems to be due, at least in large part, to the fact that days of large and days of small sun-spot area tend to occur in groups. The same is true to a certain extent of days of large and days of small magnetic range, but it is unusual for the range to be much above the average for more than 3 or 4 successive days.§ 39. The records from ordinary magnetographs, even when run at the usual rate and with normal sensitiveness, not infrequently show a repetition of regular or nearly regular small rhythmic movements, lasting sometimes for hours. The amplitudePulsations.and period on different occasions both vary widely. Periods of 2 to 4 minutes are the most common. W. van Bemmelen51has made a minute examination of these movements from several years’ traces at Batavia, comparing the results with corresponding statistics sent him from Zi-ka-wei and Kew. Table XLI. shows the diurnal variation in the frequency of occurrence of these small movements—calledpulsationsby van Bemmelen—at these three stations. The Batavia results are from the years 1885 and 1892 to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the years 1897, 1898 and 1900, as given by van Bemmelen, while (ii) answers to the period 1900-1905, as given in the Zi-ka-weiBulletinfor 1905. The Kew data are for 1897. The results are expressed as percentages of the total for the 24 hours. There is a remarkable contrast between Batavia and Zi-ka-wei on the one hand and Kew on the other, pulsations being much more numerous by night than by day at the two former stations, whereas at Kew the exact reverse holds. Van Bemmelen decided that almost all the occasions of pulsation at Zi-ka-wei were also occasions of pulsations at Batavia. The hours of commencement at the two places usually differed a little, occasionally by as much as 20 minutes; but this he ascribed to the fact that the earliest oscillations were too small at one or other of the stations to be visible on the trace. Remarkable coincidence between pulsations at Potsdam and in the north of Norway has been noted by Kr. Birkeland.49With magnetographs of greater sensitiveness and more open time scales, waves of shorter period become visible. In 1882 F. Kohlrausch52detected waves with a period of about 12 seconds. Eschenhagen53observed a great variety of short period waves, 30 seconds being amongst the most common. Some of the records he obtained suggest the superposition of regular sine waves of different periods. Employing a very sensitive galvanometer to record changes of magnetic induction through a coil traversed by the earth’s lines of force, H. Ebert54has observed vibrations whose periods are but a small fraction of a second. The observations of Kohlrausch and Eschenhagen preceded the recent great development of applications of electrical power, while longer period waves are shown in the Kew curves of 50 years ago, so that the existence of natural waves with periods of from a few seconds up to several minutes can hardly be doubted. Whether the much shorter period waves of Ebert are also natural is more open to doubt, as it is becoming exceedingly difficult in civilized countries to escape artificial disturbances.Table XLI.—Diurnal Distribution of Pulsations.Hours.0-3.3-6.6-9.9-Noon.Noon-3.3-6.6-9.9-12.Batavia28926861328Zi-ka-wei (i)33527441035Zi-ka-wei (ii)236811751426Kew4819142218114§ 40. The fact that the moon exerts a small but sensible effect on the earth’s magnetism seems to have been first discovered in 1841 by C. Kreil. Subsequently Sabine55investigated the nature of the lunar diurnal variation in declinationLunar Influence.at Kew, Toronto, Pekin, St Helena, Cape of Good Hope and Hobart. The data in Table XLII. are mostly due to Sabine. They represent the mean lunar diurnal inequality in declination for the whole year. The unit employed is 0′.001, and as in our previous tables + denotes movement to thewest. By “mean departure” is meant the arithmetic mean of the 24 hourly departures from the mean value for the lunar day; the range is the difference between the algebraically greatest and least of the hourly values. Not infrequently the mean departure gives the better idea of the importance of an inequality, especially when as in the present case two maxima and minima occur in the day. This double daily period is unusually prominent in the case of the lunar diurnal inequality, and is seen in the other elements as well as in the declination.Table XLII.—Lunar Diurnal Inequality of Declination (unit 0′.001).LunarHour.Kew.1858-1862.Toronto.1843-1848.Batavia.1883-1899.St Helena.1843-1847.Cape.1842-1846.Hobart.1841-1848.0+103+315−70− 43−148− 981+160+275−63− 5−107−1382+140+158−39+ 37− 35−1423+ 33+ 2− 8+ 70+ 43−1074+ 10−153+38+ 85+108− 455− 67−265+63+ 77+140+ 276−150−302+87+ 48+132+ 887−188−255+77+ 5+ 82+1228−160−137+40− 43+ 5+1209− 78+ 7− 4− 82− 78+ 8210+ 2+178−45−102−143+ 1711+ 92+288−80− 98−177− 5712+160+323−87− 73−165−12013+188+272−68− 32−112−15214+158+148−43+ 13− 30−14715+ 90− 17− 8+ 52+ 58−10516+ 10−180+30+ 73+132− 3517− 85−297+62+ 73+172+ 4518−142−337+72+ 52+168+11219−163−290+68+ 17+122+15220−147−170+52− 25+ 45+15221−123− 7+ 8− 58− 40+11322− 40+155−28− 73−112+ 4723+ 27+265−56− 68−153− 30Mean De-parture105200505410493Range376660174187349304Lunar action has been specially studied in connexion with observations from India and Java. Broun56at Trivandrum and C. Chambers57at Kolaba investigated lunar action from a variety of aspects. At Batavia van der Stok58and more recently S. Figee59have carried out investigations involving an enormous amount of computation. Table XLIII. gives a summary of Figee’s results for the mean lunar diurnal inequality at Batavia, for the two half-yearly periods April to September (Winter or W.), and October to March (S.). The + sign denotes movement to the west in the case of declination, but numerical increase in the case of the other elements. In the case of H and T (total force) the results for the two seasons present comparatively small differences, but in the case of D, I and V the amplitude and phase both differ widely. Consequently a mean lunar diurnal variation derived from all the months of the year gives at Batavia, and presumably at othertropical stations, an inadequate idea of the importance of the lunar influence. In January Figee finds for the range of the lunar diurnal inequality 0′.62 in D, 3.1γ in H and 3.5γ in V, whereas the corresponding ranges in June are only 0′.13, 1.1γ and 2.2γ respectively. The difference between summer and winter is essentially due to solar action, thus the lunar influence on terrestrial magnetism is clearly a somewhat complex phenomenon. From a study of Trivandrum data, Broun concluded that the action of the moon is largely dependent on the solar hour at the time, being on the average about twice as great for a day hour as for a night hour. Figee’s investigations at Batavia point to a similar conclusion. Following a method suggested by Van der Stok, Figee arrives at a numerical estimate of the “lunar activity” for each hour of the solar day, expressed in terms of that at noon taken as 100. In summer, for instance, in the case of D he finds the “activity” varying from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in the case of H are 139 at 10 a.m. and 54 at 6 a.m.Table XLIII.—Lunar Diurnal Inequality at Batavia in Winter and Summer.Declination(unit 0′.001).Inclination, S.(unit 0′.001).H.(unit 0.01γ).V.(unit 0.01γ).T.(unit0.01γ).LunarHour.W.S.W.S.W.S.W.S.W.S.0+30−170− 1+25−15− 56− 9+ 4− 17−471+21−147−23+49−40− 87−54+20− 61−672+ 5− 83−49+69−25−107−82+37− 62−763− 5− 12−51+47−21− 76−83+24− 59−554+ 1+ 76−37+43−13− 59−58+18− 39−385− 8+134−23+12+10− 9−27+11− 4− 36− 7+181− 2−21+21+ 43+ 9− 6+ 23+357−10+164+30−12+23+ 45+55+ 8+ 47+438− 7+ 86+36−21+38+ 52+71− 1+ 68+459− 80+28−23+46+ 30+64−16+ 71+1910− 5− 85+34−20+13+ 13+54−21+ 38+ 111−15−144+27−11−12− 6+31−19+ 5−1512− 9−164+19− 5−47− 230−19− 41−2913+ 1−136− 3+17−59− 46−36− 2− 69−4114− 7− 79−13+27−66− 44−55+14− 84−3215− 8− 8−32+25−53− 37−74+14− 82−2616−12+ 72−37+25−34− 17−70+26− 64− 217−13+137−33+ 4− 1+ 28−47+21− 24+3518−21+165− 2−10+20+ 47+ 8+12+ 21+4719−12+147+21−42+44+ 81+53−14+ 64+6420+10+ 95+21−62+75+107+71−28+100+8021+13+ 4+26−70+65+ 98+72−44+ 92+6522+25− 82+35−41+35+ 35+68−38+ 64+1223+36−147+34− 4− 7− 14+44−13+ 15−19Mean De-parture121502629334850185137Range573518713914121415581184156
Sabine applied his method to the data obtained during the decade 1840 to 1850 at Toronto, St Helena, Cape of Good Hope and Hobart, also to data for Pekin, Nertchinsk, Point Barrow, Port Kennedy and Kew. C. Chambers36applied it to data from Bombay. The yearly publication of the Batavia observatory gives corresponding results for that station, and Th. Moureaux33has published similar data for Parc St Maur. Tables XXX. to XXXII. are based on a selection of these data. Tables XXX. and XXXI. show the annual variation in Sabine’s disturbances, the monthly values being expressed as percentages of the arithmetic mean value for the 12 months. The Parc St Maur and Batavia data, owing to the long periods included, are especially noteworthy. Table XXX. deals with the east (E) and west (W) disturbances of declination separately. Table XXXI., dealing with disturbances in horizontal and vertical force, combines the + and − disturbances, treated numerically. At Parc St Maur the limits required to qualify for disturbance were 3′.0 in D, 20γ in H, and 12γ in V; the corresponding limits for Batavia were 1′.3, 11γ and 11γ. The limits for D at Toronto, Bombay and Hobart were respectively 3′.6, 1′.4 and 2′.4.
At Parc St Maur the disturbance data from all three elements give distinct maxima near the equinoxes; a minimum at midwinter is clearly shown, and also one at midsummer, at least in D and H. A decline in disturbance at midwinter is visible at all the stations, but at Batavia the equinoctial values for D and V are inferior to those at midsummer.
Table XXX.—Annual Variation of Disturbances (Sabine’s numbers).
Table XXXII. shows in some cases a most conspicuous diurnal variation in Sabine’s disturbances. The data are percentages of the totals for the whole 24 hours. But whilst at Batavia the easterly and westerly disturbances in D vary similarly, at Parc St Maur they follow opposite laws, the easterly showing a prominent maximum near noon, the westerly a still more prominent maximum near midnight. The figures in the second last line of the table, if divided by 0.24, will give the percentage of hours which show the species of disturbance indicated. For instance, at Parc St Maur, out of 100 hours, 3 show disturbances to the west and 3.7 to the east; or in all 6.7 show disturbances of declination. The last line gives the average size of a disturbance of each type, the unit being 1′ in D and 1γ in H and V.
Table XXXI.—Annual Variation of Disturbances.
At Batavia disturbances increasing and decreasing the element are about equally numerous, but this is exceptional. Easterly disturbances of declination predominated at Toronto, Point Barrow, Fort Kennedy, Kew, Parc St Maur, Bombay and the Falkland Islands whilst the reverse was true of St Helena, Cape of Good Hope, Pekin and Hobart. At Kew and Parc St Maur the ratios borne by theeastern to the western disturbances were 1.19 and 1.23 respectively, and so not much in excess of unity; but the preponderance of easterly disturbances at the North American37stations was considerably larger than this.
Table XXXII.—Diurnal Variation of Disturbances (Sabine’s numbers).
§ 32. From the point of view of the surveyor there is a good deal to be said for Sabine’s definition of disturbance, but it is less satisfactory from other standpoints. One objection has been already indicated, viz. the arbitrariness of applying the same limiting value at a station irrespective of the size of the normal diurnal range at the time. Similarly it is arbitrary to apply the same limit between 10 a.m. and noon, when the regular diurnal variation is most rapid, as between 10 p.m. and midnight, when it is hardly appreciable. There seems a distinct difference of phase between the diurnal inequalities on different types of days at the same season; also the phase angles in the Fourier terms vary continuously throughout the year, and much more rapidly at some stations and at some seasons than at others. Thus there may be a variety of phenomena which one would hesitate to regard as disturbances which contribute to the annual and diurnal variations in Tables XXX. to XXXII.
Sabine, as we have seen, confined his attention to the departure of the hourly reading from the mean for that hour. Another and equally natural criterion is the apparent character of the magnetograph curve. At Potsdam curves are regarded as “1” quiet, “2” moderately disturbed, or “3” highly disturbed. Any hourly value to which the numeral 3 is attached is treated as disturbed, and the annual Potsdam publication contains tables giving the annual and diurnal variations in the number of such disturbed hours for D, H and V. According to this point of view, the extent to which the hourly value departs from the mean for that hour is immaterial to the results. It is the greater or less sinuosity and irregularity of the curve that counts. Tables XXXIII. and XXXIV. give an abstract of the mean Potsdam results from 1892 to 1901. The data are percentages: in Table XXXIII. of the mean monthly total, in Table XXXIV. of the total for the day. So far as the annual variation is concerned, the results in Table XXXIII. are fairly similar to those in Table XXX. for Parc St Maur. There are pronounced maxima near the equinoxes, especially the spring equinox. The diurnal variations, however, in Tables XXXII. and XXXIV. are dissimilar. Thus in the case of H the largest disturbance numbers at Parc St Maur occurred between 6 a.m. and 6 p.m., whereas in Table XXXIV. they occur between 4 p.m. and midnight. Considering the comparative proximity of Parc St Maur and Potsdam, one must conclude that the apparent differences between the results for these two stations are due almost entirely to the difference in the definition of disturbance.
Table XXXIII.—Annual Variation of Potsdam Disturbances.
Table XXXIV.—Diurnal Variation of Potsdam Disturbances.
Table XXXV.—Disturbed Day less ordinary Day Inequality (Unit 1′, + to West).
One difficulty in the Potsdam procedure is the maintenance of a uniform standard. Unless very frequent reference is made to the curves of some standard year there must be a tendency to enter under “3” in quiet years a number of hours which would be entered under “2” in a highly disturbed year. Still, such a source of uncertainty is unlikely to have much influence on the diurnal, or even on the annual, variation.
§ 33. A third method of investigating a diurnal period in disturbances is to form a diurnal inequality from disturbed days alone, and compare it with the corresponding inequalities from ordinary or from quiet days. Table XXXV. gives some declination data for Kew, the quantity tabulated being the algebraic excess of the disturbed day hourly value over that for the ordinary day in the mean diurnal inequality for the year, as based on the 11 years 1890 to 1900.
The disturbed day inequality was corrected for non-cyclic change in the usual way. Fig. 11 shows the results of Table XXXV. graphically. The irregularities are presumably due to the limited number, 209, of disturbed days employed; to get a smooth curve would require probably a considerably longer period of years. The differences between disturbed and ordinary days at Kew are of the same general character as those between ordinary and quiet days in Table XXIX.; they are, however, very much larger, the range in Table XXXV. being fully 5½ times that in Table XXIX. If quiet days had replaced ordinary days in Table XXXV., the algebraic excess of the disturbed day would have varied from +2′.7 at 2 p.m. to −4′.1 at 11 p.m., or a range of 6′.8.
§ 34. When the mean diurnal inequality in declination for the year at Kew is analysed into Fourier waves, the chief difference, it will be remembered, between ordinary and quiet days was that the amplitude of the 24-hour term was enhanced in the ordinary days, whilst its phase angle indicated an earlier occurrence of the maximum. Similarly, the chief difference between the Fourier waves for the disturbed and ordinary day inequalities at Kew is the increase in the amplitude of the 24-hour term in the former by over 70%, and the earlier occurrence of its maximum by about 1 hour 50 minutes. It is clear from these results for Kew, and it is also a necessary inference from the differences obtained by Sabine’s method between east and west or + and − disturbances, that there is present during disturbances some influence which affects the diurnal inequality in a regular systematic way, tending to make the value of the element higher during some hours and lower during others than it is on days relatively free from disturbance. At Kew the consequence is a notable increase in the range of the regular diurnal inequality on disturbed days; but whether this is the general rule or merely a local peculiarity is a subject for further research.
§ 35. There are still other ways of attacking the problem of disturbances. W. Ellis27made a complete list of disturbed days at Greenwich from 1848 onwards, arranging them in classes according to the amplitude of the disturbance shown on the curves. Of the 18,000 days which he considered, Ellis regarded 2,119, or only about 12%, as undisturbed. On 11,898 days, or 66%, the disturbance movement in declination was under 10′; on 3614, or 20%, the disturbance, though exceeding 10′, was under 30′; on 294 days it laybetween 30′ and 60′; while on 75 days it exceeded 60′. Taking each class of disturbances separately, Ellis found, except in the case of his “minor” disturbances—those under 10′—a distinct double annual period, with maxima towards the equinoxes. Subsequently C. W. Maunder,38making use of these same data, and of subsequent data up to 1902, put at his disposal by Ellis, came to similar conclusions. Taking all the days with disturbances of declination over 10′, and dealing with 15-day periods, he found the maxima of frequency to occur the one a little before the spring equinox, the other apparently after the autumnal equinox; the two minima were found to occur early in June and in January. When the year is divided into three seasons—winter (November to February), summer (May to August), and equinox—Maunder’s figures lead to the results assigned to Greenwich disturbed days in Table XXXVI. The frequency in winter, it will be noticed, though less than at equinox, is considerably greater than in summer. This greater frequency in winter is only slightly apparent in the disturbances over 60′, but their number is so small that this may be accidental. The next figures in Table XXXVI. relate to highly disturbed days at Kew. The larger relative frequency at Kew in winter as compared to summer probably indicates no real difference from Greenwich, but is simply a matter of definition. The chief criterion at Kew for classifying the days was not so much the mere amplitude of the largest movement, as the general character of the day’s curve and its departure from the normal form. The data in Table XXXVI. as to magnetic storms at Greenwich are based on the lists given by Maunder39in theMonthly Notices, R.A.S. A storm may last for any time from a few hours to several days, and during part of its duration the disturbance may not be very large; thus it does not necessarily follow that the frequencies of magnetic storms and of disturbed days will follow the same laws. The table shows, however, that so far as Greenwich is concerned the annual variations in the two cases are closely alike. In addition to mean data for the whole 56 years, 1848 to 1903, Table XXXVI. contains separate data for the 14 years of that period which represented the highest sun-spot frequency, and the 15 years which represented lowest sun-spot frequency. It will be seen that relatively considered the seasonal frequencies of disturbance are more nearly equal in the years of many than in those of few sun-spots. Storms are more numerous as a whole in the years of many sun-spots, and this preponderance is especially true of storms of the largest size. This requires to be borne in mind in any comparisons between larger and smaller storms selected promiscuously from a long period. An unduly large proportion of the larger storms will probably come from years of large sun-spot frequency, and there is thus a risk of assigning to differences between the laws obeyed by large and small storms phenomena that are due in whole or in part to differences between the laws followed in years of many and of few sun-spots. The last data in Table XXXVI. are based on statistics for Batavia given by W. van Bemmelen,40who considers separately the storms which commence suddenly and those which do not. These sudden movements are recorded over large areas, sometimes probably all over the earth, if not absolutely simultaneously, at least too nearly so for differences in the time of occurrence to be shown by ordinary magnetographs. It is ordinarily supposed that these sudden movements, and the storms to which they serve as precursors, arise from some source extraneous to the earth, and that the commencement of the movement intimates the arrival, probably in the upper atmosphere, of some form of energy transmitted through space. In the storms which commence gradually the existence of a source external to the earth is not so prominently suggested, and it has been sometimes supposed that there is a fundamental difference between the two classes of storms. Table XXXVI. shows, however, no certain difference in the annual variation at Batavia. At the same time, this possesses much less significance than it would have if Batavia were a station like Greenwich, where the annual variation in magnetic storms is conspicuous.
Besides the annual period, there seems to be also a well-marked diurnal period in magnetic disturbances. This is apparent in Tables XXXVII. and XXXVIII., which contain some statistics for Batavia due to van Bemmelen, and some for Greenwich derived from the data in Maunder’s papers referred to above. Table XXXVII. gives the relative frequency of occurrence for two hour intervals, starting with midnight, treating separately the storms of gradual (g) and sudden (s) commencement. In Table XXXVIII. the day is subdivided into three equal parts. Batavia and Greenwich agree in showing maximum frequency of beginnings about the time of minimum frequency of endings and conversely; but the hours at which the respective maxima and minima occur at the two places differ rather notably.
§ 36. There are peculiarities in the sudden movements ushering in magnetic storms which deserve fuller mention. According to van Bemmelen the impulse consists usually at some stations of a sudden slight jerk of the magnet in one direction, followed by a larger decided movement in the opposite direction, the former being often indistinctly shown. Often we have at the very commencement but a faint outline, and thereafter a continuous movement which is only sometimes distinctly indicated, resulting after some minutes in the displacement of the trace by a finite amount from the position it occupied on the paper before the disturbance began. This may mean, as van Bemmelen supposes, a small preliminary movement in the opposite direction to the clearly shown displacement; but it may only mean that the magnet is initially set in vibration, swinging on both sides of the position of equilibrium, the real displacement of the equilibrium position being all the time in the direction of the displacement apparent after a few minutes. To prevent misconception, the direction of the displacement apparent after a few minutes has been termed the direction of the firstdecidedmovement in Table XXXIX., which contains some data as to the direction given by Ellis41and van Bemmelen.40The + sign means an increase, the − sign a decrease of the element. The sign is not invariably the same, it will be understood, but there are in all cases a marked preponderance of changes in the direction shown in the table. The fact that all the stations indicated an increase in horizontal force is of special significance.
Table XXXVI.—Disturbances, and their Annual Distribution.
Table XXXVII.—Batavia Magnetic Storms, Diurnal Distribution (percentages).
Table XXXVIII.—Greenwich Magnetic Storms, Diurnal Distribution.
§ 37. That large magnetic disturbances occur simultaneously over large areas was known in the time of Gauss, on whose initiative observations were taken at 5-minute intervals at a number of stationson prearrangedterm days. During March 1879 and August 1880 some large magnetic storms occurred, and the magnetic curves showing these at a number of stations fitted with Kew pattern magnetographs were compared by W. G. Adams.42He found the more characteristic movements to be, so far as could be judged, simultaneous at all the stations. At comparatively near stations such as Stonyhurst and Kew, or Coimbra and Lisbon, the curves were in general almost duplicates. At Kew and St Petersburg there were usually considerable differences in detail, and the movements were occasionally in opposite directions. The differences between Toronto, Melbourne or Zi-ka-wei and the European stations were still more pronounced. In 1896, on the initiative of M. Eschenhagen,43eye observations of declination and horizontal force were taken at 5-second intervals during prearranged hours at Batavia, Manila, Melbourne and nine European stations. The data from one of these occasions when appreciable disturbance prevailed were published by Eschenhagen, and were subsequently analysed by Ad. Schmidt.44Taking the stations in western Europe, Schmidt drew several series of lines, each series representing the disturbing forces at one instant of time as deduced from the departure of the elements at the several stations from their undisturbed value. The lines answering to any one instant had a general sameness of direction with more or less divergence or convergence, but their general trend varied in a way which suggested to Schmidt the passage of a species of vortex with large but finite velocity.
Table XXXIX.—Direction of First Decided Movement.
The conclusion that magnetic disturbances tend to follow one another at nearly equal intervals of time has been reached by several independent observers. J. A. Broun45pronounced for a period of about 26 days, and expressed a belief that a certain zone, or zones, of the sun’s surface might exert a prepotent influence on the earth’s magnetism during several solar rotations. Very similar views were advanced in 1904 by E. W. Maunder,39who was wholly unaware of Broun’s work. Maunder concluded that the period was 27.28 days, coinciding with the sun’s rotation period relative to an observer on the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he found the interval between the commencement of successive storms to approach closely to the above period in a considerably larger number of instances than one would have expected from mere chance. He found several successions of three or four storms, and in one instance of as many as six storms, showing his interval. In a later paper Maunder reached similar results for magnetic storms at Greenwich from 1848 to 1881. Somewhat earlier than Maunder, Arthur Harvey46deduced a period of 27.246 days from a consideration of magnetic disturbances at Toronto. A. Schuster,47examining Maunder’s data mathematically, concluded that they afforded rather strong evidence of a period of about ½ (27.28) or 13.6 days. Maunder regarded his results asdemonstratingthat magnetic disturbances originate in the sun. He regarded the solar action as arising from active areas of limited extent on the sun’s surface, and as propagated along narrow, well defined streams. The active areas he believed to be also the seats of the formation of sun-spots, but believed that their activity might precede and outlive the visible existence of the sun-spot.
Maunder did not discuss the physical nature of the phenomenon, but his views are at least analogous to those propounded somewhat earlier by Svante Arrhenius,48who suggested that small negatively charged particles are driven from the sun by the repulsion of light and reach the earth’s atmosphere, setting up electrical currents, manifest in aurora and magnetic disturbances. Arrhenius’s calculations, for the size of particle which he regarded as most probable, make the time of transmission to the earth slightly under two days. Amongst other theories which ascribe magnetic storms to direct solar action may be mentioned that of Kr. Birkeland,49who believes the vehicle to be cathode rays. Ch. Nordmann50similarly has suggested Röntgen rays. Supposing the sun the ultimate source, it would be easier to discriminate between the theories if the exact time of the originating occurrence could be fixed. For instance, a disturbance that is propagated with the velocity of light may be due to Röntgen rays, but not to Arrhenius’s particles. In support of his theory, Nordmann mentions several cases when conspicuous visual phenomena on the sun have synchronized with magnetic movements on the earth—the best known instance being the apparent coincidence in time of a magnetic disturbance at Kew on the 1st of September 1859 with a remarkable solar outburst seen by R. C. Carrington. Presumably any electrical phenomenon on the sun will set up waves in the aether, so transmission of electric and magnetic disturbances from the sun to the earth with the velocity of light is a certainty rather than a hypothesis; but it by no means follows that the energy thus transmitted can give rise to sensible magnetic disturbances. Also, when considering Nordmann’s coincidences, it must be remembered that magnetic movements are so numerous that it would be singular if no apparent coincidences had been noticed. Another consideration is that the movements shown by ordinary magnetographs are seldom very rapid. During some storms, especially those accompanied by unusually bright and rapidly varying auroral displays, large to and fro movements follow one another in close succession, the changes being sometimes too quick to be registered distinctly on the photographic paper. This, however, is exceptional, even in polar regions where disturbances are largest and most numerous. As a rule, even when the change in the direction of movement in the declination needle seems quite sudden, the movement in one direction usually lasts for several minutes, often for 10, 15 or 30 minutes. Thus the cause to which magnetic disturbances are due seems in many cases to be persistent in one direction for a considerable time.
§ 38. Attempts have been made to discriminate between the theories as to magnetic storms by a critical examination of the phenomena. A general connexion between sun-spot frequency and the amplitude of magnetic movements, regular and irregular, is generally admitted. If it is a case of cause and effect, and the interval between the solar and terrestrial phenomena does not exceed a few hours, then there should be a sensible connexion between corresponding daily values of the sun-spot frequency and the magnetic range. Even if only some sun-spots are effective, we should expect when we select from a series of years two groups of days, the one containing the days of most sun-spots, the other the days of least, that a prominent difference will exist between the mean values of the absolute daily magnetic ranges for the two groups. Conversely, if we take out the days of small and the days of large magnetic range, or the days that are conspicuously quiet and those that are highly disturbed, we should expect a prominent difference between the corresponding mean sun-spot areas. An application of this principle was made by Chree23to the five quiet days a month selected by the astronomer royal between 1890 and 1900. These days are very quiet relative to the average day and possess a much smaller absolute range. One would thus have expected on Birkeland’s or Nordmann’s theory the mean sun-spot frequency derived from Wolfer’s provisional values for these days to be much below his mean value, 41.22, for the eleven years. It proved, however, to be 41.28. This practical identity was as visible in 1892 to 1895, the years of sun-spot maximum, as it was in the years of sun-spot minimum. Use was next made of the Greenwichprojectedsun-spot areas, which are the result of exact measurement. The days of each month were divided into three groups, the first and third—each normally of ten days—containing respectively the days of largest and the days of least sun-spot area. The mean sun-spot area from group 1 was on the average about five times that for group 3. It was then investigated how the astronomer royal’s quiet days from 1890 to 1900, and how the most disturbed days of the period selected from the Kew24magnetic records, distributed themselves among the three groups of days. Nineteen months were excluded, as containing more than ten days with no sun-spots. The remaining 113 months contained 565 quiet and 191 highly disturbed days, whose distribution was as follows:
The group of days of largest sun-spot area thus contained slightly under their share of quiet days and slightly over their share of disturbed days. The differences, however, are not large, and in three years, viz. 1895, 1897 and 1899, the largest number of disturbed days actually occurred in group 3, while in 1895, 1896 and 1899 there were fewer quiet days in group 3 than in group 1. Taking the same distribution of days, the mean value of the absolute daily range of declination at Kew was calculated for the group 1 and the group 3 days of each month. The mean range from the group 1 days was the larger in 57% of the individual months as against 43% in which it was the smaller. When the days of each month were divided into groups according to the absolute declination range at Kew, the mean sun-spot area for the group 1 days (those of largest range) exceeded that for the group 3 days (those of least range) in 55% of the individual months, as against 45% of cases in which it was the smaller.
Taking next the five days of largest and the five days of least range in each month, sun-spot areas were got out not merely for these days themselves, but also for the next subsequent day and the four immediately preceding days in each case. On Arrhenius’s theory we should expect the magnetic range to vary with the sun-spot area, not on the actual day but two days previously. The following figures give the percentage excess or deficiency of the mean sun-spot area for the respective groups of days, relative to the average value for the whole epoch dealt with. n denotes the day to which the magnetic range belongs, n + 1 the day after, n − 1 the day before, andso on. Results are given for 1894 and 1895, the years which were on the whole the most favourable and the least favourable for Arrhenius’s hypothesis, as well as for the whole eleven years.
Table XL.
Taking the 11-year-means we have the sun-spot area practically normal on the day subsequent to the representative day of large magnetic range, but sensibly above its mean on that day and still more so on the four previous days. This suggests an emission from the sun taking a highly variable time to travel to the earth. The 11-year mean data for the five days of least range seem at first sight to point to the same conclusion, but the fact that the deficiency in sun-spot area is practically as prominent on the day after the representative day of small magnetic range as on that day itself, or the previous days, shows that the phenomenon is probably a secondary one. On the whole, taking into account the extraordinary differences between the results from individual years, we seem unable to come to any very positive conclusion, except that in the present state of our knowledge little if any clue is afforded by the extent of the sun’s spotted area on any particular day as to the magnetic conditions on the earth on that or any individual subsequent day. Possibly some more definite information might be extracted by considering the extent of spotted area on different zones of the sun. On theories such as those of Arrhenius or Maunder, effective bombardment of the earth would be more or less confined to spotted areas in the zones nearest the centre of the visible hemisphere, whilst all spots on this hemisphere contribute to the total spotted area. Still theprojectedarea of a spot rapidly diminishes as it approaches the edge of the visible hemisphere,i.e.as it recedes from the most effective position, so that the method employed above gives a preponderating weight to the central zones. One rather noteworthy feature in Table XL. is the tendency to a sequence in the figures in any one row. This seems to be due, at least in large part, to the fact that days of large and days of small sun-spot area tend to occur in groups. The same is true to a certain extent of days of large and days of small magnetic range, but it is unusual for the range to be much above the average for more than 3 or 4 successive days.
§ 39. The records from ordinary magnetographs, even when run at the usual rate and with normal sensitiveness, not infrequently show a repetition of regular or nearly regular small rhythmic movements, lasting sometimes for hours. The amplitudePulsations.and period on different occasions both vary widely. Periods of 2 to 4 minutes are the most common. W. van Bemmelen51has made a minute examination of these movements from several years’ traces at Batavia, comparing the results with corresponding statistics sent him from Zi-ka-wei and Kew. Table XLI. shows the diurnal variation in the frequency of occurrence of these small movements—calledpulsationsby van Bemmelen—at these three stations. The Batavia results are from the years 1885 and 1892 to 1898. Of the two sets of data for Zi-ka-wei (i) answers to the years 1897, 1898 and 1900, as given by van Bemmelen, while (ii) answers to the period 1900-1905, as given in the Zi-ka-weiBulletinfor 1905. The Kew data are for 1897. The results are expressed as percentages of the total for the 24 hours. There is a remarkable contrast between Batavia and Zi-ka-wei on the one hand and Kew on the other, pulsations being much more numerous by night than by day at the two former stations, whereas at Kew the exact reverse holds. Van Bemmelen decided that almost all the occasions of pulsation at Zi-ka-wei were also occasions of pulsations at Batavia. The hours of commencement at the two places usually differed a little, occasionally by as much as 20 minutes; but this he ascribed to the fact that the earliest oscillations were too small at one or other of the stations to be visible on the trace. Remarkable coincidence between pulsations at Potsdam and in the north of Norway has been noted by Kr. Birkeland.49
With magnetographs of greater sensitiveness and more open time scales, waves of shorter period become visible. In 1882 F. Kohlrausch52detected waves with a period of about 12 seconds. Eschenhagen53observed a great variety of short period waves, 30 seconds being amongst the most common. Some of the records he obtained suggest the superposition of regular sine waves of different periods. Employing a very sensitive galvanometer to record changes of magnetic induction through a coil traversed by the earth’s lines of force, H. Ebert54has observed vibrations whose periods are but a small fraction of a second. The observations of Kohlrausch and Eschenhagen preceded the recent great development of applications of electrical power, while longer period waves are shown in the Kew curves of 50 years ago, so that the existence of natural waves with periods of from a few seconds up to several minutes can hardly be doubted. Whether the much shorter period waves of Ebert are also natural is more open to doubt, as it is becoming exceedingly difficult in civilized countries to escape artificial disturbances.
Table XLI.—Diurnal Distribution of Pulsations.
§ 40. The fact that the moon exerts a small but sensible effect on the earth’s magnetism seems to have been first discovered in 1841 by C. Kreil. Subsequently Sabine55investigated the nature of the lunar diurnal variation in declinationLunar Influence.at Kew, Toronto, Pekin, St Helena, Cape of Good Hope and Hobart. The data in Table XLII. are mostly due to Sabine. They represent the mean lunar diurnal inequality in declination for the whole year. The unit employed is 0′.001, and as in our previous tables + denotes movement to thewest. By “mean departure” is meant the arithmetic mean of the 24 hourly departures from the mean value for the lunar day; the range is the difference between the algebraically greatest and least of the hourly values. Not infrequently the mean departure gives the better idea of the importance of an inequality, especially when as in the present case two maxima and minima occur in the day. This double daily period is unusually prominent in the case of the lunar diurnal inequality, and is seen in the other elements as well as in the declination.
Table XLII.—Lunar Diurnal Inequality of Declination (unit 0′.001).
Lunar action has been specially studied in connexion with observations from India and Java. Broun56at Trivandrum and C. Chambers57at Kolaba investigated lunar action from a variety of aspects. At Batavia van der Stok58and more recently S. Figee59have carried out investigations involving an enormous amount of computation. Table XLIII. gives a summary of Figee’s results for the mean lunar diurnal inequality at Batavia, for the two half-yearly periods April to September (Winter or W.), and October to March (S.). The + sign denotes movement to the west in the case of declination, but numerical increase in the case of the other elements. In the case of H and T (total force) the results for the two seasons present comparatively small differences, but in the case of D, I and V the amplitude and phase both differ widely. Consequently a mean lunar diurnal variation derived from all the months of the year gives at Batavia, and presumably at othertropical stations, an inadequate idea of the importance of the lunar influence. In January Figee finds for the range of the lunar diurnal inequality 0′.62 in D, 3.1γ in H and 3.5γ in V, whereas the corresponding ranges in June are only 0′.13, 1.1γ and 2.2γ respectively. The difference between summer and winter is essentially due to solar action, thus the lunar influence on terrestrial magnetism is clearly a somewhat complex phenomenon. From a study of Trivandrum data, Broun concluded that the action of the moon is largely dependent on the solar hour at the time, being on the average about twice as great for a day hour as for a night hour. Figee’s investigations at Batavia point to a similar conclusion. Following a method suggested by Van der Stok, Figee arrives at a numerical estimate of the “lunar activity” for each hour of the solar day, expressed in terms of that at noon taken as 100. In summer, for instance, in the case of D he finds the “activity” varying from 114 at 10 a.m. to only 8 at 9 p.m.; the corresponding extremes in the case of H are 139 at 10 a.m. and 54 at 6 a.m.
Table XLIII.—Lunar Diurnal Inequality at Batavia in Winter and Summer.