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.

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. Ellis[27] made 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 lay between 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,[38] making 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 Maunder[39] in the Monthly 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,[40] who 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 first decided movement in Table XXXIX., which contains some data as to the direction given by Ellis[41] and van Bemmelen.[40] The + 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.

Total
Number.		 Percentages.
Winter. Equinox. Summer.
Greenwich disturbed days, all, 1848-1902 4,214  33.9 39.2 26.9
Greenwich disturbed days, range 10′ to 30′, 1848-1902 3,830  33.9 39.0 27.1
Greenwich disturbed days range 30′ to 60′, 1848-1902 307 34.5 41.0 24.4
Greenwich disturbed days, range over 60′, 1848-1902  77 29.9 41.6 28.6
Kew highly disturbed days, 1890-1900 209 38.3 41.6 20.1
Greenwich magnetic storms, all, 1848-1903 726 32.1 42.3 25.6
Greenwich magnetic storms, range 20′ to 30′, 1848-1903 392 30.1 43.6 26.3
Greenwich magnetic storms, range over 30′, 1848-1903 334 34.4 40.7 24.9
Greenwich magnetic storms, all, 14 years of S. max. 258 35.3 38.0 26.7
Greenwich magnetic storms, all, 15 years of S. min. 127 28.4 48.0 23.6
Batavia magnetic storms, all, 1883-1899 1,008  32.9 34.9 32.2
Batavia magnetic storms of gradual commencement 679 32.4 34.8 32.8
Batavia magnetic storms of sudden commencement 329 33.7 35.3 31.0