ranges 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
TABLE XXIV.-Ranges of Diurnal Inequalities.

Pavlovsk. Ekatarinburg. Kew.

D. I. H. D. I. H. V. Dq. Iq. H, . Do.

I I Y I I Y 7 I I Y I

189011 6-32 1-33 22 5-83 1-05 18 9 6-90 20 7-32

1891, 7-31 1-79 30 6-85 1-38 25 14 8-04 1-52 28 8-48 18923 8-75 2-21 37 7-74 1-72 32 19 9-50 1-66 31 9-85 18931 9-64 2-24 38 8'83 I-80 3I 17 10-06 1-96 35 10-74 13941 363 2'17 33 7'30 P73 30 17 9'32 V94 34 9'30 18951 8-22 2'O8 33 7-29 1-64 28 15 8-59 1-66 30 9-54 13961 7'39 1'77 29 5'50 V33 25 15 7'77 V31 25 3'50 18971 6~79 1-59 26 6-OI 1-16 2I 12 6-71 1-14 22 7-76 118987 6-25 1-56 26 5-76 1-19 21 II 6-85 I°07 21 7-59 1899, 6-02 1-44 24 5-33 1-12 20 II 6-69 1-01 2I 7-30 1900,0'6-20 1-28 22 5-88 0-93 17 8 6-52 I'O6 21 6'83 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 TABLE XXV.-Absolute Ranges.

paper gives curves representing the phenomena over the whole 56 years. This period covered live complete sun-spot periods, and the approximate synchronise of the maxima and minima, and the genera parallelism of the magnetic and sun-spot changes is patent to the eye. Ellis” has 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 su n-spot frequency and magnetic range. This is expressed mathematically by the R=a+bs;ag1+<1>/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 laces. Of course, the usefulness of Wolf 's formula de ends 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 horizon ta 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 photo raphic curves. A change, however, of I' in declination has a Signigcance which alters with the intensity of the horizontal force. During the period 1850-1900 horizontal force in England increased about 15%, so that the force requisite to produce a declination change of IQ' in 1900 would in 1850 have produced a deflection of 20'. It must also be re formula membered that secular changes of declination must alter the Pavlovsk. angle between the needle and any disturbing force acting in KewDeChf'a' - afixed direction. Thus secular alteration in a and b is “On” Dmly- Daily. Monthly. Yearly. rather to be anticipated, especially in the case of the declination. Wolf's formula has been applied by Rajna” to the

q. o. a. D. H. V. D. H. V. D. H. V. yearly mean diurnal declination ranges at Milan based on - ~ - readings taken twice daily from 1836 to 1894, treating the -y -y ' -y 'y ' 'y 7 whole period together, and then the period 1871 to 1894 18901, 8-3 10-5 10-7 12-1 49 21 28-2 118 80 42-1 169 179 separately. During two sub-periods, 1837-1850 and 1854-11891, 10-0 12-8 13-7 16-0 70 39 46-3 218 233 92-3 550 614 1867, Rajna's calculated values for the range differ very 1892, 12-3 15-4 17-7 21-0 111 73 93-6 698 575 194-0 2416 1385 persistently in one'direction from those observed; Wolf's 8Q3 11-8 15-2 15-6 17-8 79 41 48-3 241 210 87-1 514 457 ormula was applied by C. Chree” to these two periods 18942 II-3 14-7 16-5 20-4 Q7 62 84-1 493 493 145-6 1227 878 separately. He also applied it to Greenwich inequality 18954 I0'6 14-8 15-6 18-1 80 46 47-4 220 '223 73-9 395 534 ranges for the years 1841 to 1896 as published by Ellis, 18965 9-5 12-9 14-5 17-5 74 43 52-4 232 236 88-7 574 608 treating the whole period and the last 32 years of it separ-13973 8-2 11-5 12-1 14-6 61 30 43-8 201 170 101-1 449 480 ately, and finally to all (a) and quiet (g) day Greenwich 1898- 8-2 11-2 I2°3 14-7 67 35 46-6 276 242 118-9 1136 888 ranges from 1889 to 1896. The results of these applications 1899, 7-9 10-5 11-3 13-1 58 27 38-3 178 150 63'8 382 527 of Wolf's formula appear in Table XXVI. 190010 7-4 8-9 9-2 I0'5 44 16 32-8 134 89 94-2 457 365 The Milan results are suggestive rather of heterogeneity E - » - - — - in the material than of any decided secular change in a or Means 9-6 I2~6 I3°6' 16-0 72 39 ' 51-1 274 246 100-2 752 629 b. The Greenwich data are suggestive of a gradual fall in a, 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 ear 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. § 27. The relationship between magnetic ranges and sun-spot frequency has been investigated in several ways. W. Ellis” has 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 and rise in b, at least in the case of the declination. Table XXVII. gives values of a, b and b/11 in Wo1f's formula calculated by Chree'5 for 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. (lit is specified whether the results were derived from all or from quiet ays.

TABLE XXVI.—Values of a and b in Wolf 's Formula. Milan. Greenwich.,

Declination Declination Horizontal Force

Epoch. (unit 1'). Epoch. (unit 1'). (unit 17).

a. b. a. b. a. b.

1836794 5'31 '047 1541*95 1 7'29 '0377 26'4 '190

1371-94 5'39 '047 1355'95 7'07 '0396 23'6 '215

1837-50 6-43 -041 1889-96(a) 6-71 ~0418 23-7 '218 1854-67 4-62 -047 1889-96(q) 6'§ 6 -0415 25-0 -213 As explained above, a would represent the range in a year of no sun-spots, while 100 b would represent the excess over this shown by the range in a year when W0lfer's sun-spot frequency is 100. Thus