at the Cape of Good Hope does not differ much from that seen at
Batavia. Only a single period is clearly shown. The maximum
occurs about 8 or 9 p.m. throughout the year. The time of the
minimum is more variable; at midsummer it occurs about II a.m.,
but at midwinter three or four hours later. At Hobart the type
varies considerably with the season. In June (midwinter) a double
period is visible. The principal minimum occurs about 8 a.m., as
at the Cape. But, corresponding to the evening maximum seen at
the Cape, there is now only a secondary maximum, the principal
maximum occurring about 1 p.m. At midsummer the principal
maximum is found-as at Kew or Greenwich-about IO or II a.m.,
the principal minimum about 4 p.m.

§ 18. Even at tropical stations a considerable seasonal change is usually seen in the amplitude of the diurnal inequality in at least one of the magnetic elements. At stations in Europe, and generally in temperate latitudes, the amplitude varies notably in all the elements. Table XIII. gives particulars of the inequality range of declination derived from hourly readings at selected stations, arranged in order of latitude from north to south. The letters “ a ” and “ q ” are used in the same sense as before. At tem erate stations in either hemisphere-e.g. Pavlovsk, Greenwich or I'l>0bart -the range is conspicuously larger in summer than in winter. In northern temperate stations a decided minimum is usually apparent in December. There is, on the other hand, comparative little variation in the range from April to August. Sometimes, as at Kew and Greenwich, there is at least a suggestion of a secondary minimum at midsummer. Manila and Trivandrum show a transition from the December minimum, characteristic of the'n0rthern stations, to the June minimum characteristic of the southern, there being two conspicuous minima in February or March and in November or October. At St Helena there are two similar minima in May and September, while a third apparently exists in December. It will be noticed that at both Pavlovsk and Kew the annual variation in the range is specially prominent in the quiet day results. Table XIV. gives a smaller number of data analogous to those of Table Xlll., comprising inequality ranges for horizontal force, vertical force and inclination. In some cases the number of years from which the data were derived seems hardly sufficient to give a smooth annual variation. It should also be noticed that unless the same group of years is employed the data from two stations are not strictly comparable. The difference between the all and quiet day vertical force data at Pavlovsk is remarkably pronounced. The general tendency in all the elements is to show a reduced range at midwinter; but in some cases there is also a distinct reduction in the range at midsummer. This double annual period is particularly well marked at Batavia.

§ 19. When discussing diurnal inequalities it is sometimes convenient to consider the components of the horizontal force in and perpendicular to the astronomical meridian, rather than the horizontal force and declination. If N and W be the components of H to astronomical north and west, and D the westerly declination, N==H cos D, W=H sin D. Thus corresponding small variations in N, W, H and D are connected by the relations 1-6N= c0sD5H -H sinD5D, 6W= sinD5H-}-H c0sD6D

If 5H and 5D denote the departures of H and D at any hour of the day from their mean values, then BN and BW represent the corresponding departures of N and W from their mean values. In this way diurnal inequalities may be calculated for N and W when those for H and D are known. The formulae suppose ED to be expressed in absolute measure, i e. 1' of arc has to be replaced by 0-0002909. If we take as an example a station at which H is 185 then H6D=-o000538(number of minutes in BD). In other words, employing I-y as unit of force, one replaces H5D by 5'386D, where 6D represents declination change expressed as usual in minutes of arc. In calculating diurnal inequalities for N and W, one ought, strictly speaking, to assign to H and D the exact mean values belonging to these elements for the month or the year being deal-t with. For practical purposes, however, a slight departure from the true mean values is immaterial, and one can make use of a constant value for several successive years without sensible error. As an example, Table XV. gives the mean diurnal inequality for the whole year in N and W at Falmouth, as calculated from the 12 years 1891 to 1902. The unit employed is 17.

The data in Table XV. are closely similar to corresponding Kew data, and are presumably fairly applicable to the whole south of England for the epoch considered. At Falmouth there is comparatively little seasonal Variation in the type of the diurnal variation in either N or W. The amplitude of the diurnal range varies, however, largely with the season, as will appear from Table XVI., which is based on the same 12 years as Table XV. Diurnal inequalities in N and W lend themselves readily to the construction of what are known as 'vector diagrams. These are curves showing the direction and intensity at each hour of the day of the horizontal component of the disturbing force to which the diurnal inequality may be regarded as due. Figs. 7 and 8, taken from the Phil. T ram. vol. 204A, will serve as examples. They refer to the mean diurnal inequalities for the months stated at Kew (1890 to 1900) and Falmouth (1891 to 1902), thick lines relating to Kew, thin to Falmouth. NS and EW represent the geographical north-south and east-west directions; their intersection answers to the origin (thick lines for Kew, thin for Falmouth). The line from the origin to M represents the magnetic meridian. The line from the origin to any cross-the number indicating the corresponding hour counted from midnight as 0-represents the magnitude and direction at that hour of the horizontal component of the disturbing force to which the diurnal inequality may be assigned. The cross marks the point whose rectangular co-ordinates are the values of 6N and:Sl/V derived from the diurnal inequalities of these elements. -In figs. 7 and 8 the distances of the points N, E, S, W from their corresponding origin represents 107. The tendency to form a loop near midnight, seen in the November and December TABLE XIV.-Ranges in the Diurnal Inequalities. Jan. Feb. March. April. May. June. July. Aug. Sept. Oct. Nov. i Dec. H (unit 1-y)

Pavlovsk . 1890-1900 12 20 32 46 47 49 49 4.4 39 32 17 II YY —~ -» 12 17 31 42 45 45 42 40 37 31 17 I0 Ekatarmburg , , 1 1 1 5 29 37 40 40 39 36 33 27 1 3 9 Kew ....., , 15 17 26 36 38 39 38 38 35 27 20 II Toronto 1843-1848 23 2I 24 28 29 29 26 28 4I 25 2I 20 Batavia . 1883-1898 49 47 54 60 51 48 50 53 58 52 43 40 St Helena 1843-1847 43 41 48 53 46 40 40 45 41 40 40 32 Mauritius 1883-1890 2I 15 2I 23 20 2I 20 22 20 21 2I 20 Cape of Good Hope 1841-1846 13 IO 13 13 15 16 14 18 2I 14 17 20 Hobart .... 1842-1848 42 43 34 28 19 17 22 23 23 35 39 42 V (unit 1-y)

Pavlovsk . 1890-1900 IS 27 29 24 26 20 23 19 23 20 I4 4 5 9 13 13 12 13 10 9 7 5 4

Ekatarinburg , , 10 15 17 2I 22 19 20 16 14 13 II 9 Kew - 1891-1900 7 IO 20 25 31 27 28 23 20 15 9 6 Toronto 1843-1848 12 14 17 23 26 14 27 32 34 25 19 18 Batavia .... 1883-1898 42 48 48 45 31 3I 32 29 41 50 40 33 St Helena 1843-1847 16 13 12 14 13 II 17 II 17 II 15 18 Mauritius 1884-1890 'I2 16 18 15 14 13 15 2I 20 16 .13 II Cape of Good Hope 1841-1846 29 47 41 38 2I 12 14 19 19 35 33 28 Hobart . 1842-1848 25 27 22 23 '24 21 22 28 26 22 23 27 I inclination ' ', ' ' ' ' '

Pavlovsk . 1890-1900 0'97 1'24 2'o7 2'79 2'72 2'88 2'85 '64 S2 2-18 1'2o 0'89 Ekatarinburg, , 079 o°94 I'7O 2'O8 2'25 2'I9 2'I8 '08 'oo 1-70 0'88 o'69 Kew . , , 0'98 1'01 1'38 1'86 2'O5 2'O2 '05 15 '98 1~57 1'27 o°63 Toronto 1843-1848 I'I5 0'94 1'19 V23 I'3I 1'37 '13 26 87 1-16 1'09 1'05 Batavia .. 1883-1898 4'88 5'22 5'56 5'62 4'2I 4'O5 4'24 '17 5'13 5-58 4'51 3-85 Cape of Good Hope 1842-1846 I°55 2'29 2'23 2'23 V60 1'41 1'54 '70 1'86 2-03 1'55 2'04 Hobart . . 1842-1848 1'95 2'16 I'72 1'62 I'23 I'I6 '28 '42 '39 1-75 2'04 2'10