§ 35. There are still other ways of atta_Encyclopaedia Britannica, 11th Edition, "McKinley, William" to "Magnetism, Terrestrial" Volume 17, Slice 3

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 | Percentages. |

| |Number.+--------+---------+--------+

+-------------------------------+-------+--------+---------+--------+

| all, 1848-1902 | 4,214 | 33.9 | 39.2 | 26.9 |

| range 10´ to 30´, 1848-1902 | 3,830 | 33.9 | 39.0 | 27.1 |

| range 30´ to 60´, 1848-1902 | 307 | 34.5 | 41.0 | 24.4 |

| range over 60´, 1848-1902 | 77 | 29.9 | 41.6 | 28.6 |

| 1890-1900 | 209 | 38.3 | 41.6 | 20.1 |

| all, 1848-1903 | 726 | 32.1 | 42.3 | 25.6 |

| range 20´ to 30´, 1848-1903 | 392 | 30.1 | 43.6 | 26.3 |

| range over 30´, 1848-1903 | 334 | 34.4 | 40.7 | 24.9 |

| all, 14 years of S. max. | 258 | 35.3 | 38.0 | 26.7 |

| all, 15 years of S. min. | 127 | 28.4 | 48.0 | 23.6 |

| all, 1883-1899 | 1,008 | 32.9 | 34.9 | 32.2 |

| gradual commencement | 679 | 32.4 | 34.8 | 32.8 |

| sudden commencement | 329 | 33.7 | 35.3 | 31.0 |

+-------------------------------+-------+--------+---------+--------+

TABLE XXXVII.--Batavia Magnetic Storms, Diurnal Distribution

(percentages).

+--------------+----+----+----+----+----+----+----+----+----+----+----+----+

| Hour. | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |

+--------------+----+----+----+----+----+----+----+----+----+----+----+----+

| Beginning /g | 5 | 5 | 5 | 6 | 20 | 16 | 7 | 5 | 6 | 9 | 8 | 8 |

| \s | 7 | 5 | 7 | 10 | 10 | 11 | 10 | 8 | 8 | 9 | 8 | 7 |

| Maximum /g | 12 | 10 | 6 | 5 | 4 | 9 | 9 | 6 | 6 | 6 | 12 | 15 |

| \s | 14 | 7 | 5 | 2 | 2 | 9 | 9 | 5 | 8 | 10 | 13 | 16 |

| End all | 15 | 16 | 19 | 13 | 5 | 3 | 6 | 5 | 4 | 5 | 4 | 5 |

+--------------+----+----+----+----+----+----+----+----+----+----+----+----+

TABLE XXXVIII.--Greenwich Magnetic Storms, Diurnal Distribution.

+------------------------+--------+-------+-----------------------------+

| Epoch. | Class. | Total +---------+---------+---------+

| | |Number.| 1-8 p.m.| 9 p.m.- | 5 a.m.- |

| | | | | 4 a.m. | noon. |

+------------------------+--------+-------+---------+---------+---------+

| / 1848-1903 | all | 721 | 60.1 | 21.9 | 18.0 |

| Beginning < 1882-1903 | " | 276 | 58.0 | 18.8 | 23.2 |

| \ " " | sudden | 77 | 45.4 | 27.3 | 27.3 |

| | | | | | |

| / 1848-1903 | all | 720 | 9.4 | 44.6 | 46.0 |

| End < 1882-1903 | " | 276 | 7.2 | 41.7 | 51.1 |

| \ " " | sudden | 77 | 11.7 | 35.1 | 53.2 |

+------------------------+--------+-------+---------+---------+---------+

§ 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 stations on

prearranged _term 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.[42] He 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,[43] eye 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.[44]

Taking 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.

+-----------+-------------+------------------+----------------+

+-----------+-------------+------------------+----------------+

| Pavlovsk | West | + | + |

| Potsdam | West | + | - |

| Greenwich | West | + | + |

| Zi-ka-wei | East | + | - |

| Kolaba | East | + | - |

| Batavia | West | + | - |

| Mauritius | East | + | + |

| Cape Horn | West | + | - |

+-----------+-------------+------------------+----------------+

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. Broun[45] pronounced 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,[39] who 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 Harvey[46] deduced a

period of 27.246 days from a consideration of magnetic disturbances at

Toronto. A. Schuster,[47] examining 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 as

_demonstrating_ that 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,[48] who 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,[49] who believes the vehicle to be

cathode rays. Ch. Nordmann[50] similarly 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 Chree[23] to 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 Greenwich _projected_ sun-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 Kew[24] magnetic

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:

+----------------+---------+---------+---------+

| +---------+---------+---------+

| Quiet days | 179 | 195 | 191 |

| Disturbed days | 68 | 65 | 58 |

+----------------+---------+---------+---------+

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, and so 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 - 4 | n - 3 | n - 2 | n - 1 | n | n + 1 |

+-------------------------+-------+-------+-------+-------+--------+-------+

| Five days of \ 1894 | +12 | + 9 | +11 | +12 | +11 | + 6 |

| largest range > 1895 | -16 | -17 | -15 | -12 | -11 | -10 |

| / 11 yrs. | + 9 | + 8 | + 8 | + 7 | + 5 | + 0.5|

| Five days of \ 1894 | -15 | -17 | -19 | -21 | -21 | -19 |

| least range > 1895 | +17 | +10 | + 1 | - 2 | - 2 | - 4 |

| / 11 yrs. | - 4 | - 4 | - 7 | - 7 | - 7 | - 6 |

+-------------------------+-------+-------+-------+-------+--------+-------+

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 the _projected_ area 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.

Pulsations.

§ 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 amplitude and period on different

occasions both vary widely. Periods of 2 to 4 minutes are the most

common. W. van Bemmelen[51] has 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--called _pulsations_ by 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-wei _Bulletin_

for 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. Kohlrausch[52]

detected waves with a period of about 12 seconds. Eschenhagen[53]

observed 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. Ebert[54]

has 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.|

+---------------+-----+-----+-----+--------+--------+-----+-----+------+

| Batavia | 28 | 9 | 2 | 6 | 8 | 6 | 13 | 28 |

| Zi-ka-wei (i) | 33 | 5 | 2 | 7 | 4 | 4 | 10 | 35 |

| " (ii) | 23 | 6 | 8 | 11 | 7 | 5 | 14 | 26 |

| Kew | 4 | 8 | 19 | 14 | 22 | 18 | 11 | 4 |

+---------------+-----+-----+-----+--------+--------+-----+-----+------+

Lunar Influence.

§ 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 Sabine[55] investigated the nature of the lunar

diurnal variation in declination 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 the _west_. 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).

+----------+-----------+-----------+-----------+-----------+-----------+-----------+

| Hour. | 1858-1862.| 1843-1848.| 1883-1899.| 1843-1847.| 1842-1846.| 1841-1848.|

+----------+-----------+-----------+-----------+-----------+-----------+-----------+

| 0 | +103 | +315 | -70 | - 43 | -148 | - 98 |

| 1 | +160 | +275 | -63 | - 5 | -107 | -138 |

| 2 | +140 | +158 | -39 | + 37 | - 35 | -142 |

| 3 | + 33 | + 2 | - 8 | + 70 | + 43 | -107 |

| 4 | + 10 | -153 | +38 | + 85 | +108 | - 45 |

| 5 | - 67 | -265 | +63 | + 77 | +140 | + 27 |

| 6 | -150 | -302 | +87 | + 48 | +132 | + 88 |

| 7 | -188 | -255 | +77 | + 5 | + 82 | +122 |

| 8 | -160 | -137 | +40 | - 43 | + 5 | +120 |

| 9 | - 78 | + 7 | - 4 | - 82 | - 78 | + 82 |

| 10 | + 2 | +178 | -45 | -102 | -143 | + 17 |

| 11 | + 92 | +288 | -80 | - 98 | -177 | - 57 |

| 12 | +160 | +323 | -87 | - 73 | -165 | -120 |

| 13 | +188 | +272 | -68 | - 32 | -112 | -152 |

| 14 | +158 | +148 | -43 | + 13 | - 30 | -147 |

| 15 | + 90 | - 17 | - 8 | + 52 | + 58 | -105 |

| 16 | + 10 | -180 | +30 | + 73 | +132 | - 35 |

| 17 | - 85 | -297 | +62 | + 73 | +172 | + 45 |

| 18 | -142 | -337 | +72 | + 52 | +168 | +112 |

| 19 | -163 | -290 | +68 | + 17 | +122 | +152 |

| 20 | -147 | -170 | +52 | - 25 | + 45 | +152 |

| 21 | -123 | - 7 | + 8 | - 58 | - 40 | +113 |

| 22 | - 40 | +155 | -28 | - 73 | -112 | + 47 |

| 23 | + 27 | +265 | -56 | - 68 | -153 | - 30 |

+----------+-----------+-----------+-----------+-----------+-----------+-----------+

| parture /| 105 | 200 | 50 | 54 | 104 | 93 |

+----------+-----------+-----------+-----------+-----------+-----------+-----------+

| Range | 376 | 660 | 174 | 187 | 349 | 304 |

+----------+-----------+-----------+-----------+-----------+-----------+-----------+

Lunar action has been specially studied in connexion with observations

from India and Java. Broun[56] at Trivandrum and C. Chambers[57] at

Kolaba investigated lunar action from a variety of aspects. At Batavia

van der Stok[58] and more recently S. Figee[59] have 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 other tropical 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, 3.1[gamma] in H and

3.5[gamma] in V, whereas the corresponding ranges in June are only

0´.13, 1.1[gamma] and 2.2[gamma] 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.

+----------+---------------+----------------+----------------+----------------+----------------+

+----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+

| Hour. | W. | S. | W. | S. | W. | S. | W. | S. | W. | S. |

+----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+

| 0 | +30 | -170 | - 1 | +25 | -15 | - 56 | - 9 | + 4 | - 17 | -47 |

| 1 | +21 | -147 | -23 | +49 | -40 | - 87 | -54 | +20 | - 61 | -67 |

| 2 | + 5 | - 83 | -49 | +69 | -25 | -107 | -82 | +37 | - 62 | -76 |

| 3 | - 5 | - 12 | -51 | +47 | -21 | - 76 | -83 | +24 | - 59 | -55 |

| 4 | + 1 | + 76 | -37 | +43 | -13 | - 59 | -58 | +18 | - 39 | -38 |

| 5 | - 8 | +134 | -23 | +12 | +10 | - 9 | -27 | +11 | - 4 | - 3 |

| 6 | - 7 | +181 | - 2 | -21 | +21 | + 43 | + 9 | - 6 | + 23 | +35 |

| 7 | -10 | +164 | +30 | -12 | +23 | + 45 | +55 | + 8 | + 47 | +43 |

| 8 | - 7 | + 86 | +36 | -21 | +38 | + 52 | +71 | - 1 | + 68 | +45 |

| 9 | - 8 | 0 | +28 | -23 | +46 | + 30 | +64 | -16 | + 71 | +19 |

| 10 | - 5 | - 85 | +34 | -20 | +13 | + 13 | +54 | -21 | + 38 | + 1 |

| 11 | -15 | -144 | +27 | -11 | -12 | - 6 | +31 | -19 | + 5 | -15 |

| 12 | - 9 | -164 | +19 | - 5 | -47 | - 23 | 0 | -19 | - 41 | -29 |

| 13 | + 1 | -136 | - 3 | +17 | -59 | - 46 | -36 | - 2 | - 69 | -41 |

| 14 | - 7 | - 79 | -13 | +27 | -66 | - 44 | -55 | +14 | - 84 | -32 |

| 15 | - 8 | - 8 | -32 | +25 | -53 | - 37 | -74 | +14 | - 82 | -26 |

| 16 | -12 | + 72 | -37 | +25 | -34 | - 17 | -70 | +26 | - 64 | - 2 |

| 17 | -13 | +137 | -33 | + 4 | - 1 | + 28 | -47 | +21 | - 24 | +35 |

| 18 | -21 | +165 | - 2 | -10 | +20 | + 47 | + 8 | +12 | + 21 | +47 |

| 19 | -12 | +147 | +21 | -42 | +44 | + 81 | +53 | -14 | + 64 | +64 |

| 20 | +10 | + 95 | +21 | -62 | +75 | +107 | +71 | -28 | +100 | +80 |

| 21 | +13 | + 4 | +26 | -70 | +65 | + 98 | +72 | -44 | + 92 | +65 |

| 22 | +25 | - 82 | +35 | -41 | +35 | + 35 | +68 | -38 | + 64 | +12 |

| 23 | +36 | -147 | +34 | - 4 | - 7 | - 14 | +44 | -13 | + 15 | -19 |

+----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+

| parture /| 12 | 150 | 26 | 29 | 33 | 48 | 50 | 18 | 51 | 37 |

+----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+

| Range | 57 | 351 | 87 | 139 | 141 | 214 | 155 | 81 | 184 | 156 |

+----------+-------+-------+--------+-------+--------+-------+--------+-------+--------+-------+

The question whether lunar influence increases with sun-spot frequency

is obviously of considerable theoretical interest. Balfour Stewart in

the 9th edition of this encyclopaedia gave some data indicating an

appreciably enhanced lunar influence at Trivandrum during years of

sun-spot maximum, but he hesitated to accept the result as finally

proved. Figee recently investigated this point at Batavia, but with

inconclusive results. Attempts have also been made to ascertain how

lunar influence depends on the moon's declination and phase, and on

her distance from the earth. The difficulty in these investigations is

that we are dealing with a small effect, and a very long series of

data would be required satisfactorily to eliminate other periodic

influences.

Planetary Influence.

§ 41. From an analysis of seventeen years data at St Petersburg and

Pavlovsk, Leyst[60] concluded that all the principal planets sensibly

influence the earth's magnetism. According to his figures, all the

planets except Mercury--whose influence he found opposite to that of

the others--when nearest the earth tended to deflect the declination

magnet at St Petersburg to the west, and also increased the range of

the diurnal inequality of declination, the latter effect being the

more conspicuous. Schuster,[61] who has considered the evidence

advanced by Leyst from the mathematical standpoint, considers it to be

inconclusive.

Magnetic Surveys.

§ 42. The best way of carrying out a magnetic survey depends on where

it has to be made and on the object in view. The object that probably

still comes first in importance is a knowledge of the declination, of

sufficient accuracy for navigation in all navigable waters. One might

thus infer that magnetic surveys consist mainly of observations at

sea. This cannot however be said to be true of the past, whatever it

may be of the future, and this for several reasons. Observations at

sea entail the use of a ship, specially constructed so as to be free

from disturbing influence, and so are inherently costly; they are

also apt to be of inferior accuracy. It might be possible in quiet

weather, in a large vessel free from vibration, to observe with

instruments of the highest precision such as a unifilar magnetometer,

but in the ordinary surveying ship apparatus of less sensitiveness has

to be employed. The declination is usually determined with some form

of compass. The other elements most usually found directly at sea are

the inclination and the total force, the instrument employed being a

special form of inclinometer, such as the Fox circle, which was

largely used by Ross in the Antarctic, or in recent years the

Lloyd-Creak. This latter instrument differs from the ordinary

dip-circle fitted for total force observations after H. Lloyd's method

mainly in that the needles rest in pivots instead of on agate edges.

To overcome friction a projecting pin on the framework is scratched

with a roughened ivory plate.

The most notable recent example of observations at sea is afforded by

the cruises of the surveying ships "Galilee" and "Carnegie" under the

auspices of the Carnegie Institution of Washington, which includes in

its magnetic programme a general survey. To see where the ordinary

land survey assists navigation, let us take the case of a country with

a long seaboard. If observations were taken every few miles along the

coast results might be obtained adequate for the ordinary wants of

coasting steamers, but it would be difficult to infer what the

declination would be 50 or even 20 miles off shore at any particular

place. If, however, the land area itself is carefully surveyed, one

knows the trend of the lines of equal declination, and can usually

extend them with considerable accuracy many miles out to sea. One also

can tell what places if any on the coast suffer from local

disturbances, and thus decide on the necessity of special

observations. This is by no means the only immediately useful purpose

which is or may be served by magnetic surveys on land. In Scandinavia

use has been made of magnetic observations in prospecting for iron

ore. There are also various geological and geodetic problems to whose

solution magnetic surveys may afford valuable guidance. Among the most

important recent surveys may be mentioned those of the British Isles

by A. Rücker and T. E. Thorpe,[62] of France and Algeria by

Moureaux,[63] of Italy by Chistoni and Palazzo,[64] of the Netherlands

by Van Ryckevorsel,[65] of South Sweden by Carlheim Gyllenskiöld,[66]

of Austria-Hungary by Liznar,[67] of Japan by Tanakadate,[68] of the

East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A

survey of the United States has been proceeding for a good many years,

and many results have appeared in the publications of the U.S. Coast

and Geodetic Survey, especially Bauer's _Magnetic Tables and Magnetic

Charts_, 1908. Additions to our knowledge may also be expected from

surveys of India, Egypt and New Zealand.

For the satisfactory execution of a land survey, the observers must

have absolute instruments such as the unifilar magnetometer and dip

circle, suitable for the accurate determination of the magnetic

elements, and they must be able to fix the exact positions of the

spots where observations are taken. If, as usual, the survey occupies

several years, what is wanted is the value of the elements not at the

actual time of observation, but at some fixed epoch, possibly some

years earlier or later. At a magnetic observatory, with standardized

records, the difference between the values of a magnetic element at

any two specified instants can be derived from the magnetic curves.

But at an ordinary survey station, at a distance from an observatory,

the information is not immediately available. Ordinarily the reduction

to a fixed epoch is done in at least two stages, a correction being

applied for secular change, and a second for the departure from the

mean value for the day due to the regular diurnal inequality and to

disturbance.

The reduction to a fixed epoch is at once more easy and more accurate

if the area surveyed contains, or has close to its borders, a well

distributed series of magnetic observatories, whose records are

comparable and trustworthy. Throughout an area of the size of France

or Germany, the secular change between any two specified dates can

ordinarily be expressed with sufficient accuracy by a formula of the

type

[delta] = [delta]0 + a(l - l0) + b([lambda] - [lambda]0) (i),

where [delta] denotes secular change, l latitude and [lambda]

longitude, the letters with suffix _0_ relating to some convenient

central position. The constants [delta]0, a, b are to be determined

from the observed secular changes at the fixed observatories whose

geographical co-ordinates are accurately known. Unfortunately, as a

rule, fixed observatories are few in number and not well distributed

for survey purposes; thus the secular change over part at least of the

area has usually to be found by repeating the observations after some

years at several of the field stations. The success attending this

depends on the exactitude with which the sites can be recovered, on

the accuracy of the observations, and on the success with which

allowance is made for diurnal changes, regular and irregular. It is

thus desirable that the observations at repeat stations should be

taken at hours when the regular diurnal changes are slow, and that

they should not be accepted unless taken on days that prove to be

magnetically quiet. Unless the secular change is exceptionally rapid,

it will usually be most convenient in practice to calculate it from or

to the middle of the month, and then to allow for the difference

between the mean value for the month and the value at the actual hour

of observation. There is here a difficulty, inasmuch as the latter

part of the correction depends on the diurnal inequality, and so on

the local time of the station. No altogether satisfactory method of

surmounting this difficulty has yet been proposed. Rücker and Thorpe

in their British survey assumed that the divergence from the mean

value at any hour at any station might be regarded as made up of a

regular diurnal inequality, identical with that at Kew when both were

referred to _local_ time, and of a disturbance element identical with

that existing at the same absolute time at Kew. Suppose, for instance,

that at hour h G.M.T. the departure at Kew from the mean value for the

month is d, then the corresponding departure from the mean at a

station [lambda] degrees west of Kew is d - e, where e is the increase

in the element at Kew due to the regular diurnal inequality between

hour h - [lambda]/15 and hour h. This procedure is simple, but is

exposed to various criticisms. If we define a diurnal inequality as

the result obtained by combining hourly readings from all the days of

a month, we can assign a definite meaning to the diurnal inequality

for a particular month of a particular year, and after the curves have

been measured we can give exact numerical figures answering to this

definition. But the diurnal inequality thus obtained differs, as has

been pointed out, from that derived from a limited number of the

quietest days of the month, not merely in amplitude but in phase, and

the view that the diurnal changes on any individual day can be

regarded as made up of a regular diurnal inequality of definite

character and of a disturbance element is an hypothesis which is

likely at times to be considerably wide of the mark. The extent of the

error involved in assuming the regular diurnal inequality the same in

the north of Scotland, or the west of Ireland, as in the south-east of

England remains to be ascertained. As to the disturbance element, even

if the disturbing force were of given magnitude and direction all over

the British Isles--which we now know is often very far from the

case--its effects would necessarily vary very sensibly owing to the

considerable variation in the direction and intensity of the local

undisturbed force. If observations were confined to hours at which the

regular diurnal changes are slow, and only those taken on days of

little or no disturbance were utilized, corrections combining the

effects of regular and irregular diurnal changes could be derived from

the records of fixed observations, supposed suitably situated,

combined in formulae of the same type as (i).

§ 43. The field results having been reduced to a fixed epoch, it

remains to combine them in ways likely to be useful. In most cases the

results are embodied in charts, usually of at least two kinds, one set

showing only general features, the other the chief local

peculiarities. Charts of the first kind resemble the world charts

(figs. 1 to 4) in being free from sharp twistings and convolutions. In

these the declination for instance at a fixed geographical position on

a particular isogonal is to be regarded as really a mean from a

considerable surrounding area.

Various ways have been utilized for arriving at these _terrestrial

isomagnetics_--as Rücker and Thorpe call them--of which an elaborate

discussion has been made by E. Mathias.[69] From a theoretical

standpoint the simplest method is perhaps that employed by Liznar for

Austria-Hungary. Let l and [lambda] represent latitude and longitude

relative to a certain central station in the area. Then assume that

throughout the area the value E of any particular magnetic element is

given by a formula

E = E0 + al + b[lambda] + cl² + d[lambda]² + el[lambda],

where E0, a, b, c, d, e are absolute constants to be determined from

the observations. When determining the constants, we write for E in

the equation the observed value of the element (corrected for secular

change, &c.) at each station, and for l and [lambda] the latitude and

longitude of the station relative to the central station. Thus each

station contributes an equation to assist in determining the six

constants. They can thus be found by least squares or some simpler

method. In Liznar's case there were 195 stations, so that the labour

of applying least squares would be considerable. This is one objection

to the method. A second is that it may allow undesirably large weight

to a few highly disturbed stations. In the case of the British Isles,

Rücker and Thorpe employed a different method. The area was split up

into _districts_. For each district a mean was formed of the observed

values of each element, and the mean was assigned to an imaginary

central station, whose geographical co-ordinates represented the mean

of the geographical co-ordinates of the actual stations. Want of

uniformity in the distribution of the stations may be allowed for by

weighting the results. Supposing E0 the value of the element found for

the central station of a district, it was assumed that the value E at

any actual station whose latitude and longitude exceeded those of the

central station by l and [lambda] was given by E = E0 + al +

b[lambda], with a and b constants throughout the district. Having

found E0, a and b, Rücker and Thorpe calculated values of the element

for points defined by whole degrees of longitude (from Greenwich) and

half degrees of latitude. Near the common border of two districts

there would be two calculated values, of which the arithmetic mean was

accepted.

The next step was to determine by interpolation where isogonals--or

other isomagnetic lines--cut successive lines of latitude. The curves

formed by joining these successive points of intersection were called

_district_ lines or curves. Rücker and Thorpe's next step was to

obtain formulae by trial, giving smooth curves of continuous

curvature--terrestrial isomagnetics--approximating as closely as

possible to the district lines. The curves thus obtained had somewhat

complicated formulae. For instance, the isogonals south of 54°.5

latitude were given for the epoch Jan. 1, 1891 by

D = 18° 37´ + 18´.5(l - 49.5) - 3´.5 cos {45°(l - 49.5)}

+ {26´.3 + 1´.5(l - 49.5)} ([lambda] - 4)

+ 0´.01([lambda] - 4)² (l - 54.5)²,

where D denotes the westerly declination. Supposing, what is at least

approximately true, that the secular change in Great Britain since

1891 has been uniform south of lat. 54°.5, corresponding formulae for

the epochs Jan. 1, 1901, and Jan. 1, 1906, could be obtained by

substituting for 18° 37´ the values 17° 44´ and 17° 24´ respectively.

In their very laborious and important memoir E. Mathias and B.

Baillaud[69] have applied to Rücker and Thorpe's observations a method

which is a combination of Rücker and Thorpe's and of Liznar's. Taking

Rücker and Thorpe's nine districts, and the magnetic data found for

the nine imaginary central stations, they employed these to determine

the six constants of Liznar's formula. This is an immense

simplification in arithmetic. The declination formula thus obtained

for the epoch Jan. 1, 1891, was

D = 20° 45´.89 + .53474[lambda] + .34716l + .000021[lambda]²

+ .000343l[lambda] - .000239l²,

where l + (53° 30´.5) represents the latitude, and ([lambda] + 5°

35´.2) the west longitude of the station. From this and the

corresponding formulae for the other elements, values were calculated

for each of Rücker and Thorpe's 882 stations, and these were compared

with the observed values. A complete record is given of the

differences between the observed and calculated values, and of the

corresponding differences obtained by Rücker and Thorpe from their own

formulae. The mean numerical (calculated ~ observed) differences from

the two different methods are almost exactly the same--being

approximately 10´ for declination, 5´½ for inclination, and 70[gamma]

for horizontal force. The applications by Mathias[69] of his method to

the survey data of France obtained by Moureaux, and those of the

Netherlands obtained by van Rïjckevorsel, appear equally successful.

The method dispenses entirely with district curves, and the parabolic

formulae are perfectly straightforward both to calculate and to apply;

they thus appear to possess marked advantages. Whether the method

could be applied equally satisfactorily to an area of the size of

India or the United States actual trial alone would show.

Local Disturbances.

§ 44. Rücker and Thorpe regarded their terrestrial isomagnetics and

the corresponding formulae as representing the normal field that would

exist in the absence of disturbances peculiar to the neighbourhood.

Subtracting the forces derived from the formulae from those observed,

we obtain forces which may be ascribed to regional disturbance.

When the vertical disturbing force is downwards, or the observed

vertical component larger than the calculated, Rücker and Thorpe

regard it as positive, and the loci where the largest positive values

occur they termed _ridge lines_. The corresponding loci where the

largest negative values occur were called _valley lines_. In the

British Isles Rücker and Thorpe found that almost without exception,

in the neighbourhood of a ridge line, the horizontal component of the

disturbing force pointed towards it, throughout a considerable area on

both sides. The phenomena are similar to what would occur if ridge

lines indicated the position of the summits of underground masses of

magnetic material, magnetized so as to attract the north-seeking pole

of a magnet. Rücker and Thorpe were inclined to believe in the real

existence of these subterranean magnetic mountains, and inferred that

they must be of considerable extent, as theory and observation alike

indicate that thin basaltic sheets or dykes, or limited masses of trap

rock, produce no measurable magnetic effect except in their immediate

vicinity. In support of their conclusions, Rücker and Thorpe dwell on

the fact that in the United Kingdom large masses of basalt such as

occur in Skye, Mull, Antrim, North Wales or the Scottish coalfield,

are according to their survey invariably centres of attraction for the

north-seeking pole of a magnet. Various cases of repulsion have,

however, been described by other observers in the northern hemisphere.

§ 45. Rücker and Thorpe did not make a very minute examination of

disturbed areas, so that purely local disturbances larger than any

noticed by them may exist in the United Kingdom. But any that exist

are unlikely to rival some that have been observed elsewhere, notably

those in the province of Kursk in Russia described by Moureaux[70] and

by E. Leyst.[71] In Kursk Leyst observed declinations varying from 0°

to 360°, inclinations varying from 39°.1 to 90°; he obtained values of

the horizontal force varying from 0 to 0.856 C.G.S., and values of the

vertical force varying from 0.371 to 1.836. Another highly disturbed

Russian district Krivoi Rog (48° N. lat. 33° E. long.) was

elaborately surveyed by Paul Passalsky.[72] The extreme values

observed by him differed, the declination by 282° 40´, the inclination

by 41° 53´, horizontal force by 0.658, and vertical force by 1.358. At

one spot a difference of 116°½ was observed between the declinations

at two positions only 42 metres apart. In cases such as the last

mentioned, the source of disturbance comes presumably very near the

surface. It is improbable that any such enormously rapid changes of

declination can be experienced anywhere at the surface of a deep

ocean. But in shallow water disturbances of a not very inferior order

of magnitude have been met with. Possibly the most outstanding case

known is that of an area, about 3 m. long by 1¼ m. at its widest, near

Port Walcott, off the N.W. Australian coast. The results of a minute

survey made here by H.M.S. "Penguin" have been discussed by Captain E.

W. Creak.[73] Within the narrow area specified, declination varied

from 26° W. to 56° E., and inclination from 50° to nearly 80°, the

observations being taken some 80 ft. above sea bottom. Another

noteworthy case, though hardly comparable with the above, is that of

East Loch Roag at Lewis in the Hebrides. A survey by H.M.S. "Research"

in water about 100 ft. deep--discussed by Admiral A. M.

Field[74]--showed a range of 11° in declination. The largest observed

disturbances in horizontal and vertical force were of the order 0.02

and 0.05 C.G.S. respectively. An interesting feature in this case was

that vertical force was reduced, there being a well-marked valley

line.

In some instances regional magnetic disturbances have been found to be

associated with geodetic anomalies. This is true of an elongated area

including Moscow, where observations were taken by Fritsche.[75]

Again, Eschenhagen[76] detected magnetic anomalies in an area

including the Harz Mountains in Germany, where deflections of the

plumb line from the normal had been observed. He found a magnetic

ridge line running approximately parallel to the line of no deflection

of the plumb line.

§ 46. A question of interest, about which however not very much is

known, is the effect of local disturbance on secular change and on the

diurnal inequality. The determination of secular change in a highly

disturbed locality is difficult, because an unintentional slight

change in the spot where the observations are made may wholly falsify

the conclusions drawn. When the disturbed area is very limited in

extent, the magnetic field may reasonably be regarded as composed of

the normal field that would have existed in the absence of local

disturbance, plus a disturbance field arising from magnetic material

which approaches nearly if not quite to the surface. Even if no

sensible change takes place in the disturbance field, one would hardly

expect the secular change to be wholly normal. The changes in the

rectangular components of the force may possibly be the same as at a

neighbouring undisturbed station, but this will not give the same

change in declination and inclination. In the case of the diurnal

inequality, the presumption is that at least the declination and

inclination changes will be influenced by local disturbance. If, for

example, we suppose the diurnal inequality to be due to the direct

influence of electric currents in the upper atmosphere, the

declination change will represent the action of the component of a

force of given magnitude which is perpendicular to the position of the

compass needle. But when local disturbance exists, the direction of

the needle and the intensity of the controlling field are both altered

by the local disturbance, so it would appear natural for the

declination changes to be influenced also. This conclusion seems borne

out by observations made by Passalsky[72] at Krivoi Rog, which showed

diurnal inequalities differing notably from those experienced at the

same time at Odessa, the nearest magnetic observatory. One station

where the horizontal force was abnormally low gave a diurnal range of

declination four times that at Odessa; on the other hand, the range of

the horizontal force was apparently reduced. It would be unsafe to

draw general conclusions from observations at two or three stations,

and much completer information is wanted, but it is obviously

desirable to avoid local disturbance when selecting a site for a

magnetic observatory, assuming one's object is to obtain data

reasonably applicable to a large area. In the case of the older

observatories this consideration seems sometimes to have been lost

sight of. At Mauritius, for instance, inside of a circle of only 56

ft. radius, having for centre the declination pillar of the absolute

magnetic hut of the Royal Alfred Observatory, T. F. Claxton[77] found

that the declination varied from 4° 56´ to 13° 45´ W., the inclination

from 50° 21´ to 58° 34´ S., and the horizontal force from 0.197 to

0.244 C.G.S. At one spot he found an alteration of 1°1/3 in the

declination when the magnet was lowered from 4 ft. above the ground to

2. Disturbances of this order could hardly escape even a rough

investigation of the site.

Gaussian Potential and Constants.

§ 47. If we assume the magnetic force on the earth's surface derivable

from a potential V, we can express V as the sum of two series of solid

spherical harmonics, one containing negative, the other positive

integral powers of the radius vector r from the earth's centre. Let

[lambda] denote east longitude from Greenwich, and let µ = cos(½[pi] -

l), where l is latitude; and also let

_ _

| (n - m)(n - m - 1) |

H_n^m = (1 - µ²)^(½m) |µ^(n-m) - ------------------ µ^(n-m-2) + ...|,

|_ 2(2n - 1) _|

where n and m denote any positive integers, m being not greater than

n. Then denoting the earth's radius by R, we have

V/R = [Sigma](R/r)^(n+1) [H_n^m (g_n^m cos m[lambda] + h_n^m sin m[lambda])]

+ [Sigma](r/R)^n [H_n^m (g_(-n)^m cos m[lambda] + h_(-n)^m sin m[lambda])],

where [Sigma] denotes summation of m from 0 to n, followed by

summation of n from 0 to [infinity]. In this equation g_n^m, &c. are

constants, those with positive suffixes being what are generally

termed _Gaussian constants_. The series with negative powers of r

answers to forces with a source internal to the earth, the series with

positive powers to forces with an external source. Gauss found that

forces of the latter class, if existent, were very small, and they are

usually left out of account. There are three Gaussian constants of the

first order, g1^0, g1¹, h1¹, five of the second order, seven of the

third, and so on. The coefficient of a Gaussian constant of the n^th

order is a spherical harmonic of the n^th degree. If R be taken as

unit length, as is not infrequent, the first order terms are given by

V1 = r^(-2) [g1^0 sin l + (g1¹ cos [lambda] + h1¹ sin [lambda]) cos l].

The earth is in reality a spheroid, and in his elaborate work on the

subject J. C. Adams[78] develops the treatment appropriate to this

case. Here we shall as usual treat it as spherical. We then have for

the components of the force at the surface

X = -R^(-1)(1 - µ²)^½ (dV/dµ) towards the astronomical north,

Y = -R^(-1)(1 - µ²)^-½ (dV/d[lambda]) " " " west,

Z = -dV/dr vertically downwards.

Supposing the Gaussian constants known, the above formulae would give

the force all over the earth's surface. To determine the Gaussian

constants we proceed of course in the reverse direction, equating the

observed values of the force components to the theoretical values

involving g_n^m, &c. If we knew the values of the component forces at

regularly distributed stations all over the earth's surface, we could

determine each Gaussian constant independently of the others. Our

knowledge however of large regions, especially in the Arctic and

Antarctic, is very scanty, and in practice recourse is had to methods

in which the constants are not determined independently. The

consequence is unfortunately that the values found for some of the

constants, even amongst the lower orders, depend very sensibly on how

large a portion of the polar regions is omitted from the calculations,

and on the number of the constants of the higher orders which are

retained.

TABLE XLIV.--Gaussian Constants of the First Order.

+------+---------+---------+---------+---------+---------+---------+---------+

| | 1829 | | | | | | |

| | Erman- | 1830 | 1845 | 1880 | 1885 | 1885 | 1885 |

+------+---------+---------+---------+---------+---------+---------+---------+

| g1^0 | +.32007 | +.32348 | +.32187 | +.31684 | +.31572 | +.31735 | +.31635 |

| g1^1 | +.02835 | +.03111 | +.02778 | +.02427 | +.02481 | +.02356 | +.02414 |

| h1^1 | -.06011 | -.06246 | -.05783 | -.06030 | -.06026 | -.05984 | -.05914 |

+------+---------+---------+---------+---------+---------+---------+---------+

Table XLIV. gives the values obtained for the Gaussian constants of

the first order in some of the best-known computations, as collected

by W. G. Adams.[79]

§ 48. Allowance must be made for the difference in the epochs, and for

the fact that the number of constants assumed to be worth retaining

was different in each case. Gauss, for instance, assumed 24 constants

sufficient, whilst in obtaining the results given in the table J. C.

Adams retained 48. Some idea of the uncertainty thus arising may be

derived from the fact that when Adams assumed 24 constants sufficient,

he got instead of the values in the table the following:--

g1^0 g1¹ h1¹

1842-1845 +.32173 +.02833 -.05820

1880 +.31611 +.02470 -.06071

Some of the higher constants were relatively much more affected. Thus,

on the hypotheses of 48 and of 24 constants respectively, the values

obtained for g2^0 in 1842-1845 were -.00127 and -.00057, and those

obtained for h3¹ in 1880 were +.00748 and +.00573. It must also be

remembered that these values assume that the series in positive powers

of r, with coefficients having negative suffixes, is absolutely

non-existent. If this be not assumed, then in any equation determing X

or Y, g_n^m must be replaced by g_n^m + g_(-n)^m, and in any equation

determining Z by g_n^m - n/(n + 1) g_n^m; similar remarks apply to

h_n^m and h_(-n)^m. It is thus theoretically possible to check the

truth of the assumption that the positive power series is non-existent

by comparing the values obtained for g_n^m and h_n^m from the X and Y

or from the Z equations, when g_(-n)^m and h_(-n)^m are assumed zero.

If the values so found differ, values can be found for g_(-n)^m and

h_(-n)^m which will harmonize the two sets of equations. Adams gives

the values obtained from the X, Y and the Z equations separately for

the Gaussian constants. The following are examples of the values

thence deducible for the coefficients of the positive power series:--

g_(-1)^0 g_(-1)^1 h_(-1)^1 g_(-4)^0 g_(-5)^0 g_(-6)^0

1842-1845 +.0018 -.0002 -.0014 +.0064 +.0072 +.0124

1880 -.0002 -.0012 +.0015 -.0043 -.0021 -.0013

Compared to g4^0, g5^0 and g6^0 the values here found for g_(-4)^0,

g_(-5)^0 and g_(-6)^0 are far from insignificant, and there would be

no excuse for neglecting them if the observational data were

sufficient and reliable. But two outstanding features claim attention,

first the smallness of g_(-1)^0, g_(-1)^1 and h_(-1)^1, the

coefficients least likely to be affected by observational

deficiencies, and secondly the striking dissimilarity between the

values obtained for the two epochs. The conclusion to which these and

other facts point is that observational deficiencies, even up to the

present date, are such that no certain conclusion can be drawn as to

the existence or non-existence of the positive power series. It is

also to be feared that considerable uncertainties enter into the

values of most of the Gaussian constants, at least those of the higher

orders. The introduction of the positive power series necessarily

improves the agreement between observed and calculated values of the

force, but it is more likely than not to be disadvantageous

physically, if the differences between observed values and those

calculated from the negative power series alone arise in large measure

from observational deficiencies.

TABLE XLV.--Axis and Moment of First Order Gaussian Coefficients.

+-------+-------------------+-----------+------------+--------------+

+-------+-------------------+-----------+------------+--------------+

| | | ° ´ | ° ´ | |

| 1650 | H. Fritsche | 82 50 | 42 55 | .3260 |

| 1836 | " | 78 27 | 63 35 | .3262 |

| 1845 | J. C. Adams | 78 44 | 64 20 | .3282 |

| 1880 | " | 78 24 | 68 4 | .3234 |

| 1885 | Neumayer-Petersen | | | |

| | and Bauer | 78 3 | 67 3 | .3224 |

| 1885 | Neumayer, Schmidt | 78 34 | 68 31 | .3230 |

+-------+-------------------+-----------+------------+--------------+

§ 49. The first order Gaussian constants have a simple physical

meaning. The terms containing them represent the potential arising

from the uniform magnetization of a sphere parallel to a fixed axis,

the moment M of the spherical magnet being given by

M = R³{(g1^0)² + (g1^1)² + (h1^1)²}^½,

where R is the earth's radius. The position of the north end of the

axis of this uniform magnetization and the values of M/R^3, derived

from the more important determinations of the Gaussian constants, are

given in Table XLV. The data for 1650 are of somewhat doubtful value.

If they were as reliable as the others, one would feel greater

confidence in the reality of the apparent movement of the north end of

the axis from east to west. The table also suggests a slight

diminution in M since 1845, but it is open to doubt whether the

apparent change exceeds the probable error in the calculated values.

It should be carefully noticed that the data in the table apply only

to the first order Gaussian terms, and so only to a portion of the

earth's magnetization, and that the Gaussian constants have been

calculated on the assumption that the negative power series alone

exists. The field answering to the first order terms--or what Bauer

has called the _normal_ field--constitutes much the most important

part of the whole magnetization. Still what remains is very far from

negligible, save for rough calculations. It is in fact one of the weak

points in the Gaussian analysis that when one wishes to represent the

observed facts with high accuracy one is obliged to retain so many

terms that calculation becomes burdensome.

Earth-air Currents.

§ 50. The possible existence of a positive power series is not the

only theoretical uncertainty in the Gaussian analysis. There is the

further possibility that part of the earth's magnetic field may not

answer to a potential at all. Schmidt[80] in his calculation of

Gaussian constants regarded this as a possible contingency, and the

results he reached implied that as much as 2 or 3% of the entire field

had no potential. If the magnetic force F on the earth's surface comes

from a potential, then the line integral [int]F ds taken round any

closed circuit s should vanish. If the integral does not vanish, it

equals 4[pi]I, where I is the total electric current traversing the

area bounded by s. A + sign in the result of the integration means

that the current is downwards (i.e. from air to earth) or upwards,

according as the direction of integration round the circuit, as viewed

by an observer above ground, has been clockwise or anti-clockwise. In

applications of the formula by W. von Bezold[81] and Bauer[82] the

integral has been taken along parallels of latitude in the direction

west to east. In this case a + sign indicates a resultant upward

current over the area between the parallel of latitude traversed and

the north geographical pole. The difference between the results of

integration round two parallels of latitude gives the total vertical

current over the zone between them. Schmidt's final estimate of the

average intensity of the earth-air current, irrespective of sign, for

the epoch 1885 was 0.17 ampere per square kilometre. Bauer employing

the same observational data as Schmidt, reached somewhat similar

conclusions from the differences between integrals taken round

parallels of latitude at 5° intervals from 60° N. to 60° S. H.

Fritsche[83] treating the problem similarly, but for two epochs, 1842

and 1885, got conspicuously different results for the two epochs,

Bauer[84] has more recently repeated his calculations, and for three

epochs, 1842-1845 (Sabine's charts), 1880 (Creak's charts), and 1885

(Neumayer's charts), obtaining the mean value of the current per sq.

km. for 5° zones. Table XLVI. is based on Bauer's figures, the unit

being 0.001 ampere, and + denoting an _upwardly_ directed current.

TABLE XLVI.--Earth-air Currents, after Bauer.

+-------------+----------------------+---------------------+

| | Northern Hemisphere. | Southern Hemisphere.|

| Latitude. +--------+------+------+-------+------+------+

| | 1842-5.| 1880.| 1885.|1842-5.| 1880.| 1885.|

+-------------+--------+------+------+-------+------+------+

| 0° to 15° | - 1 | -32 | -34 | +66 | + 30 | + 36 |

| 15° " 30° | -70 | -59 | -68 | + 2 | - 62 | - 63 |

| 30° " 45° | + 3 | +14 | -22 | +26 | - 11 | - 14 |

| 45° " 60° | -31 | -21 | +78 | + 5 | +276 | +213 |

+-------------+--------+------+------+-------+------+------+

In considering the significance of the data in Table XLVI., it should

be remembered that the currents must be regarded as mean values

derived from all hours of the day, and all months of the year.

Currents which were upwards during certain hours of the day, and

downwards during others, would affect the diurnal inequality; while

currents which were upwards during certain months, and downwards

during others, would cause an annual inequality in the absolute

values. Thus, if the figures be accepted as real, we must suppose that

between 15° N. and 30° N. there are preponderatingly downward

currents, and between 0° S. and 15° S. preponderatingly upward

currents. Such currents might arise from meteorological conditions

characteristic of particular latitudes, or be due to the relative

distribution of land and sea; but, whatever their cause, any

considerable real change in their values between 1842 and 1885 seems

very improbable. The most natural cause to which to attribute the

difference between the results for different epochs in Table XLVI. is

unquestionably observational deficiencies. Bauer himself regards the

results for latitudes higher than 45° as very uncertain, but he seems

inclined to accept the reality of currents of the average intensity of

1/30 ampere per sq. km. between 45° N. and 45° S.

Currents of the size originally deduced by Schmidt, or even those of

Bauer's latest calculations, seem difficult to reconcile with the

results of atmospheric electricity (q.v.).

§ 51. There is no single parallel of latitude along the whole of which

magnetic elements are known with high precision. Thus results of

greater certainty might be hoped for from the application of the line

integral to well surveyed countries. Such applications have been made,

e.g. to Great Britain by Rücker,[85] and to Austria by Liznar,[86] but

with negative results. The question has also been considered in detail

by Tanakadate[68] in discussing the magnetic survey of Japan. He makes

the criticism that the taking of a line integral round the _boundary_

of a surveyed area amounts to utilizing the values of the magnetic

elements where least accurately known, and he thus considers it

preferable to replace the line integral by the surface integral.

4[pi]I = [int][int] (dY/dx - dX/dy) dx dy.

He applied this formula not merely to his own data for Japan, but also

to British and Austrian data of Rücker and Thorpe and of Liznar. The

values he ascribes to X and Y are those given by the formulae

calculated to fit the observations. The result reached was "a line of

no current through the middle of the country; in Japan the current is

upward on the Pacific side and downward on the Siberian side; in

Austria it is upward in the north and downward in the south; in Great

Britain upward in the east and downward in the west." The results

obtained for Great Britain differed considerably according as use was

made of Rücker and Thorpe's own district equations or of a series of

general equations of the type subsequently utilized by Mathias.

Tanakadate points out that the fact that his investigations give in

each case a line of no current passing through the middle of the

surveyed area, is calculated to throw doubt on the reality of the

supposed earth-air currents, and he recommends a suspension of

judgment.

§ 52. A question of interest, and bearing a relationship to the

Gaussian analysis, is the law of variation of the magnetic elements

with height above sea-level. If F represent the value at sea-level,

and F + [delta]F that at height h, of any component of force answering

to Gaussian constants of the n^th order, then 1 + [delta]F/F = (1 +

h/R)^(-n-2), where R is the earth's radius. Thus at heights of only a

few miles we have very approximately [delta]F/F = -(n + 2)h/R. As we

have seen, the constants of the first order are much the most

important, thus we should expect as a first approximation [delta]X/X =

[delta]Y/Y = [delta]Z/Z = -3h/R. This equation gives the same rate of

decrease in all three components, and so no change in declination or

inclination. Liznar[86a] compared this equation with the observed

results of his Austrian survey, subdividing his stations into three

groups according to altitude. He considered the agreement not

satisfactory. It must be remembered that the Gaussian analysis,

especially when only lower order terms are retained, applies only to

the earth's field freed from local disturbances. Now observations at

individual high level stations may be seriously influenced not merely

by regional disturbances common to low level stations, but by magnetic

material in the mountain itself. A method of arriving at the vertical

change in the elements, which theoretically seems less open to

criticism, has been employed by A. Tanakadate.[68] If we assume that a

potential exists, or if admitting the possibility of earth-air

currents we assume their effort negligible, we have dX/dz = dZ/dx,

dY/dz = dZ/dy. Thus from the observed rates of change of the vertical

component of force along the parallels of latitude and longitude, we

can deduce the rate of change in the vertical direction of the two

rectangular components of horizontal force, and thence the rates of

change of the horizontal force and the declination. Also we have dZ/dz

= 4[pi][rho] - (dX/dx + dY/dy), where [rho] represents the density of

free magnetism at the spot. The spot being above ground we may neglect

[rho], and thus deduce the variation in the vertical direction of the

vertical component from the observed variations of the two horizontal

components in their own directions. Tanakadate makes a comparison of

the vertical variations of the magnetic elements calculated in the two

ways, not merely for Japan, but also for Austria-Hungary and Great

Britain. In each country he took five representative points, those for

Great Britain being the central stations of five of Rücker and

Thorpe's districts. Table XLVII. gives the mean of the five values

obtained. By method (i.) is meant the formula involving 3h/R, by

method (ii.) Tanakadate's method as explained above. H, V, D, and I

are used as defined in § 5. In the case of H and V unity represents

1[gamma].

TABLE XLVII.--Change per Kilometre of Height.

+---------+-----------------+-----------------+-----------------+

+---------+-------+---------+-------+---------+-------+---------+

| Method. | (i.) | (ii.) | (i.) | (ii.) | (i.) | (ii.) |

+---------+-------+---------+-------+---------+-------+---------+

| H | - 8.1 | - 6.7 | -10.1 | - 8.7 | -13.9 | -14.0 |

| V | -21.2 | -19.4 | -19.0 | -18.1 | -17.1 | -17.4 |

| D (west)| .. | - 0´.04 | .. | + 0´.10 | .. | - 0´.27 |

| I | .. | - 0´.05 | .. | - 0´.06 | .. | - 0´.01 |

+---------+-------+---------+-------+---------+-------+---------+

The - sign in Table XLVII. denotes a decrease in the numerical values

of H, V and I, and a diminution in westerly declination. If we except

the case of the westerly component of force--not shown in the

table--the accordance between the results from the two methods in the

case of Japan is extraordinarily close, and there is no very marked

tendency for the one method to give larger values than the other. In

the case of Great Britain and Austria the differences between the two

sets of calculated values though not large are systematic, the 3h/R

formula invariably showing the larger reduction with altitude in both

H and V. Tanakadate was so satisfied with the accordance of the two

methods in Japan, that he employed his method to reduce all observed

Japanese values to sea-level. At a few of the highest Japanese

stations the correction thus introduced into the value of H was of

some importance, but at the great majority of the stations the

corrections were all insignificant.

Schuster's Diurnal Variation Potential.

§ 53. Schuster[87] has calculated a potential analogous to the

Gaussian potential, from which the regular diurnal changes of the

magnetic elements all over the earth may be derived. From the mean

summer and winter diurnal variations of the northerly and easterly

components of force during 1870 at St Petersburg, Greenwich, Lisbon

and Bombay, he found the values of 8 constants analogous to Gaussian

constants; and from considerations as to the hours of occurrence of

the maxima and minima of vertical force, he concluded that the

potential, unlike the Gaussian, must proceed in positive powers of r,

and so answer to forces external to the earth. Schuster found,

however, that the calculated amplitudes of the diurnal vertical force

inequality did not accord well with observation; and his conclusion

was that while the original cause of the diurnal variation is

external, and consists probably of electric currents in the

atmosphere, there are induced currents inside the earth, which

increase the horizontal components of the diurnal inequality while

diminishing the vertical. The problem has also been dealt with by H.

Fritsche,[88] who concludes, in opposition to Schuster, that the

forces are partly internal and partly external, the two sets being of

fairly similar magnitude. Fritsche repeats the criticism (already made

in the last edition of this encyclopaedia) that Schuster's four

stations were too few, and contrasts their number with the 27 from

which his own data were derived. On the other hand, Schuster's data

referred to one and the same year, whereas Fritsche's are from epochs

varying from 1841 to 1896, and represent in some cases a single year's

observations, in other cases means from several years. It is clearly

desirable that a fresh calculation should be made, using synchronous

data from a considerable number of well distributed stations; and it

should be done for at least two epochs, one representing large, the

other small sun-spot frequency. The year 1870 selected by Schuster

had, as it happened, a sun-spot frequency which has been exceeded

only once since 1750; so that the magnetic data which he employed were

far from representative of average conditions.

Magnetization of Vases, &c.

§ 54. It was discovered by Folgheraiter[89] that old vases from

Etruscan and other sources are magnetic, and from combined observation

and experiment he concluded that they acquired their magnetization

when cooling after being baked, and retained it unaltered. From

experiments, he derived formulae connecting the magnetization shown by

new clay vases with their orientation when cooling in a magnetic

field, and applying these formulae to the phenomena observed in the

old vases he calculated the magnetic dip at the time and place of

manufacture. His observations led him to infer that in Central Italy

inclination was actually southerly for some centuries prior to 600

B.C., when it changed sign. In 400 B.C. it was about 20°N.; since 100

B.C. the change has been relatively small. L. Mercanton[90] similarly

investigated the magnetization of baked clay vases from the lake

dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800

B.C. The results he obtained were, however, closely similar to those

observed in recent vases made where the inclination was about 63°N.,

and he concluded in direct opposition to Folgheraiter that inclination

in southern Europe has not undergone any very large change during the

last 2500 years. Folgheraiter's methods have been extended to natural

rocks. Thus B. Brunhes[91] found several cases of clay metamorphosed

by adjacent lava flows and transformed into a species of natural

brick. In these cases the clay has a determinate direction of

magnetization agreeing with that of the volcanic rock, so it is

natural to assume that this direction coincided with that of the dip

when the lava flow occurred. In drawing inferences, allowance must of

course be made for any tilting of the strata since the volcanic

outburst. From one case in France in the district of St Flour, where

the volcanic action is assigned to the Miocene Age, Brunhes inferred a

southerly dip of some 75°. Until a variety of cases have been

critically dealt with, a suspension of judgment is advisable, but if

the method should establish its claims to reliability it obviously may

prove of importance to geology as well as to terrestrial magnetism.

Polar Phenomena.

§ 55. Magnetic phenomena in the polar regions have received

considerable attention of late years, and the observed results are of

so exceptional a character as to merit separate consideration. One

feature, the large amplitude of the regular diurnal inequality, is

already illustrated by the data for Jan Mayen and South Victoria Land

in Tables VIII. to XI. In the case, however, of declination allowance

must be made for the small size of H. If a force F perpendicular to

the magnetic meridian causes a change [Delta]D in D then [Delta]D =

F/H. Thus at the "Discovery's" winter quarters in South Victoria Land,

where the value of H is only about 0.36 of that at Kew, a change of

45´ in D would be produced by a force which at Kew would produce a

change of only 16´. Another feature, which, however, may not be

equally general, is illustrated by the data for Fort Rae and South

Victoria Land in Table XVII. It will be noticed that it is the 24-hour

term in the Fourier analysis of the regular diurnal inequality which

is specially enhanced. The station in South Victoria Land--the winter

quarters of the "Discovery" in 1902-1904--was at 77° 51´ S. lat.; thus

the sun did not set from November to February (midsummer), nor rise

from May to July (midwinter). It might not thus have been surprising

if there had been an outstandingly large seasonal variation in the

type of the diurnal inequality. As a matter of fact, however, the type

of the inequality showed exceptionally small variation with the

season, and the amplitude remained large throughout the whole year.

Thus, forming diurnal inequalities for the three midsummer months and

for the three midwinter months, we obtain the following amplitudes for

the range of the several elements[92]:--

D. H. V. I.

Midsummer 64´.1 57[gamma] 58[gamma] 2´.87

Midwinter 26´.8 25[gamma] 18[gamma] 1´.23

The most outstanding phenomenon in high latitudes is the frequency and

large size of the disturbances. At Kew, as we saw in § 25, the

absolute range in D exceeds 20´ on only 12% of the total number of

days. But at the "Discovery's" winter quarters, about sun-spot

minimum, the range exceeded 1° on 70%, 2° on 37%, and 3° on fully 15%

of the total number of days. One day in 25 had a range exceeding 4°.

During the three midsummer months, only one day out of 111 had a range

under 1°, and even at midwinter only one day in eight had a range as

small as 30´. The H range at the "Discovery's" station exceeded

100[gamma] on 40% of the days, and the V range exceeded 100[gamma] on

32% of the days.

The special tendency to disturbance seen in equinoctial months in

temperate latitudes did not appear in the "Discovery's" records in the

Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days,

but on 40% of midsummer days. The preponderance of large movements at

midsummer was equally apparent in the other elements. Thus the

percentage of days having a V range over 200[gamma] was 21 at

midsummer, as against 3 in the four equinoctial months.

At the "Discovery's" station small oscillations of a few minutes'

duration were hardly ever absent, but the character of the larger

disturbances showed a marked variation throughout the 24 hours. Those

of a very rapid oscillatory character were especially numerous in the

morning between 4 and 9 a.m. In the late afternoon and evening

disturbances of a more regular type became prominent, especially in

the winter months. In particular there were numerous occurrences of a

remarkably regular type of disturbance, half the total number of cases

taking place between 7 and 9 p.m. This "special type of disturbance"

was divisible into two phases, each lasting on the average about 20

minutes. During the first phase all the elements diminished in value,

during the second phase they increased. In the case of D and H the

rise and fall were about equal, but the rise in V was about 3½ times

the preceding fall. The disturbing force--on the north pole--to which

the first phase might be attributed was inclined on the average about

5°½ below the horizon, the horizontal projection of its line of action

being inclined about 41°½ to the north of east. The amplitude and

duration of the disturbances of the "special type" varied a good deal;

in several cases the disturbing force considerably exceeded

200[gamma]. A somewhat similar type of disturbance was observed by Kr.

Birkeland[93] at Arctic stations also in 1902-1903, and was called by

him the "polar elementary" storm. Birkeland's record of disturbances

extends only from October 1902 to March 1903, so it is uncertain

whether "polar elementary" storms occur during the Arctic summer.

Their usual time of occurrence seems to be the evening. During their

occurrence Birkeland found that there was often a great difference in

amplitude and character between the disturbances observed at places so

comparatively near together as Iceland, Nova Zembla and Spitzbergen.

This led him to assign the cause to electric currents in the Arctic,

at heights not exceeding a few hundred kilometres, and he inferred

from the way in which the phenomena developed that the seat of the

disturbances often moved westward, as if related in some way to the

sun's position. Contemporaneously with the "elementary polar" storms

in the Arctic Birkeland found smaller but distinct movements at

stations all over Europe; these could generally be traced as far as

Bombay and Batavia, and sometimes as far as Christchurch, New Zealand.

Chree,[92] on the other hand, working up the 1902-1904 Antarctic

records, discovered that during the larger disturbances of the

"special type" corresponding but much smaller movements were visible

at Christchurch, Mauritius, Kolaba, and even at Kew. He also found

that in the great majority of cases the Antarctic curves were

specially disturbed during the times of Birkeland's "elementary polar"

storms, the disturbances in the Arctic and Antarctic being of the same

order of magnitude, though apparently of considerably different type.

Examining the more prominent of the sudden commencements of magnetic

disturbances in 1902-1903 visible simultaneously in the curves from

Kew, Kolaba, Mauritius and Christchurch, Chree found that these were

all represented in the Antarctic curves by movements of a considerably

larger size and of an oscillatory character. In a number of cases

Birkeland observed small simultaneous movements in the curves of his

co-operating stations, which appeared to be at least sometimes

decidedly larger in the equatorial than the northern temperate

stations. These he described as "equatorial" perturbations, ascribing

them to electric currents in or near the plane of the earth's magnetic

equator, at heights of the order of the earth's radius. It was found,

however, by Chree that in many, if not all, of these cases there were

synchronous movements in the Antarctic, similar in type to those which

occurred simultaneously with the sudden commencements of magnetic

storms, and that these Antarctic movements were considerably larger

than those described by Birkeland at the equatorial stations. This

result tends of course to suggest a somewhat different explanation

from Birkeland's. But until our knowledge of facts has received

considerable additions all explanations must be of a somewhat

hypothetical character.

Magnetic Poles.

In 1831 Sir James Ross[94] observed a dip of 89° 59´ at 70° 5´ N., 96°

46´ W., and this has been accepted as practically the position of the

north magnetic pole at the time. The position of the south magnetic

pole in 1840 as deduced from the Antarctic observations made by the

"Erebus" and "Terror" expedition is shown in Sabine's chart as about

73° 30´ S., 147° 30´ E. In the more recent chart in J. C. Adams's

_Collected Papers_, vol. 2, the position is shown as about 73° 40´ S.,

147° 7´ E. Of late years positions have been obtained for the south

magnetic pole by the "Southern Cross" expedition of 1898-1900 (A), by

the "Discovery" in 1902-1904 (B), and by Sir E. Shackleton's

expedition 1908-1909 (C). These are as follow:

(A) 72° 40´ S., 152° 30´ E.

(B) 72° 51´ S., 156° 25´ E.

Unless the diurnal inequality vanishes in its neighbourhood, a

somewhat improbable contingency considering the large range at the

"Discovery's" winter quarters, the position of the south magnetic pole

has probably a diurnal oscillation, with an average amplitude of

several miles, and there is not unlikely a larger annual oscillation.

Thus even apart from secular change, no single spot of the earth's

surface can probably claim to be a magnetic pole in the sense

popularly ascribed to the term. If the diurnal motion were absolutely

regular, and carried the point where the needle is vertical round a

closed curve, the centroid of that curve--though a spot where the

needle is never absolutely vertical--would seem to have the best

claim to the title. It should also be remembered that when the dip is

nearly 90° there are special observational difficulties. There are

thus various reasons for allowing a considerable uncertainty in

positions assigned to the magnetic poles. Conclusions as to change of

position of the south magnetic pole during the last ten years based on

the more recent results (A), (B) and (C) would, for instance, possess

a very doubtful value. The difference, however, between these recent

positions and that deduced from the observations of 1840-1841 is more

substantial, and there is at least a moderate probability that a

considerable movement towards the north-east has taken place during

the last seventy years.

See publications of individual magnetic observatories, more especially

the Russian (_Annales de l'Observatoire Physique Central_), the French

(_Annales du Bureau Central Météorologique de France_), and those of

Kew, Greenwich, Falmouth, Stonyhurst, Potsdam, Wilhelmshaven, de Bilt,

Uccle, O'Gyalla, Prague, Pola, Coimbra, San Fernando, Capo di Monte,

Tiflis, Kolaba, Zi-ka-wei, Hong-Kong, Manila, Batavia, Mauritius,

Agincourt (Toronto), the observatories of the U.S. Coast and Geodetic

Survey, Rio de Janeiro, Melbourne.

In the references below the following abbreviations are used: B.A. =

_British Association Reports_; Batavia = _Observations made at the

Royal ... Observatory at Batavia_; M.Z. = _Meteorologische

Zeitschrift_, edited by J. Hann and G. Hellman; P.R.S. = _Proceedings

of the Royal Society of London_; P.T. = _Philosophical Transactions_;

R. = _Repertorium für Meteorologie_, St Petersburg; T.M. =

_Terrestrial Magnetism_, edited by L. A. Bauer; R.A.S. Notices =

_Monthly Notices of the Royal Astronomical Society_. Treatises are

referred to by the numbers attached to them; e.g. (1) p. 100 means p.

100 of Walker's _Terrestrial Magnetism_.

FOOTNOTES:

[A] For explanation of these numbers, see end of article.

[1] E. Walker, _Terrestrial and Cosmical Magnetism_ (Cambridge and

London, 1856).

[1a]: H. Lloyd, _A Treatise on Magnetism General and Terrestrial_

(London, 1874). [2] E. Mascart, _Traité de magnétisme terrestre_

(Paris, 1900).

[3] L. A. Bauer, _United States Magnetic Declination Tables and

Isogonic Charts, and Principal Facts relating to the Earth's

Magnetism_ (Washington, 1902).

[4] Balfour Stewart, "Terrestrial Magnetism" (under "Meteorology"),

_Ency. brit._ 9th ed.

[5] C. Chree, "Magnetism, Terrestrial," _Ency. brit._ 10th ed.

[6] _M.Z._ 1906, 23, p. 145.

[7] (3) p. 62.

[8] _K. Akad. van Wetenschappen_ (Amsterdam, 1895; Batavia, 1899,

&c.).

[9] _Atlas des Erdmagnetismus_ (Riga, 1903).

[10] (1) p. 16, &c.

[11] _Kolaba (Colaba) Magnetical and Meteorological Observations_,

1896. Appendix Table II.

[12] (1) p. 21.

[13] _Report_ for 1906, App. 4, see also (3) p. 102.

[14] (1) p. 166.

[15] _Ergebnisse der mag. Beobachtungen in Potsdam_, 1901, p. xxxvi.

[16] _U.S. Coast and Geodetic Survey Report_ for 1895, App. 1, &c.

[17] _T.M._ 1, pp. 62, 89, and 2, p. 68.

[18] (3) p. 45.

[19] _Die Elemente des Erdmagnetismus_, pp. 104.108.

[20] _Zur täglichen Variation der mag. Deklination (aus Heft II. des

Archivs des Erdmagnetismus)_ (Potsdam, 1906).

[21] _M.Z._ 1888, 5, p. 225.

[22] _M.Z._ 1904, 21, p. 129.

[23] _P.T._ 202 A, p. 335.

[23a] _Comb. Phil. Soc. Trans._ 20, p. 165.

[24] _P.T._ 208 A, p. 205.

[25] _P.T._ 203 A, p. 151.

[26] _P.T._ 171. p. 541; _P.R.S._ 63, p. 64.

[27] _R.A.S. Notices_ 60, p. 142.

[28] _Rendiconti del R. Ist. Lomb._ 1902, Series II. vol. 35.

[29] _R._ 1889, vol. 12, no. 8.

[30] _B.A. Report_, 1898, p. 80.

[31] _P.R.S._ (A) 79, p. 151.

[32] _P.T._ 204 A, p. 373.

[33] _Ann. du Bureau Central Météorologique, année 1897_, 1 Mem. p.

B65.

[34] _P.T._ 161, p. 307.

[35] _M.Z._ 1895, 12, p. 321.

[35a] _P.T._ 1851, p. 123; and 1852, p. 103, see also (4) § 38.

[36] _P.T._ 159, p. 363.

[37] (1) p. 92.

[38] _R.A.S. Notices_ 65, p. 666.

[39] _R.A.S. Notices_, 65, pp. 2 and 538.

[40] _K. Akad. van Wetenschappen_ (Amsterdam, 1906) p. 266.

[41] _R.A.S. Notices_ 65, p. 520.

[42] _B.A. Reports_, 1880, p. 201 and 1881, p. 463.

[43] _Anhang Ergebnisse der mag. Beob. in Potsdam_, 1896.

[44] _M.Z._ 1899, 16, p. 385.

[45] _P.T._ 166, p. 387.

[46] _Trans. Can. Inst._ 1898-1899, p. 345, and Proc. Roy. Ast. Soc.

of Canada, 1902-1903, p. 74, 1904, p. xiv., &c.

[47] _R.A.S. Notices_ 65, p. 186.

[48] _T.M._ 10, p. 1.

[49] _Expédition norvégienne de 1899-1900_ (Christiania, 1901).

[50] _Thèses présentées à la Faculté des Sciences_ (Paris, 1903).

[51] _Nat. Tijdschrift voor Nederlandsch-Indië_, 1902, p. 71.

[52] _Wied. Ann._ 1882, p. 336.

[53] _Sitz. der k. preuss. Akad. der Wiss._, 24th June 1897, &c.

[54] _T.M._ 12, p. 1.

[55] _P.T._ 143, p. 549; _St Helena Observations_, vol. ii., p.

cxlvi., &c., (1) § 62.

[56] _Trans. R.S.E._ 24, p. 669.

[57] _P.T._ 178 A, p. 1.

[58] _Batavia_, vol. 16, &c.

[59] _Batavia_, Appendix to vol. 26.

[60] _R._ vol. 17, no. 1.

[61] _T.M._ 3, p. 1, &c.

[62] _P.T._ 181 A, p. 53 and 188 A.

[63] _Ann. du Bureau Central Mét._ vol. i. for years 1884 and 1887 to

1895.

[64] _Ann. dell' Uff. Centrale Met. e Geod._ vol. 14, pt. i. p. 57.

[65] _A Magnetic Survey of the Netherlands for the Epoch 1st Jan.

1891_ (Rotterdam, 1895).

[66] _Kg. Svenska Vet. Akad. Handlingar_, 1895, vol. 27, no. 7.

[67] _Denkschriften der math. naturwiss. Classe der k. Akad. des

Wiss._ (Wien), vols. 62 and 67.

[68] _Journal of the College of Science, Tokyo_, 1904, vol. 14.

[69] _Ann. de l'observatoire ... de Toulouse_, 1907, vol. 7.

[70] _Ann. du Bureau Central Mét._ 1897, I. p. B36.

[71] _T.M._ 7, p. 74.

[72] _Bull. Imp. Univ. Odessa_ 85, p. 1, and _T.M._ 7, p. 67.

[73] _P.T._ 187 A, p. 345.

[74] _P.R.S._ 76 A, p. 181.

[75] _Bull. Soc. Imp. des Naturalistes de Moskau_, 1893, no. 4, p.

381, and _T.M._ 1, p. 50.

[76] _Forsch. zur deut. Landes- u. Volkskunde_, 1898, Bd. xi, 1, and

_T.M._ 3, p. 77.

[77] _P.R.S._ 76 A, p. 507.

[78] Adams, _Scientific Papers_, II. p. 446.

[79] _B.A. Report_ for 1898, p. 109.

[80] _Abhand. der bayer, Akad. der Wiss._, 1895, vol. 19.

[81] _Sitz. k. Akad. der Wiss_. (Berlin), 1897, no. xviii., also

_T.M._ 3, p. 191.

[82] _T.M._ 2, p. 11.

[83] _Die Elemente des Erdmagnetismus_ (St Petersburg, 1899), p.

103.

[84] _T.M._ 9, p. 113.

[85] _T.M._ 1, p. 77, and Nature, 57, pp. 160 and 180.

[86] _M.Z._ 15, p. 175.

[86a] _Sitz, der k. k. Akad. der Wiss. Wien, math. nat. Classe_,

1898, Bd. cvii., Abth. ii.

[87] _P.T._ (A) 180, p. 467.

[88] _Die Tägliche Periode der erdmagnetischen Elemente_ (St

Petersburg, 1902).

[89] _R. Accad. Lincei Atti_, viii. 1899, pp. 69, 121, 176, 269 and

previous volumes, see also _Séances de la Soc. Franc. de Physique_,

1899, p. 118.

[90] _Bull. Soc. Vaud., Sc. Nat._ 1906, 42, p. 225.

[91] _Comptes rendus_, 1905, 141, p. 567.

[92] _National Antarctic Expedition 1901-1904_, "Magnetic

Observations."

[93] _The Norwegian Aurora Polaris Expedition 1902-1903_, vol. i.

[94] (1) p. 163.

(C. Ch.)

Encyclopaedia Britannica, 11th Edition, "McKinley, William" to "Magnetism, Terrestrial" Volume 17, Slice 3 · 第 45 / 45 章

§ 35. There are still other ways of attacking the problem of