Chapter LXIII: repeats the promise of freedom to the English church (7)

[107] _Phil. Mag._, 1897, 44, 293; 1898, 46, 528.

MAGNETISM, TERRESTRIAL, the science which has for its province the study of the magnetic phenomena of the earth.

Historical.

§ 1. Terrestrial magnetism has a long history. Its early growth was slow, and considerable uncertainty prevails as to its earliest developments. The properties of the magnet (see MAGNETISM) were to some small extent known to the Greeks and Romans before the Christian era, and compasses (see COMPASS) of an elementary character seem to have been employed in Europe at least as early as the 12th century. In China and Japan compasses of a kind seem to have existed at a much earlier date, and it is even claimed that the Chinese were aware of the declination of the compass needle from the true north before the end of the 11th century. Early scientific knowledge was usually, however, a mixture of facts, very imperfectly ascertained, with philosophical imaginings. When an early writer makes a statement which to a modern reader suggests a knowledge of the declination of the compass, he may have had no such definite idea in his mind. So far as Western civilization is concerned, Columbus is usually credited with the discovery--in 1492 during his first voyage to America--that the pointing of the compass needle to the true north represents an exceptional state of matters, and that a _declination_ in general exists, varying from place to place. The credit of these discoveries is not, however, universally conceded to Columbus. G. Hellmann[6][A] considers it almost certain that the departure of the needle from the true north was known in Europe before the time of Columbus. There is indirect evidence that the declination of the compass was not known in Europe in the early part of the 15th century, through the peculiarities shown by early maps believed to have been drawn solely by regard to the compass. Whether Columbus was the first to observe the declination or not, his date is at least approximately that of its discovery.

The next fundamental discovery is usually ascribed to Robert Norman, an English instrument maker. In _The Newe Attractive_ (1581) Norman describes his discovery made some years before of the _inclination_ or _dip_. The discovery was made more or less by accident, through Norman's noticing that compass needles which were truly balanced so as to be horizontal when unmagnetized, ceased to be so after being stroked with a magnet. Norman devised a form of dip-circle, and found a value for the inclination in London which was at least not very wide of the mark.

Another fundamental discovery, that of the secular change of the declination, was made in England by Henry Gellibrand, professor of mathematics at Gresham College, who described it in his _Discourse Mathematical on the Variation of the Magneticall Needle together with its Admirable Diminution lately discovered_ (1635). The history of this discovery affords a curious example of knowledge long delayed. William Borough, in his _Discourse on the Variation of the Compas or Magneticall Needle_ (1581), gave for the declination at Limehouse in October 1580 the value 11°¼ E. approximately. Observations were repeated at Limehouse, Gellibrand tells us, in 1622 by his colleague Edmund Gunter, professor of astronomy at Gresham College, who found the much smaller value 6° 13´. The difference seems to have been ascribed at first to error on Borough's part, and no suspicion of the truth seems to have been felt until 1633, when some rough observations gave a value still lower than that found by Gunter. It was not until midsummer 1634 that Gellibrand felt sure of his facts, and yet the change of declination since 1580 exceeded 7°. The delay probably arose from the strength of the preconceived idea, apparently universally held, that the declination was absolutely fixed. This idea, it would appear, derived some of its strength from the positive assertion made on the point by Gilbert of Colchester in his _De magnete_ (1600).

A third fundamental discovery, that of the diurnal change in the declination, is usually credited to George Graham (1675-1751), a London instrument maker. Previous observers, e.g. Gellibrand, had obtained slightly different values for the declination at different hours of the day, but it was natural to assign them to instrumental uncertainties. In those days the usual declination instrument was the compass with pivoted needles, and Graham himself at first assigned the differences he observed to friction. The observations on which he based his conclusions were made in 1722; an account of them was communicated to the Royal Society and published in the _Philosophical Transactions_ for 1724.

The movements of the compass needle throughout the average day represent partly a regular diurnal variation, and partly irregular changes in the declination. The distinction, however, was not at first very clearly realized. Between 1756 and 1759 J. Canton observed the declination-changes on some 600 days, and was thus able to deduce their general character. He found that the most prominent part of the regular diurnal change in England consisted of a westerly movement of the north-pointing pole from 8 or 9 a.m. to 1 or 2 p.m., followed by a more leisurely return movement to the east. He also found that the amplitude of the movement was considerably larger in summer than in winter. Canton further observed that in a few days the movements were conspicuously irregular, and that aurora was then visible. This association of magnetic disturbance and aurora had, however, been observed somewhat before this time, a description of one conspicuous instance being contributed to the Royal Society in 1750 by Pehr Vilhelm Wargentin (1717-1783), a Swede.

Another landmark in the history of terrestrial magnetism was the discovery towards the end of the 18th century that the intensity of the resultant magnetic force varies at different parts of the earth. The first observations clearly showing this seem to be those of a Frenchman, Paul de Lamanon, who observed in 1785-1787 at Teneriffe and Macao, but his results were not published at the time. The first published observations seem to be those made by the great traveller Humboldt in tropical America between 1798 and 1803. The delay in this discovery may again be attributed to instrumental imperfections. The method first devised for comparing the force at different places consisted in taking the time of oscillation of the dipping needle, and even with modern circles this is hardly a method of high precision. Another discovery worth chronicling was made by Arago in 1827. From observations made at Paris he found that the inclination of the dipping needle and the intensity of the horizontal component of the magnetic force both possessed a diurnal variation.

§ 2. Whilst Italy, England and France claim most of the early observational discoveries, Germany deserves a large share of credit for the great improvement in instruments and methods during the first half of the 19th century. Measurements of the intensity of the magnetic force were somewhat crude until Gauss showed how absolute results could be obtained, and not merely relative data based on observations with some particular needle. Gauss also devised the bifilar magnetometer, which is still largely represented in instruments measuring changes of the horizontal force; but much of the practical success attending the application of his ideas to instruments seems due to Johann von Lamont (1805-1879), a Jesuit of Scottish origin resident in Germany.

The institution of special observatories for magnetic work is largely due to Humboldt and Gauss. The latter's observatory at Göttingen, where regular observations began in 1834, was the centre of the Magnetic Union founded by Gauss and Weber for the carrying out of simultaneous magnetic observations and it was long customary to employ Göttingen time in schemes of international co-operation.

In the next decade, mainly through the influence of Sir Edward Sabine (1788-1883), afterwards president of the Royal Society, several magnetic observatories were established in the British colonies, at St Helena, Cape of Good Hope, Hobarton (now Hobart) and Toronto. These, with the exception of Toronto, continued in full action for only a few years; but their records--from their widely distributed positions--threw much fresh light on the differences between magnetic phenomena in different regions of the globe. The introduction of regular magnetic observatories led ere long to the discovery that there are notable differences between the amplitudes of the regular daily changes and the frequency of magnetic disturbances in different years. The discovery that magnetic phenomena have a period closely similar to, if not absolutely identical with, the "eleven year" period in sun-spots, was made independently and nearly simultaneously about the middle of the 19th century by Lamont, Sabine and R. Wolf.

The last half of the 19th century showed a large increase in the number of observatories taking magnetic observations. After 1890 there was an increased interest in magnetic work. One of the contributory causes was the magnetic survey of the British Isles made by Sir A. Rücker and Sir T. E. Thorpe, which served as a stimulus to similar work elsewhere; another was the institution by L. A. Bauer of a magazine. _Terrestrial Magnetism_, specially devoted to the subject. This increased activity added largely to the stock of information, sometimes in forms of marked practical utility; it was also manifested in the publication of a number of papers of a speculative character. For historical details the writer is largely indebted to the works of E. Walker[1] and L. A. Bauer.[3]

Observational Methods and Records.

§ 3. All the more important magnetic observatories are provided with
instruments of two kinds. Those of the first kind give the absolute
value of the magnetic elements at the time of observation. The
unifilar magnetometer (q.v.), for instance, gives the absolute values
of the declination and horizontal force, whilst the inclinometer
(q.v.) or dip circle gives the inclination of the dipping needle.
Instruments of the second kind, termed magnetographs (q.v.), are
differential and self-recording, and show the changes constantly
taking place in the magnetic elements. The ordinary form of
magnetograph records photographically. Light reflected from a fixed
mirror gives a base line answering to a constant value of the element
in question; the light is cut off every hour or second hour so that
the base line also serves to make the time. Light reflected from a
mirror carried by a magnet gives a curved line answering to the
changes in position of the magnet. The length of the ordinate or
perpendicular drawn from any point of the curved line on to the base
line is proportional to the extent of departure of the magnet from a
standard position. If then we know the absolute value of the element
which corresponds to the base line, and the equivalent of 1 cm. of
ordinate, we can deduce the absolute value of the element answering to
any given instant of time. In the case of the declination the value of
1 cm. of ordinate is usually dependent almost entirely on the distance
of the mirror carried by the magnet from the photographic paper, and
so remains invariable or very nearly so. In the case of the horizontal
force and vertical force magnetographs--these being the two force
components usually recorded--the value of 1 cm. of ordinate alters
with the strength of the magnet. It has thus to be determined from
time to time by observing the deflection shown on the photographic
paper when an auxiliary magnet of known moment, at a measured
distance, deflects the magnetograph magnet. Means are provided for
altering the sensitiveness, for instance, by changing the effective
distance in the bifilar suspension of the horizontal force magnet, and
by altering the height of a small weight carried by the vertical force
magnet. It is customary to aim at keeping the sensitiveness as
constant as possible. A very common standard is to have 1 cm. of
ordinate corresponding to 10´ of arc in the declination and to
50[gamma] (1[gamma] = 0.00001 C.G.S.) in the horizontal and vertical
force magnetographs.

As an example of how the curves are standardized, suppose that
absolute observations of declination are taken four times a month, and
that in a given month the mean of the observed values is 16° 34´.6 W.
The curves are measured at the places which correspond to the times of
the four observations, and the mean length of the four ordinates is,
let us say, 2.52 cms. If 1 cm. answers to 10´, then 2.52 cms.
represents 25´.2, and thus the value of the base line--i.e. the value
which the declination would have if the curve came down to the base
line--is for the month in question 16° 34´.6 less 25´.2 or 16° 9´.4.
If now we wish to know the declination at any instant in this
particular month all we have to do is to measure the corresponding
ordinate and add its value, at the rate of 10´ per cm., to the base
value 16° 9´.4 just found. Matters are a little more complicated in
the case of the horizontal and vertical force magnetographs. Both
instruments usually possess a sensible temperature coefficient, i.e.
the position of the magnet is dependent to some extent on the
temperature it happens to possess, and allowance has thus to be made
for the difference from a standard temperature. In the case of the
vertical force an "observed" value is derived by combining the
observed value of the inclination with the simultaneous value of the
horizontal force derived from the horizontal force magnetograph after
the base value of the latter has been determined. In themselves the
results of the absolute observations are of minor interest. Their main
importance is that they provide the means of fixing the value of the
base line in the curves. Unless they are made carefully and
sufficiently often the information derivable from the curves suffers
in accuracy, especially that relating to the secular change. It is
from the curves that information is derived as to the regular diurnal
variation and irregular changes. In some observatories it is customary
to publish a complete record of the values of the magnetic elements at
every hour for each day of the year. A useful and not unusual addition
to this is a statement of the absolutely largest and smallest values
of each element recorded during each day, with the precise times of
their occurrence. On days of large disturbance even hourly readings
give but a very imperfect idea of the phenomena, and it is customary
at some observatories, e.g. Greenwich, to reproduce the more disturbed
curves in the annual volume. In calculating the regular diurnal
variation it is usual to consider each month separately. So far as is
known at present, it is entirely or almost entirely a matter of
accident at what precise hours specially high or low values of an
element may present themselves during an individual highly disturbed
day; whilst the range of the element on such a day may be 5, 10 or
even 20 times as large as on the average undisturbed day of the month.
It is thus customary when calculating diurnal inequalities to omit the
days of largest disturbance, as their inclusion would introduce too
large an element of uncertainty. Highly disturbed days are more than
usually common in some years, and in some months of the year, thus
their omission may produce effects other than that intended. Even on
days of lesser disturbance difficulties present themselves. There may
be to and fro movements of considerable amplitude occupying under an
hour, and the hour may come exactly at the crest or at the very lowest
part of the trough. Thus, if the reading represents in every case the
ordinate at the precise hour a considerable element of chance may be
introduced. If one is dealing with a mean from several hundred days
such "accidents" can be trusted to practically neutralize one another,
but this is much less fully the case when the period is as short as a
month. To meet this difficulty it is customary at some observatories
to derive hourly values from a freehand curve of continuous curvature,
drawn so as to smooth out the apparently irregular movements. Instead
of drawing a freehand curve it has been proposed to use a planimeter,
and to accept as the hourly value of the ordinate the mean derived
from a consideration of the area included between the curve, the base
line and ordinates at the thirty minutes before and after each hour.

§ 4. Partly on account of the uncertainties due to disturbances, and
partly with a view to economy of labour, it has been the practice at
some observatories to derive diurnal inequalities from a comparatively
small number of undisturbed or quiet days. Beginning with 1890, five
days a month were selected at Greenwich by the astronomer royal as
conspicuously quiet. In the selection regard was paid to the
desirability that the arithmetic mean of the five dates should answer
to near the middle of the month. In some of the other English
observatories the routine measurement of the curves was limited to
these selected quiet days. At Greenwich itself diurnal inequalities
were derived regularly from the quiet days alone and also from all the
days of the month, excluding those of large disturbance. If a quiet
day differed from an ordinary day only in that the diurnal variation
in the latter was partly obscured by irregular disturbances, then
supposing enough days taken to smooth out irregularities, one would
get the same diurnal inequality from ordinary and from quiet days. It
was found, however, that this was hardly ever the case (see §§ 29 and
30). The quiet day scheme thus failed to secure exactly what was
originally aimed at; on the other hand, it led to the discovery of a
number of interesting results calculated to throw valuable sidelights
on the phenomena of terrestrial magnetism.

The idea of selecting quiet days seems due originally to H. Wild. His
selected quiet days for St Petersburg and Pavlovsk were very few in
number, in some months not even a single day reaching his standard of
freedom from disturbance. In later years the International Magnetic
Committee requested the authorities of each observatory to arrange the
days of each month in three groups representing the quiet, the
moderately disturbed and the highly disturbed. The statistics are
collected and published on behalf of the committee, the first to
undertake the duty being M. Snellen. The days are in all cases counted
from Greenwich midnight, so that the results are strictly synchronous.
The results promise to be of much interest.

§ 5. The intensity and direction of the resultant magnetic force at a
spot--i.e. the force experienced by a unit magnetic pole--are known if
we know the three components of force parallel to any set of
orthogonal axes. It is usual to take for these axes the vertical at
the spot and two perpendicular axes in the horizontal plane; the
latter are usually taken in and perpendicular to the geographical
meridian. The usual notation in mathematical work is X to the north, Y
to the west or east, and Z vertically downwards. The international
magnetic committee have recommended that Y be taken positive to the
east, but the fact that the declination is westerly over most of
Europe has often led to the opposite procedure, and writers are not
always as careful as they should be in stating their choice. Apart
from mathematical calculations, the more usual course is to define the
force by its horizontal and vertical components--usually termed H and
V--and by the declination or angle which the horizontal component
makes with the astronomical meridian. The declination is sometimes
counted from 0° to 360°, 0° answering to the case when the so-called
north pole (or north seeking pole) is directed towards geographical
north, 90° to the case when it is directed to the east, and so on. It
is more usual, however, to reckon declination only from 0° to 180°,
characterizing it as easterly or westerly according as the north pole
points to the east or to the west of the geographical meridian. The
force is also completely defined by H or V, together with D the
declination, and I the inclination to the horizon of the dipping
needle. Instead of H and D some writers make use of N the northerly
component, and W the westerly (or E the easterly). The resultant force
itself is denoted sometimes by R, sometimes by T (total force). The
following relationships exist between the symbols

X [equiv] N, Y [equiv] W or E, Z [equiv] V, R [equiv] T,

H [equiv] [root](X² + Y²), R [equiv] [root](X² + Y² + Z²),

tan D = Y/X, tan I = V/H.

The term _magnetic element_ is applied to R or any of the components,
and even to the angles D and I.

Charts.

§ 6. Declination is the element concerning which our knowledge is most complete and most reliable. With a good unifilar magnetometer, at a fixed observatory distant from the magnetic poles, having a fixed mark of known azimuth, the observational uncertainty in a single observation should not exceed 0´.5 or at most 1´.0. It cannot be taken for granted that different unifilars, even by the best makers, will give absolutely identical values for the declination, but as a matter of fact the differences observed are usually very trifling. The chief source of uncertainty in the observation lies in the torsion of the suspension fibre, usually of silk or more rarely of phosphor bronze or other metal. A very stout suspension must be avoided at all cost, but the fibre must not be so thin as to have a considerable risk of breaking even in skilled hands. Near a magnetic pole the directive force on the declination magnet is reduced, and the effects of torsion are correspondingly increased. On the other hand, the regular and irregular changes of declination are much enhanced. If an observation consisting of four readings of declination occupies twelve minutes, the chances are that in this time the range at an English station will not exceed 1´, whereas at an arctic or antarctic station it will frequently exceed 10´. Much greater uncertainty thus attaches to declination results in the Arctic and Antarctic than to those in temperate latitudes. In the case of secular change data one important consideration is that the observations should be taken at an absolutely fixed spot, free from any artificial source of disturbance. In the case of many of the older observations of which records exist, the precise spot cannot be very exactly fixed, and not infrequently the site has become unsuitable through the erection of buildings not free from iron. Apart from buildings, much depends on whether the neighbourhood is free from basaltic and other magnetic rocks. If there are no local disturbances of this sort, a few yards difference is usually without appreciable influence, and even a few miles difference is of minor importance when one is calculating the mean secular change for a long period of years. When, however, local disturbances exist, even a few feet difference in the site may be important, and in the absence of positive knowledge to the contrary it is only prudent to act as if the site were disturbed. Near a magnetic pole the declination naturally changes very rapidly when one travels in the direction perpendicular to the lines of equal declination, so that the exact position of the site of observation is there of special importance.

The usual method of conveying information as to the value of the
declination at different parts of the earth's surface is to draw
curves on a map--the so-called _isogonals_--such that at all points on
any one curve the declination at a given specified epoch has the same
value. The information being of special use to sailors, the
preparation of magnetic charts has been largely the work of naval
authorities--more especially of the hydrographic department of the
British admiralty. The object of the admiralty world charts--four of
which are reproduced here, on a reduced scale, by the kind permission
of the Hydrographer--is rather to show the general features boldly
than to indicate minute details. Apart from the immediate necessities
of the case, this is a counsel of prudence. The observations used have
mostly been taken at dates considerably anterior to that to which the
chart is intended to apply. What the sailor wants is the declination
now or for the next few years, not what it was five, ten or twenty
years ago. Reliable secular change data, for reasons already
indicated, are mainly obtainable from fixed observatories, and there
are enormous areas outside of Europe where no such observatories
exist. Again, as we shall see presently, the rate of the secular
change sometimes alters greatly in the course of a comparatively few
years. Thus, even when the observations themselves are thoroughly
reliable, the prognostication made for a future date by even the most
experienced of chart makers may be occasionally somewhat wide of the
mark. Fig. 1 is a reduced copy of the British admiralty declination
chart for the epoch 1907. It shows the isogonals between 70° N. and
65° S. latitude. Beyond the limits of this chart, the number of exact
measurements of declination is somewhat limited, but the general
nature of the phenomena is easily inferred. The geographical and the
magnetic poles--where the dipping needle is vertical--are fundamental
points. The north magnetic pole is situated in North America near the
edge of the chart. We have no reason to suppose that the magnetic pole
is really a fixed point, but for our present purpose we may regard it
as such. Let us draw an imaginary circle round it, and let us travel
round the circle in the direction, west, north, east, south, starting
from a point where the north pole of a magnet (i.e. the pole which in
Europe or the United States points to the north) is directed exactly
towards the astronomical north. The point we start from is to the
geographical south of the magnetic pole. As we go round the circle the
needle keeps directed to the magnetic pole, and so points first
slightly to the east of geographical north, then more and more to the
east, then directly east, then to south of east, then to due south, to
west of south, to west, to north-west, and finally when we get round
to our original position due north once more. Thus, during our course
round the circle the needle will have pointed in all possible
directions. In other words, isogonals answering to all possible values
of the declination have their origin in the north magnetic pole. The
same remark applies of course to the south magnetic pole.

Now, suppose ourselves at the north geographical pole of the earth.
Neglecting as before diurnal variation and similar temporary changes,
and assuming no abnormal local disturbance, the compass needle at and
very close to this pole will occupy a fixed direction relative to the
ground underneath. Let us draw on the ground through the pole a
straight line parallel to the direction taken there by the compass
needle, and let us carry a compass needle round a _small_ circle whose
centre is the pole. At all points on the circle the positions of the
needle will be parallel; but whereas the north pole of the magnet will
point exactly towards the centre of the circle at one of the points
where the straight line drawn on the ground cuts the circumference, it
will at the opposite end of the diameter point exactly away from the
centre. The former part is clearly on the isogonal where the
declination is 0°, the latter on the isogonal where it is 180°.
Isogonals will thus radiate out from the north geographical pole (and
similarly of course from the south geographical pole) in all
directions. If we travel along an isogonal, starting from the north
magnetic pole, our course will generally take us, often very
circuitously, to the north geographical pole. If, for example, we
select the isogonal of 10° E., we at first travel nearly south, but
then more and more westerly, then north-westerly across the north-east
of Asia; the direction then gets less northerly, and makes a dip to
the south before finally making for the north geographical pole. It is
possible, however, according to the chart, to travel direct from the
north magnetic to the south geographical pole, provided we select an
isogonal answering to a small westerly or easterly declination (from
about 19° W. to 7° E.).

Special interest attaches to the isogonals answering to declination
0°. These are termed _agonic lines_, but sailors often call them
_lines of no variation_, the term _variation_ having at one time been
in common use in the sense of declination. If we start from the north
magnetic pole the agonic line takes us across Canada, the United
States and South America in a fairly straight course to the south
geographical pole. A curve continuous with this can be drawn from the
south geographical to the south magnetic pole at every point of which
the needle points in the geographical meridian; but here the north
pole of the needle is pointing south, not north, so that this portion
of curve is really an isogonal of 180°. In continuation of this there
emanates from the south magnetic pole a second isogonal of 0°, or
agonic line, which traverses Australia, Arabia and Russia, and takes
us to the north geographical pole. Finally, we have an isogonal of
180°, continuous with this second isogonal of 0° which takes us to the
north magnetic pole, from which we started. Throughout the whole area
included within these isogonals of 0° and 180°--excluding locally
disturbed areas--the declination is westerly; outside this area the
declination is in general easterly. There is, however, as shown in the
chart, an isogonal of 0° enclosing an area in eastern Asia inside
which the declination is westerly though small.

§ 7. Fig. 2 is a reduced copy of the admiralty chart of inclination or
dip for the epoch 1907. The places where the dip has the same value
lie on curves called _isoclinals_. The dip is northerly (north pole
dips) or southerly (south pole dips) according as the place is north
or south of the isoclinal of 0°. At places actually on this isoclinal
the dipping needle is horizontal. The isoclinal of 0° is nowhere very
far from the geographical equator, but lies to the north of it in Asia
and Africa, and to the south of it in South America. As we travel
north from the isoclinal of 0° along the meridian containing the
magnetic pole the dipping needle's north pole dips more and more,
until when we reach the magnetic pole the needle is vertical. Going
still farther north, we have the dip diminishing. The northerly
inclination is considerably less in Europe than in the same latitudes
of North America; and correspondingly the southerly inclination is
less in South America than in the same latitudes of Africa.

Fig. 3 is a reduced copy of the admiralty horizontal force chart for
1907. The curves, called _isomagnetics_, connect the places where the
horizontal force has the same value; the force is expressed in C.G.S.
units. The horizontal force vanishes of course at the magnetic poles.
The chart shows a maximum value of between 0.39 and 0.40 in an oval
including the south of Siam and the China Sea. The horizontal force is
smaller in North America than in corresponding latitudes in Europe.

Charts are sometimes drawn for other magnetic elements, especially
vertical force (fig. 4) and total force. The isomagnetic of zero
vertical force coincides necessarily with that of zero dip, and there
is in general considerable resemblance between the forms of lines of
equal vertical force and those of equal dip. The highest values of the
vertical force occur in areas surrounding the magnetic poles, and are
fully 50% larger than the largest values of the horizontal force. The
total force is least in equatorial regions, where values slightly
under 0.4 C.G.S. are encountered. In the northern hemisphere there are
two distinct maxima of total force. One of these so-called _foci_ is
in Canada, the other in the north-east of Siberia, the former having
the higher value of the force. There are, however, higher values of
the total force than at either of these _foci_ throughout a
considerable area to the south of Australia. In the northern
hemisphere the lines of equal total force--called _isodynamic_
lines--form two sets more or less distinct, consisting of closed
ovals, one set surrounding the Canadian the other the Siberian focus.

Magnetic Elements and their Secular Change.

§ 8. As already explained, magnetic charts for the world or for large
areas give only a general idea of the values of the elements. If the
region is undisturbed, very fairly approximate values are derivable
from the charts, but when the highest accuracy is necessary the only
thing to do is to observe at the precise spot. In disturbed areas
local values often depart somewhat widely from what one would infer
from the chart, and occasionally there are large differences between
places only a few miles apart. Magnetic observatories usually publish
the mean value for the year of their magnetic elements. It has been
customary for many years to collect and publish these results in the
annual report of the Kew Observatory (Observatory Department of the
National Physical Laboratory). The data in Tables I. and II. are
mainly derived from this source. The observatories are arranged in
order of latitude, and their geographical co-ordinates are given in
Table II., longitude being reckoned from Greenwich. Table I. gives the
mean values of the declination, inclination and horizontal force for
January 1, 1901; they are in the main arithmetic means of the mean
annual values for the two years 1900 and 1901. The mean annual secular
changes given in this table are derived from a short period of
years--usually 1898 to 1903--the centre of which fell at the beginning
of 1901. Table II. is similar to Table I., but includes vertical force
results; it is more extensive and contains more recent data. In it the
number of years is specified from which the mean secular change is
derived; in all cases the last year of the period employed was that to
which the absolute values assigned to the element belong. The great
majority of the stations have declination west and inclination north;
it has thus been convenient to attach the + sign to increasing
westerly (or decreasing easterly) declination and to increasing
northerly (or decreasing southerly) inclination. In other words, in
the case of the declination + means that the north end of the needle
is moving to the west, while in the case of the inclination + means
that the north end (whether the dipping end or not) is moving towards
the nadir. In the case, however, of the vertical force + means simply
_numerical_ increase, irrespective of whether the north or the south
pole dips. The unit employed in the horizontal and vertical force
secular changes is 1[gamma], i.e. 0.00001 C.G.S. Even in the
declination, at the very best observatories, it is hardly safe to
assume that the apparent change from one year to the next is
absolutely truthful to nature. This is especially the case if there
has been any change of instrument or observer, or if any alteration
has been made to buildings in the immediate vicinity. A change of
instrument is a much greater source of uncertainty in the case of
horizontal force or dip than in the case of declination, and dip
circles and needles are more liable to deterioration than
magnetometers. Thus, secular change data for inclination and vertical
force are the least reliable. The uncertainties, of course, are much
less, from a purely mathematical standpoint, for secular changes
representing a mean from five or ten years than for those derived from
successive years' values of the elements. The longer, however, the
period of years, the greater is the chance that one of the elements
may in the course of it have passed through a maximum or minimum
value. This possibility should always be borne in mind in cases where
a mean secular change appears exceptionally small.

As Tables I. and II. show, the declination needle is moving to the
east all over Europe, and the rate at which it is moving seems not to
vary much throughout the continent. The needle is also moving to the
east throughout the western parts of Asia, the north and east of
Africa, and the east of North America. It is moving to the west in the
west of North America, in South America, and in the south and east of
Asia, including Japan, south-east Siberia, eastern China and most of
India.

§ 9. The information in figs. 1, 2, 3 and 4 and in Tables I. and II.
applies only to recent years. Owing to secular change, recent charts
differ widely from the earliest ones constructed. The first charts
believed to have been constructed were those of Edmund Halley the
astronomer. According to L. A. Bauer,[7] who has made a special study
of the subject, Halley issued two declination charts for the epoch
1700; one, published in 1701, was practically confined to the Atlantic
Ocean, whilst the second, published in 1702, contained also data for
the Indian Ocean and part of the Pacific. These charts showed the
isogonic lines, but only over the ocean areas. Though the charts for
1700 were the first published, there are others which apply to earlier
epochs. W. van Bemmelen[8] has published charts for the epochs 1500,
1550, 1600, 1650 and 1700, whilst H. Fritsche[9] has more recently
published charts of declination, inclination and horizontal force for
1600, 1700, 1780, 1842 and 1915. A number of early declination charts
were given in Hansteen's Atlas and in G. Hellmann's reprints. _Die
Altesten Karten der Isogonen, Isoklinen, Isodynamen_ (Berlin, 1895).
The data for the earlier epochs, especially those prior to 1700, are
meagre, and in many cases probably of indifferent accuracy, so that
the reliability of the charts for these epochs is somewhat open to
doubt.

If we take either Hansteen's or Fritsche's declination chart for 1600
we notice a profound difference from fig. 1. In 1600 the agonic line
starting from the north magnetic pole, after finding its way south to
the Gulf of Mexico, doubled back to the north-east, and passed across
or near Iceland. After getting well to the north of Iceland it doubled
again to the south, passing to the east of the Baltic. The second
agonic line which now lies to the west of St Petersburg appears in
1600 to have continued, after traversing Australia, in a nearly
northerly direction through the extreme east of China. The nature of
the changes in declination in western Europe will be understood from
Table III., the data from which, though derived from a variety of
places in the south-east of England,[10] may be regarded as
approximately true of London. The earliest result is that obtained by
Borough at Limehouse. Those made in the 16th century are due to
Gunter, Gellibrand, Henry Bond and Halley. The observations from 1787
to 1805 were due to George Gilpin, who published particulars of his
own and the earlier observations in the _Phil. Trans._ for 1806. The
data for 1817 and 1820 were obtained by Col. Mark Beaufoy, at Bushey,
Herts. They seem to come precisely at the time when the needle, which
had been continuously moving to the west since the earliest
observations, began to retrace its steps. The data from 1860 onwards
apply to Kew.

TABLE I.--Magnetic Elements and their Rate of Secular Change for
January 1, 1901.

+----------------+------------------------------+----------------------+
| | Absolute values. | Secular change. |
| Place. +----------+----------+--------+-------+------+-------+
| | D. | I. | H. | D. | I. | H. |
+----------------+----------+----------+--------+-------+------+-------+
| | ° ´ | ° ´ | | ´ | ´ |[gamma]|
| Pavlovsk | 0 39.8E | 70 36.8N | .16553 | - 4.1 | -0.8 | + 7 |
| Ekatarinburg | 10 6.3E | 70 40.5N | .17783 | - 4.6 | +0.5 | -13 |
| Copenhagen | 10 10.4W | 68 38.5N | .17525 | | | |
| Stonyhurst | 18 10.3W | 68 48.0N | .17330 | - 4.0 | | +22 |
| Wilhelmshaven | 12 26.0W | 67 39.7N | .18108 | - 4.1 | -2.1 | +20 |
| Potsdam | 9 54.2W | 66 24.5N | .18852 | - 4.2 | -1.6 | +16 |
| Irkutsk | 2 1.0E | 70 15.8N | .20122 | + 0.5 | +1.6 | -14 |
| de Bilt | 13 48.3W | 66 55.5N | .18516 | - 4.4 | -2.2 | +14 |
| Kew | 16 50.8W | 67 10.6N | .18440 | - 4.2 | -2.2 | +25 |
| Greenwich | 16 27.5W | 67 7.3N | .18465 | - 4.0 | -2.2 | +23 |
| Uccle | 14 11.0W | 66 8.8N | .18954 | - 4.2 | -2.1 | +23 |
| Falmouth | 18 27.3W | 66 44.0N | .18705 | - 3.8 | -2.7 | +26 |
| Prague | 9 4.4W | | .19956 | - 4.4 | | +20 |
| St Helier | 16 58.1W | 65 44.1N | | - 3.5 | -2.7 | |
| Parc St Maur | 14 43.4W | 64 52.3N | .19755\| - 4.0 | -2.2 | +23 |
| Val Joyeux | 15 13.7W | 65 0.0N | .19670/| | | |
| Munich | 10 25.8W | 63 18.1N | .20629 | - 4.8 | -2.7 | +21 |
| O'Gyalla | 7 26.1W | | .21164 | - 4.8 | | +13 |
| Pola | 9 22.7W | 60 14.5N | .22216 | - 4.0 | | +23 |
| Toulouse | 14 16.4W | 60 55.9N | .21945 | - 3.9 | -2.5 | +25 |
| Perpignan | 13 34.7W | 59 57.6N | .22453 | | | |
| Capo di Monte | 9 8.0W | 56 22.3N | | - 5.2 | -2.3 | |
| Madrid | 15 39.0W | | | | | |
| Coimbra | 17 18.1W | 59 22.0N | .22786 | - 3.7 | -4.3 | +34 |
| Lisbon | 17 15.7W | 57 53.0N | .23548 | | | |
| Athens | 5 38.2W | 52 7.5N | .26076 | | | |
| San Fernando | 15 57.5W | 55 8.8N | .24648 | | | |
| Tokyo | 4 34.9W | 49 0.3N | .29932 | | | |
| Zi-ka-wei | 2 23.5W | 45 43.5N | .32875 | + 1.5 | -1.5 | +37 |
| Helwan | 3 39.7W | 40 30.8N | .30136 | - 7.0 | -0.4 | - 7 |
| Hong-Kong | 0 17.5E | 31 22.8N | .36753 | + 1.8 | -4.3 | +45 |
| Kolaba | 0 23.2E | 21 26.5N | .37436 | + 2.2 | +7.0 | - 9 |
| Manila | 0 52.2E | 16 13.5N | .38064 | + 0.1 | -5.3 | +47 |
| Batavia | 1 7.3E | 30 35.5S | .36724 | + 3.0 | -7.3 | -11 |
| Mauritius | 9 25.2W | 54 9.4S | .23820 | - 4.7 | +4.6 | -39 |
| Rio de Janeiro | 8 2.9W | 13 20.1S | .2501 | +10.4 | -2.3 | |
| Melbourne | 8 25.6E | 67 24.6S | .23295 | | | |
+----------------+----------+----------+--------+-------+------+-------+

The rate of movement of the needle to the east at London--and
throughout Europe generally--fell off markedly subsequent to 1880. The
change of declination in fact between 1880 and 1895 was only about 75%
of that between 1865 and 1880, and the mean annual change from 1895 to
1900 was less than 75% of the mean annual change of the preceding
fifteen years. Thus in 1902 it was at least open to doubt whether a
change in the sign of the secular change were not in immediate
prospect. Subsequent, however, to that date there was little further
decline in the rate of secular change, and since 1905 there has been
very distinct acceleration. Thus, if we derive a mean value from the
eighteen European stations for which declination secular changes are
given in Tables I. and II. we find

mean value from table I. -4.18
" " " " II. -5.21

The epoch to which the data in Table II. refer is somewhat variable,
but is in all cases more recent than the epoch, January 1, 1901, for
Table I., the mean difference being about 5 years.

§ 10. At Paris there seems to have been a maximum of easterly
declination (about 9°) about 1580; the needle pointed to true north
about 1662, and reached its extreme westerly position between 1812 and
1814. The phenomena at Rome resembled those at Paris and London, but
the extreme westerly position is believed to have been attained
earlier. The rate of change near the turning point seems to have been
very slow, and as no fixed observatories existed in those days, the
precise time of its occurrence is open to some doubt.

Perhaps the most complete observations extant as to the declination
phenomena near a turning point relate to Kolaba observatory at Bombay;
they were given originally by N. A. F. Moos,[11] the director of the
observatory. Some of the more interesting details are given in Table
IV.; here W denotes movement to be west, and so answers to a numerical
diminution in the declination, which is easterly.

Prior to 1880 the secular change at Kolaba was unmistakably to the
east, and subsequent to 1883 it was clearly to the west; but between
these dates opinions will probably differ as to what actually
happened. The fluctuations then apparent in the sign of the annual
change may be real, but it is at least conceivable that they are of
instrumental origin. From 1870 to 1875 the mean annual change was
-1´.2; from 1885 to 1890 it was +1´.5, from 1890 to 1895 it was +2´.0,
while from 1895 to 1905 it was +2´.35, the + sign denoting movement to
the west. Thus, in this case the rate of secular change has increased
fairly steadily since the turning point was reached.

Table V. contains some data for St Helena and the Cape of Good
Hope,[12] both places having a long magnetic history. The remarkable
feature at St Helena is the uniformity in the rate of secular change.
The figures for the Cape show a reversal in the direction of the
secular change about 1840, but after a few years the arrested movement
to the west again became visible. According, however, to J. C.
Beattie's _Magnetic Survey of South Africa_ the movement to the west
ceased shortly after 1870. A persistent movement to the east then set
in, the mean annual change increasing from 1´.8 between 1873 and 1890
to 3´.8 between 1890 and 1900.

§ 11. Secular changes of declination have been particularly
interesting in the United States, an area about which information is
unusually complete, thanks to the labours and publications of the
United States Coast and Geodetic Survey.[13] At present the agonic
line passes in a south-easterly direction from Lake Superior to South
Carolina. To the east of the agonic line the declination is westerly,
and to the west it is easterly. In 1905 the declination varied from
about 21° W. in the extreme north-east to about 24° E. in the extreme
north-west. At present the motion of the agonic line seems to be
towards the west, but it is very slow. To the east of the agonic line
westerly declination is increasing, and to the west of the line, with
the exception of a narrow strip immediately adjacent to it, easterly
declination is increasing. The phenomena in short suggest a motion
southwards in the north magnetic pole. Since 1750 declination has
always been westerly in the extreme east of the States, and always
easterly in the extreme west, but the position of the agonic line has
altered a good deal. It was to the west of Richmond, Virginia, from
1750 to about 1772, then to the east of it until about 1838 when it
once more passed to the west; since that time it has travelled farther
to the west. Table VI. is intended to show the nature of the secular
change throughout the whole country. As before, + denotes that the
north pole of the magnet is moving to the west,--that it is moving to
the east.

The data in Table VI. represent the mean change of declination per
annum, derived from the period (ten years, except for 1900-1905) which
ended in the year put at the top of the column. The stations are
arranged in four groups, the first group representing the extreme
eastern, the last group the extreme western states, the other two
groups being intermediate. In each group the stations are arranged, at
least approximately, in order of latitude. The data are derived from
the values of the declination given in the Geodetic Survey's _Report_
for 1906, appendix 4, and _Magnetic Tables and Magnetic Charts_ by L.
A. Bauer, 1908. The values seem, in most cases, based to some extent
on calculation, and very probably the secular change was not in
reality quite so regular as the figures suggest. For the Western
States the earliest data are comparatively recent, but for some of the
eastern states data earlier than any in the table appear in the
_Report of the Coast and Geodetic Survey_ for 1902. These data
indicate that the easterly movement of the magnet, visible in all the
earlier figures for the Eastern States in Table VI., existed in all of
them at least as far back as 1700. There is not very much evidence as
to the secular change between 1700 and 1650, the earliest date to
which the Coast and Geodetic Survey's figures refer. The figures show
a maximum of westerly declination about 1670 in New Jersey and about
1675 in Maryland. They suggest that this maximum was experienced all
along the Atlantic border some time in the 17th century, but earlier
in the extreme north-east than in New York or Maryland.

Examination of Table VI. shows that the needle continued to move to
the east for some time after 1750 even in the Eastern States. But the
rate of movement was clearly diminishing, and about 1765 the extreme
easterly position was reached in Eastport, Maine, the needle then
beginning to retrace its steps to the west. The phenomena visible at
Maine are seen repeating themselves at places more and more to the
west, in Boston about 1785, in Albany about 1800, in Washington, D.C.,
about 1805, in Columbus (Ohio) about 1815, in Montgomery (Alabama)
about 1825, in Bloomington (Ill.) about 1830, in Des Moines (Iowa)
about 1840, in Santa Rosa (New Mexico) about 1860 and in Salt Lake
about 1870. In 1885 the needle was moving to the west over the whole
United States with the exception of a comparatively narrow strip along
the Pacific coast. Even an acute observer would have been tempted to
prophesy in 1885 that at no distant date the secular change would be
pronouncedly westerly right up to the Pacific. But in a few years a
complete change took place. The movement to the east, which had become
exceedingly small, if existent, in the Pacific states, began to
accelerate; the movement to the west continued in the central, as in
the eastern states, but perceptibly slackened. In 1905 the area
throughout which the movement to the west still continued had greatly
contracted and lay to the east of a line drawn from the west end of
Lake Superior to the west of Georgia. If we take a station like Little
Rock (Arkansas), we have the secular change to the west lasting for
about sixty years. Further west the period shortens. At Pueblo
(Colorado) it is about forty years, at Salt Lake under thirty years,
at Prescott (Arizona) about twenty years. Considering how fast the
area throughout which the secular change is easterly has extended to
the east since 1885, one would be tempted to infer that at no distant
date it will include the whole of the United States. In the extreme
north-east, however, the movement of the needle to the west, which had
slackened perceptibly after 1860 or 1870, is once more accelerating.
Thus the auspices do not all point one way, and the future is as
uncertain as it is interesting.

TABLE II.--Recent Values of the Magnetic Elements and their Rate of
Secular Change.