[1] _Eratosthenes Batavus, seu de terrae ambitus vera quantitate
suscitatus, a Willebrordo Snellio, Lugduni-Batavorum_ (1617).
[2] O. Callandreau, "Memoire sur la theorie de la figure des
planetes," _Ann. obs. de Paris_ (1889); G.H. Darwin, "The Theory of
the Figure of the Earth carried to the Second Order of Small
Quantities," _Mon. Not. R.A.S._, 1899; E. Wiechert, "Ueber die
Massenverteilung im Innern der Erde," _Nach. d. koen. G. d. W. zu
Goett._, 1897.
[3] See I. Todhunter, _Proc. Roy. Soc._, 1870.
[4] J.H. Jeans, "On the Vibrations and Stability of a Gravitating
Planet," _Proc. Roy. Soc._ vol. 71; G.H. Darwin, "On the Figure and
Stability of a liquid Satellite," _Phil. Trans._ 206, p. 161; A.E.H.
Love, "The Gravitational Stability of the Earth," _Phil. Trans._ 207,
p. 237; _Proc. Roy. Soc._ vol. 80.
[5] _Survey of India_, "The Attraction of the Himalaya Mountains upon
the Plumb Line in India" (1901), p. 98.
[6] _Account of Experiments to Determine the Figure of the Earth by
means of a Pendulum vibrating Seconds in Different Latitudes_ (1825).
[7] Helmert, _Theorien d. hoeheren Geod._ ii., Leipzig, 1884.
[8] Helmert, _Sitzber. d. kgl. preuss. Ak. d. Wiss. zu Berlin_
(1901), p. 336.
[9] "Bestimmung der absoluten Groesse der Schwerkraft zu Potsdam mit
Reversionspendeln" (_Veroeffentlichung des kgl. preuss. Geod. Inst._,
N.F., No. 27).
[10] _Die Koenigl. Observatorien fuer Astrophysik, Meteorologie und
Geodaesie bei Potsdam_ (Berlin, 1890); _Verhandlungen der I.
Allgemeinen Conferenz der Bevollmaechtigten zur mitteleurop.
Gradmessung_, October, 1864, in Berlin (Berlin, 1865); A. Hirsch,
_Verhandlungen der VIII. Allg. Conf. der Internationalen Erdmessung_,
October, 1886, in Berlin (Berlin, 1887); and _Verhandlungen der XI.
Allg. Conf. d. I. E._, October, 1895, in Berlin (1896).
[11] Ibanez and Perrier, _Jonction geod. et astr. de l'Algerie avec
l'Espagne_ (Paris, 1886); _Memorial du depot general de la guerre_,
t. xii.: _Nouvelle meridienne de France_ (Paris, 1885, 1902, 1904);
_Comptes rendus des seances de la 12^e-19^e conference generale de
l'Assoc. Geod. Internat._, 1898 at Stuttgart, 1900 at Paris, 1903 at
Copenhagen, 1906 at Budapest (Berlin, 1899, 1901, 1904, 1908); A.
Ferrero, _Rapport sur les triangulations, pres. a la 12^e conf. gen.
1898_.
[12] R. Schumann, _C. r. de Budapest_, p. 244.
[13] O. and A. Boersch, "Verbindung d. russ.-skandinav. mit der
franz.-engl. Breitengradmessung" (_Verhandlungen der 9. Allgem. Conf.
d. I. E. in Paris, 1889_, Ann. xi.).
[14] U.S. Coast and Geodetic Survey; H.S. Pritchett, superintendent.
_The Transcontinental Triangulation and the American Arc of the
Parallel_, by C.A. Schott (Washington, 1900).
[15] U.S. Coast and Geodetic Survey; O.H. Tittmann, superintendent.
_The Eastern Oblique Arc of the United States_, by C.A. Schott
(1902).
[16] _Missions scientifiques pour la mesure d'un arc de meridien au
Spitzberg entreprises en 1899-1902 sous les auspices des
gouvernements russe et suedois._ _Mission russe_ (St Petersbourg,
1904); _Mission suedoise_ (Stockholm, 1904).
[17] Sir David Gill, _Report on the Geodetic Survey of South Africa,
1833-1892_ (Cape Town, 1896), vol. ii. 1901, vol. iii. 1905.
[18] O. Hecker, _Bestimmung der Schwerkraft a. d. Atlantischen Ozean_
(Veroeffentl. d. Kgl. Preuss. Geod. Inst. No. 11), Berlin, 1903.
[19] F.R. Helmert. "Neuere Fortschritte in der Erkenntnis der math.
Erdgestalt" (_Verhandl. des VII. Internationalen
Geographen-Kongresses, Berlin, 1899_), London, 1901.
[20] C. Lallemand, "Rapport sur les travaux du service du nivellement
general de la France, de 1900 a 1906" (_Comp. rend. de la 14^e conf.
gen. de l'Assoc. Geod-Intern., 1903_, p. 178).
[21] T. Albrecht, _Resultate des internat. Breitendienstes_, i. and
ii. (Berlin, 1903 and 1906); F. Klein and A. Sommerfeld, _Ueber die
Theorie des Kreisels_, iii. p. 672; R. Spitaler, "Die periodischen
Luftmassenverschiebungen und ihr Einfluss auf die Lagenaenderung der
Erdaxe" (_Petermanns Mitteilungen, Ergaenzungsheft_, 137); S. Newcomb,
"Statement of the Theoretical Laws of the Polar Motion"
(_Astronomical Journal_, 1898, xix. 158); F.R. Helmert, "Zur
Erklaerung der beobachteten Breitenaenderungen" (_Astr. Nachr._ No.
3014); J. Weeder, "The 14-monthly period of the motion of the Pole
from determinations of the azimuth of the meridian marks of the
Leiden observatory" (_Kon. Ak. van Wetenschappen to Amsterdam_,
1900); A. Sokolof, "Determination du mouvement du pole terr. au moyen
des mires meridiennes de Poulkovo" (_Mel. math. et astr._ vii.,
1894); J. Bonsdorff, "Beobachtungen von [delta] Cassiopejae mit dem
grossen Zenitteleskop" (_Mitteilungen der Nikolai-Hauptsternwarte zu
Pulkowo_, 1907); J. Larmor and E.H. Hills, "The irregular movement of
the Earth's axis of rotation: a contribution towards the analysis of
its causes" (_Monthly Notices R.A.S._, 1906, lxvii. 22); A.S.
Cristie, "The latitude variation Tide" (_Phil. Soc. of Wash._, 1895,
_Bull._ xiii. 103); H.G. van de Sande Bakhuysen, "Ueber die Aenderung
der Polhoehe" (_Astr. Nachr._ No. 3261); A.V. Baecklund, "Zur Frage
nach der Bewegung des Erdpoles" (_Astr. Nachr._ No. 3787); R.
Schumann, "Ueber die Polhoehenschwankung" (_Astr. Nachr._ No. 3873);
"Numerische Untersuchung" (_Ergaenzungshefte zu den Astr. Nachr._ No.
11); _Weitere Untersuchungen_ (No. 4142); _Bull. astr._, 1900, June,
report of different theoretical memoirs.
EARTH CURRENTS. After the invention of telegraphy it was soon found that
telegraph lines in which the circuit is completed by the earth are
traversed by natural electric currents which occasionally interfere
seriously with their use, and which are known as "earth currents."
1. Amongst the pioneers in investigating the subject were several English
telegraphists, e.g. W.H. Barlow (1) and C.V. Walker (2), who were in
charge respectively of the Midland and South-Eastern telegraph systems.
Barlow noticed the existence of a more or less regular diurnal variation,
and the result--confirmed by all subsequent investigators--that earth
currents proper occur in a line only when both ends are earthed. Walker,
as the result of general instructions issued to telegraph clerks,
collected numerous statistics as to the phenomena during times of large
earth currents. His results and those given by Barlow both indicate that
the lines to suffer most from earth currents in England have the general
direction N.E. to S.W. As Walker points out, it is the direction of the
terminal plates relative to one another that is the essential thing. At
the same time he noticed that whilst at any given instant the currents in
parallel lines have with rare exceptions the same direction, some lines
show normally stronger currents than others, and he suggested that
differences in the geological structure of the intervening ground might
be of importance. This is a point which seems still somewhat obscure.
Our present knowledge of the subject owes much to practical men, but
even in the early days of telegraphy the fact that telegraph systems are
commercial undertakings, and cannot allow the public to wait the
convenience of science, was a serious obstacle to their employment for
research. Thus Walker feelingly says, when regretting his paucity of
data during a notable earth current disturbance: "Our clerks were at
their wits' end to clear off the telegrams.... At a time when
observations would have been very highly acceptable they were too much
occupied with their ordinary duties." Some valuable observations have,
however, been made on long telegraph lines where special facilities have
been given.
Amongst these may be mentioned the observations on French lines in 1883
described by E.E. Blavier (3), and those on two German lines
Berlin-Thorn and Berlin-Dresden during 1884 to 1888 discussed by B.
Weinstein (4).
2. Of the experimental lines specially constructed perhaps the best
known are the Greenwich lines instituted by Sir G.B. Airy (5), the lines
at Pawlowsk due to H. Wild (6), and those at Parc Saint Maur, near Paris
(7).
_Experimental Lines._--At Greenwich observations were commenced in 1865,
but there have been serious disturbances due to artificial currents from
electric railways for many years. There are two lines, one to Dartford
distant about 10 m., in a direction somewhat south of east, the other to
Croydon distant about 8 m., in a direction west of south.
Information from a single line is incomplete, and unless this is clearly
understood erroneous ideas may be derived. The times at which the
current is largest and least, or when it vanishes, in an east-west line,
tell nothing directly as to the amplitude at the time of the resultant
current. The lines laid down at Pawlowsk in 1883 lay nearly in and
perpendicular to the geographical meridian, a distinct desideratum, but
were only about 1 km. long. The installation at Parc Saint Maur,
discussed by T. Moureaux, calls for fuller description. There are three
lines, one having terminal earth plates 14.8 km. apart in the
geographical meridian, a second having its earth plates due east and
west of one another, also 14.8 km. apart, and the third forming a closed
circuit wholly insulated from the ground. In each of the three lines is
a Deprez d'Arsonval galvanometer. Light reflected from the galvanometer
mirrors falls on photographic paper wound round a drum turned by
clockwork, and a continuous record is thus obtained.
3. Each galvanometer has a resistance of about 200 ohms, but is shunted
by a resistance of only 2 ohms. The total effective resistances in the
N.-S. and E.-W. lines are 225 and 348 ohms respectively. If i is the
current recorded, L, g and s the resistances of the line, galvanometer
and shunt respectively, then E, the difference of potential between the
two earth plates, is given by
E = i(1 + g/s) {L + gs/(g + s)}.
To calibrate the record, a Daniell cell is put in a circuit including
1000 ohms and the three galvanometers as shunted. If i' be the current
recorded, e the E.M.F. of the cell, then e = i'(1 + g/s){1000 + 3gs/(g +
s)}. Under the conditions at Parc Saint Maur we may write 2 for gs/(g +
s), and 1.072 for e, and thence we have approximately E = 0.240(i/i')
for the N.-S. line, and E = -0.371(i/i') for the E.-W. line.
The method of standardization assumes a potential difference between
earth plates which varies slowly enough to produce a practically steady
current. There are several causes producing currents in a telegraph wire
which do not satisfy this limitation. During thunderstorms surgings may
arise, at least in overhead wires, without these being actually struck.
Again, if the circuit includes a variable magnetic field, electric
currents will be produced independently of any direct source of
potential difference. In the third circuit at Parc Saint Maur, where no
earth plates exist, the current must be mainly due to changes in the
earth's vertical magnetic field, with superposed disturbances due to
atmospheric electricity or aerial waves. Even in the other circuits,
magnetic and atmospheric influences play some part, and when their
contribution is important, the galvanometer deflection has an uncertain
value. What a galvanometer records when traversed by a suddenly varying
current depends on other things than its mere resistance.
Even when the current is fairly steady, its exact significance is not
easily stated. In the first place there is usually an appreciable E.M.F.
between a plate and the earth in contact with it, and this E.M.F. may
vary with the temperature and the dryness of the soil. Naturally one
employs similar plates buried to the same depth at the two ends, but
absolute identity and invariability of conditions can hardly be secured.
In some cases, in short lines (8), there is reason to fear that plate
E.M.F.'s have been responsible for a good deal that has been ascribed to
true earth currents. With deep earth plates, in dry ground, this source
of uncertainty can, however, enter but little into the diurnal
inequality.
4. Another difficulty is the question of the resistance in the earth
itself. A given E.M.F. between plates 10 m. apart may mean very
different currents travelling through the earth, according to the
chemical constitution and condition of the surface strata.
According to Professor A. Schuster (9), if [rho] and [rho]' be the
specific resistances of the material of the wire and of the soil, the
current i which would pass along an underground cable formed of actual
soil, equal in diameter to the wire connecting the plates, is given by i
= i'[rho]/[rho]', where i' is the observed current in the wire. As
[rho]' will vary with the depth, and be different at different places
along the route, while discontinuities may arise from geological faults,
water channels and so on, it is clear that even the most careful
observations convey but a general idea as to the absolute intensity of
the currents in the earth itself. In Schuster's formula, as in the
formulae deduced for Parc Saint Maur, it is regarded as immaterial
whether the wire connecting the plates is above or below ground. This
view is in accordance with records obtained by Blavier (3) from two
lines between Paris and Nancy, the one an air line, the other
underground.
5. The earliest quantitative results for the regular diurnal changes in
earth currents are probably those deduced by Airy (5) from the records
at Greenwich between 1865 and 1867. Airy resolved the observed currents
from the two Greenwich lines in and perpendicular to the _magnetic_
meridian (then about 21 deg. to the west of astronomical north). The
information given by Airy as to the precise meaning of the quantities he
terms "magnetic tendency" to north and to west is somewhat scanty, but
we are unlikely to be much wrong in accepting his figures as
proportional to the earth currents from magnetic east to west and from
magnetic north to south respectively. Airy gives mean hourly values for
each month of the year. The corresponding mean diurnal inequality for
the whole year appears in Table 1., the unit being arbitrary. In every
month the algebraic mean of the 24 hourly values represented a current
from north to south in the magnetic meridian, and from east to west in
the perpendicular direction; in the same arbitrary units used in Table
I. the mean values of these two "constant" currents were respectively
777 and 559.
6. _Diurnal Variation._--Probably the most complete records of diurnal
variation are those discussed by Weinstein (4), which depend on several
years' records on lines from Berlin to Dresden and to Thorn. Relative to
Berlin the geographical co-ordinates of the other two places are:
Thorn 0 deg. 29' N. lat. 5 deg. 12' E. long.
Dresden 1 deg. 28' S. lat. 0 deg. 21' E. long.
Thus the Berlin-Dresden line was directed about 81/2 deg. east of south, and
the Berlin-Thorn line somewhat more to the north of east. The latter
line had a length about 2.18 times that of the former. The resistances
in the two lines were made the same, so if we suppose the difference of
potential between earth plates along a given direction to vary as their
distance apart, the current observed in the Thorn-Berlin line has to be
divided by 2.18 to be comparable with the other. In this way, resolving
along and perpendicular to the geographical meridian, Weinstein gives as
proportional to the earth currents from east to west and from south to
north respectively
J = 0.147i' + 0.435i, and J' = 0.989i' - 0.100i,
where i and i' are the observed currents in the Thorn-Berlin and
Dresden-Berlin lines respectively, both being counted positive when
flowing towards Berlin.
It is tacitly assumed that the average earth conductivity is the same
between Berlin and Thorn as between Berlin and Dresden. It should also
be noticed that local time at Berlin and Thorn differs by fully 20
minutes, while the crests of the diurnal variations in _short_ lines at
the two places would probably occur about the same local time. The
result is probably a less sharp occurrence of maxima and minima, and a
relatively smaller range, than in a short line having the same
orientation.