Chapter X: Part 10

The values of a given above are in terms of the international metre; the earlier ones in legal metres, while the gravity formulae are in international metres.

_The International Geodetic Association (Internationale Erdmessung)._

On the proposition of the Prussian lieutenant-general, Johann Jacob Baeyer, a conference of delegates of several European states met at Berlin in 1862 to discuss the question of a "Central European degree-measurement." The first general conference took place at Berlin two years later; shortly afterwards other countries joined the movement, which was then named "The European degree-measurement." From 1866 till 1886 Prussia had borne the expense incident to the central bureau at Berlin; but when in 1886 the operations received further extension and the title was altered to "The International Earth-measurement" or "International Geodetic Association," the co-operating states made financial contributions to this purpose. The central bureau is affiliated with the Prussian Geodetic Institute, which, since 1892, has been situated on the Telegraphenberg near Potsdam. After Baeyer's death Prof. Friedrich Robert Helmert was appointed director. The funds are devoted to the advancement of such scientific works as concern all countries and deal with geodetic problems of a general or universal nature. During the period 1897-1906 the following twenty-one countries belonged to the association:--Austria, Belgium, Denmark, England, France, Germany, Greece, Holland, Hungary, Italy, Japan, Mexico, Norway, Portugal, Rumania, Russia, Servia, Spain, Sweden, Switzerland and the United States of America. At the present time general conferences take place every three years.[10]

Baeyer projected the investigation of the curvature of the meridians and the parallels of the mathematical surface of the earth stretching from Christiania to Palermo for 12 degrees of longitude; he sought to co-ordinate and complete the network of triangles in the countries through which these meridians passed, and to represent his results by a common unit of length. This proposition has been carried out, and extended over the greater part of Europe; as a matter of fact, the network has, with trifling gaps, been carried over the whole of western and central Europe, and, by some chains of triangles, over European Russia. Through the co-operation of France, the network has been extended into north Africa as far as the geographical latitude of 32 deg.; in Greece a network, united with those of Italy and Bosnia, has been carried out by the Austrian colonel, Heinrich Hartl; Servia has projected similar triangulations; Rumania has begun to make the triangle measurements, and three base lines have been measured by French officers with Brunner's apparatus. At present, in Rumania, there is being worked a connexion between the arc of parallel in lat. 47 deg./48 deg. in Russia (stretching from Astrakan to Kishinev) with Austria-Hungary. In the latter country and in south Bavaria the connecting triangles for this parallel have been recently revised, as well as the French chain on the Paris parallel, which has been connected with the German net by the co-operation of German and French geodesists. This will give a long arc of parallel, really projected in the first half of the 19th century. The calculation of the Russian section gives, with an assumed ellipticity of 1/299.15, the value a = 6377350 metres; this is rather uncertain, since the arc embraces only 19 deg. in longitude.

We may here recall that in France geodetic studies have recovered their former expansion under the vigorous impulse of Colonel (afterwards General) Francois Perrier. When occupied with the triangulation of Algeria, Colonel Perrier had conceived the possibility of the geodetic junction of Algeria to Spain, over the Mediterranean; therefore the French meridian line, which was already connected with England, and was thus produced to the 60th parallel, could further be linked to the Spanish triangulation, cross thence into Algeria and extend to the Sahara, so as to form an arc of about 30 deg. in length. But it then became urgent to proceed to a new measurement of the French arc, between Dunkirk and Perpignan. In 1869 Perrier was authorized to undertake that revision. He devoted himself to that work till the end of his career, closed by premature death in February 1888, at the very moment when the _Depot de la guerre_ had just been transformed into the Geographical Service of the Army, of which General F. Perrier was the first director. His work was continued by his assistant, Colonel (afterwards General) J.A.L. Bassot. The operations concerning the revision of the French arc were completed only in 1896. Meanwhile the French geodesists had accomplished the junction of Algeria to Spain, with the help of the geodesists of the Madrid Institute under General Carlos Ibanez (1879), and measured the meridian line between Algiers and El Aghuat (1881). They have since been busy in prolonging the meridians of El Aghuat and Biskra, so as to converge towards Wargla, through Ghardaia and Tuggurt. The fundamental co-ordinates of the Pantheon have also been obtained anew, by connecting the Pantheon and the Paris Observatory with the five stations of Bry-sur-Marne, Morlu, Mont Valerien, Chatillon and Montsouris, where the observations of latitude and azimuth have been effected.[11]

According to the calculations made at the central bureau of the international association on the great meridian arc extending from the Shetland Islands, through Great Britain, France and Spain to El Aghuat in Algeria, a = 6377935 metres, the ellipticity being assumed as 1/299.15. The following table gives the difference: astronomical-geodetic latitude. The net does not follow the meridian exactly, but deviates both to the west and to the east; actually, the meridian of Greenwich is nearer the mean than that of Paris (Helmert, _Groesse d. Erde_).

_West Europe-Africa Meridian-arc._[12]

Name. Latitude. A.-G.
deg. ' "
Saxavord 60 49.6 -4.0
Balta 60 45.0 -6.1
Ben Hutig 58 33.1 +0.3
Cowhythe 57 41.1 +7.3
Great Stirling 57 27.8 -2.3
Kellie Law 56 14.9 -3.7
Calton Hill 55 57.4 +3.5
Durham 54 46.1 -0.9
Burleigh Moor 54 34.3 +2.1
Clifton Beacon 53 27.5 +1.3
Arbury Hill 52 13.4 -3.0
Greenwich 51 28.6 -2.5
Nieuport 51 7.8 -0.4
Rosendael 51 2.7 -0.9
Lihons 49 49.9 +0.5
Pantheon 48 50.8 -0.0
Chevry 48 0.5 +2.2
Saligny le Vif 47 2.7 +3.0
Arpheuille 46 13.7 +6.3
Puy de Dome 45 46.5 +7.0
Rodez 44 21.4 +1.7
Carcassonne 43 13.3 +0.7
Rivesaltes 42 45.2 -0.7
Montolar 41 38.5 +3.6
Lerida 41 37.0 -0.2
Javalon 40 13.8 -0.2
Desierto 40 5.0 -4.5
Chinchilla 38 55.2 +2.2
Mola de Formentera 38 39.9 -1.2
Tetica 37 15.2 +3.5
Roldan 36 56.6 -6.0
Conjuros 36 44.4 -12.6
Mt. Sabiha 35 39.6 +6.5
Nemours 35 5.8 +7.4
Bouzareah 36 48.0 +2.9
Algiers (Voirol) 36 45.1 -9.1
Guelt es Stel 35 7.8 -1.0
El Aghuat 33 48.0 -2.8

While the radius of curvature of this arc is obviously not uniform (being, in the mean, about 600 metres greater in the northern than in the southern part), the Russo-Scandinavian meridian arc (from 45 deg. to 70 deg.), on the other hand, is very uniformly curved, and gives, with an ellipticity of 1/299.15, a = 6378455 metres; this arc gives the plausible value 1/298.6 for the ellipticity. But in the case of this arc the orographical circumstances are more favourable.

The west-European and the Russo-Scandinavian meridians indicate another anomaly of the geoid. They were connected at the Central Bureau by means of east-to-west triangle chains (principally by the arc of parallel measurements in lat. 52 deg.); it was shown that, if one proceeds from the west-European meridian arcs, the differences between the astronomical and geodetic latitudes of the Russo-Scandinavian arc become some 4" greater.[13]

The central European meridian, which passes through Germany and the countries adjacent on the north and south, is under review at Potsdam (see the publications of the Kgl. Preuss. Geod. Inst., _Lotabweichungen_, Nos. 1-3). Particular notice must be made of the Vienna meridian, now carried southwards to Malta. The Italian triangulation is now complete, and has been joined with the neighbouring countries on the north, and with Tunis on the south.

The United States Coast and Geodetic Survey has published an account of the transcontinental triangulation and measurement of an arc of the parallel of 39 deg., which extends from Cape May (New Jersey), on the Atlantic coast, to Point Arena (California), on the Pacific coast, and embraces 48 deg. 46' of longitude, with a linear development of about 4225 km. (2625 miles). The triangulation depends upon ten base-lines, with an aggregate length of 86 km. the longest exceeding 17 km. in length, which have been measured with the utmost care. In crossing the Rocky Mountains, many of its sides exceed 100 miles in length, and there is one side reaching to a length of 294 km., or 183 miles; the altitude of many of the stations is also considerable, reaching to 4300 metres, or 14,108 ft., in the case of Pike's Peak, and to 14,421 ft. at Elbert Peak, Colo. All geometrical conditions subsisting in the triangulation are satisfied by adjustment, inclusive of the required accord of the base-lines, so that the same length for any given line is found, no matter from what line one may start.[14]

Over or near the arc were distributed 109 latitude stations, occupied with zenith telescopes; 73 azimuth stations; and 29 telegraphically determined longitudes. It has thus been possible to study in a very complete manner the deviations of the vertical, which in the mountainous regions sometimes amount to 25 seconds, and even to 29 seconds.

With the ellipticity 1/299.15, a = 6377897 +- 65 metres (prob. error); in this calculation, however, some exceedingly perturbed stations are excluded; for the employed stations the mean perturbation in longitude is +- 4.9" (zenith-deflection east-to-west +- 3.8").

The computations relative to another arc, the "eastern oblique arc of the United States," are also finished.[15] It extends from Calais (Maine) in the north-east, to the Gulf of Mexico, and terminates at New Orleans (Louisiana), in the south. Its length is 2612 km. (1623 miles), the difference of latitude 15 deg. 1', and of longitude 22 deg. 47'. In the main, the triangulation follows the Appalachian chain of mountains, bifurcating once, so as to leave an oval space between the two branches. It includes among its stations Mount Washington (1920 metres) and Mount Mitchell (2038 metres). It depends upon six base-lines, and the adjustment is effected in the same manner as for the arc of the parallel. The astronomical data have been afforded by 71 latitude stations, 17 longitude stations, and 56 azimuth stations, distributed over the whole extent of the arc. The resulting dimensions of an osculating spheroid were found to be

a = 6378157 metres +- 90 (prob. error),
e(ellipticity) = 1/304.5 +- 1.9 (prob. error).

With the ellipticity 1/399.15, a = 6378041 metres +- 80 (prob. er.).

During the years 1903-1906 the United States Coast and Geodetic Survey, under the direction of O.H. Tittmann and the special management of John F. Hayford, executed a calculation of the best ellipsoid of rotation for the United States. There were 507 astronomical determinations employed, all the stations being connected through the net-work of triangles. The observed latitudes, longitude and azimuths were improved by the attractions of the earth's crust on the hypothesis of isostasis for three depths of the surface of 114, 121 and 162 km., where the isostasis is complete. The land-masses, within the distance of 4126 km., were taken into consideration. In the derivation of an ellipsoid of rotation, the first case proved itself the most favourable, and there resulted:--

a = 6378283 metres +- 74 (prob. er.), ellipticity
= 1/297.8 +- 0.9 (prob. er.).

The most favourable value for the depth of the isostatic surface is approximately 114 km.

The measurement of a great meridian arc, in long. 98 deg. W., has been commenced; it has a range of latitude of 23 deg., and will extend over 50 deg. when produced southwards and northwards by Mexico and Canada. It may afterwards be connected with the arc of Quito. A new measurement of the meridian arc of Quito was executed in the years 1901-1906 by the _Service geographique_ of France under the direction of the Academie des Sciences, the ground having been previously reconnoitred in 1899. The new arc has an amplitude in latitude of 5 deg. 53' 33", and stretches from Tulcan (lat. 0 deg. 48' 25") on the borders of Columbia and Ecuador, through Columbia to Payta (lat. -5 deg. 5' 8") in Peru. The end-points, at which the chain of triangles has a slight north-easterly trend, show a longitude difference of 3 deg.. Of the 74 triangle points, 64 were latitude stations; 6 azimuths and 8 longitude-differences were measured, three base-lines were laid down, and gravity was determined from six points, in order to maintain indications over the general deformation of the geoid in that region. Computations of the attraction of the mountains on the plumb-line are also being considered. The work has been much delayed by the hardships and difficulties encountered. It was conducted by Lieut.-Colonel Robert Bourgeois, assisted by eleven officers and twenty-four soldiers of the geodetic branch of the _Service geographique_. Of these officers mention may be made of Commandant E. Maurain, who retired in 1904 after suffering great hardships; Commandant L. Massenet, who died in 1905; and Captains I. Lacombe, A. Lallemand, and Lieut. Georges Perrier (son of General Perrier). It is conceivable that the chain of triangles in longitude 98 deg. in North America may be united with that of Ecuador and Peru: a continuous chain over the whole of America is certainly but a question of time. During the years 1899-1902 the measurement of an arc of meridian was made in the extreme north, in Spitzbergen, between the latitudes 76 deg. 38' and 80 deg. 50', according to the project of P.G. Rosen. The southern part was determined by the Russians--O. Baecklund, Captain D.D. Sergieffsky, F.N. Tschernychev, A. Hansky and others--during 1899-1901, with the aid of 1 base-line, 15 trigonometrical, 11 latitude and 5 gravity stations. The northern part, which has one side in common with the southern part, has been determined by Swedes (Professors Rosen, father and son, E. Jaederin, T. Rubin and others), who utilized 1 base-line, 9 azimuth measurements, 18 trigonometrical, 17 latitude and 5 gravity stations. The party worked under excessive difficulties, which were accentuated by the arctic climate. Consequently, in the first year, little headway was made.[16]

Sir David Gill, when director of the Royal Observatory, Cape Town, instituted the magnificent project of working a latitude-degree measurement along the meridian of 30 deg. long. This meridian passes through Natal, the Transvaal, by Lake Tanganyika, and from thence to Cairo; connexion with the Russo-Scandinavian meridian arc of the same longitude should be made through Asia Minor, Turkey, Bulgaria and Rumania. With the completion of this project a continuous arc of 105 deg. in latitude will have been measured.[17]

Extensive triangle chains, suitable for latitude-degree measurements, have also been effected in Japan and Australia.

Besides, the systematization of gravity measurements is of importance, and for this purpose the association has instituted many reforms. It has ensured that the relative measurements made at the stations in different countries should be reduced conformably with the absolute determinations made at Potsdam; the result was that, in 1906, the intensities of gravitation at some 2000 stations had been co-ordinated. The intensity of gravity on the sea has been determined by the comparison of barometric and hypsometric observations (Mohn's method). The association, at the proposal of Helmert, provided the necessary funds for two expeditions:--English Channel--Rio de Janeiro, and the Red Sea--Australia--San Francisco--Japan. Dr O. Hecker of the central bureau was in charge; he successfully overcame the difficulties of the work, and established the tenability of the isostatic hypothesis, which necessitates that the intensity of gravity on the deep seas has, in general, the same value as on the continents (without regard to the proximity of coasts).[18]

As the result of the more recent determinations, the ellipticity, compression or flattening of the ellipsoid of the earth may be assumed to be very nearly 1/298.3; a value determined in 1901 by Helmert from the measurements of gravity. The semi-major axis, a, of the meridian ellipse may exceed 6,378,000 inter. metres by about 200 metres. The central bureau have adopted, for practical reasons, the value 1/299.15, after Bessel, for which tables exist; and also the value a = 6377397.155(1 + 0.0001).

The methods of theoretical astronomy also permit the evaluation of these constants. The semi-axis a is calculable from the parallax of the moon and the acceleration of gravity on the earth; but the results are somewhat uncertain: the ellipticity deduced from lunar perturbations is 1/297.8 +- 2 (Helmert, _Geodaesie_, ii. pp. 460-473); William Harkness (_The Solar Parallax and its related Constants_, 1891) from all possible data derived the values: ellipticity = 1/300.2 +- 3, a = 6377972 +- 125 metres. Harkness also considered in this investigation the relation of the ellipticity to precession and nutation; newer investigations of the latter lead to the limiting values 1/296, 1/298 (Wiechert). It was clearly noticed in this method of determination that the influence of the assumption as to the density of the strata in the interior of the earth was but very slight (Radau, _Bull. astr._ ii. (1885) 157). The deviations of the geoid from the flattened ellipsoid of rotation with regard to the heights (the directions of normals being nearly the same) will scarcely exceed +- 100 metres (Helmert).[19]

The basis of the degree- and gravity-measurements is actually formed by a stationary sea-surface, which is assumed to be level. However, by the influence of winds and ocean currents the mean surface of the sea near the coasts (which one assumes as the fundamental sea-surface) can deviate somewhat from a level surface. According to the more recent levelling it varies at the most by only some decimeters.[20]

It is well known that the masses of the earth are continually undergoing small changes; the earth's crust and sea-surface reciprocally oscillate, and the axis of rotation vibrates relatively to the body of the earth. The investigation of these problems falls in the programme of the Association. By continued observations of the water-level on sea-coasts, results have already been obtained as to the relative motions of the land and sea (cf. GEOLOGY); more exact levelling will, in the course of time, provide observations on countries remote from the sea-coast. Since 1900 an international service has been organized between some astronomical stations distributed over the north parallel of 39 deg. 8', at which geographical latitudes are observed whenever possible. The association contributes to all these stations, supporting four entirely: two in America, one in Italy, and one in Japan; the others partially (Tschardjui in Russia, and Cincinnati observatory). Some observatories, especially Pulkowa, Leiden and Tokyo, take part voluntarily. Since 1906 another station for South America and one for Australia in latitude -31 deg. 55' have been added. According to the existing data, geographical latitudes exhibit variations amounting to +-0.25", which, for the greater part, proceed from a twelve- and a fourteen-month period.[21] (A. R. C; F. R. H.)

FOOTNOTES:

[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.

TABLE I.

+-----------------------------------------------------+------------------------------+
| Mean Diurnal Inequalities for the year. |Numerical Values of resultant |
| | current. |
+----------------------+------------------------------+------------------------------+
| Greenwich. | Thorn-Berlin-Dresden. | Thorn-Berlin-Dresden. |
+--------+-------------+--------+-------+------+------+------------------------------+
| |North | East | Berlin | Thorn |North | East | Mean hourly values from |
| Hour. | to | to | to | to | to | to +-----+-------+--------+-------+
| |South | West |Dresden.|Berlin.|South | West |Year.|Winter.|Equinox.|Summer.|
| |(Mag.)|(Mag.)| | |(Ast.)|(Ast.)| | | | |
+--------+------+------+--------+-------+------+------+-----+-------+--------+-------+
| 1 | -94 | -41 | -17 | -13 | -20 | -10 | 81 | 94 | 51 | 98 |
| 2 | -68 | -24 | -6 | -13 | -9 | -11 | 84 | 115 | 39 | 97 |
| 3 | -44 | -8 | -1 | -1 | -1 | -1 | 84 | 113 | 31 | 108 |
| 4 | -18 | +9 | -20 | +15 | -17 | +17 | 101 | 94 | 58 | 127 |
| 5 | -30 | -1 | -79 | +21 | -74 | +32 | 122 | 58 | 78 | 230 |
| 6 | -63 | -33 | -139 | +5 | -136 | +26 | 148 | 80 | 139 | 225 |
| 7 | -121 | -80 | -138 | -36 | -144 | -14 | 166 | 155 | 206 | 136 |
| 8 | -175 | -123 | -7 | -98 | -28 | -92 | 203 | 152 | 185 | 271 |
| 9 | -156 | -137 | +249 | -156 | +212 | -184 | 305 | 67 | 272 | 575 |
| 10 | -43 | -77 | +540 | -184 | +494 | -254 | 557 | 232 | 628 | 811 |
| 11 | +82 | +1 | +722 | -165 | +678 | -263 | 728 | 411 | 885 | 887 |
| Noon | +207 | +66 | +673 | -107 | +642 | -200 | 675 | 441 | 848 | 735 |
| 1 | +245 | +94 | +404 | -20 | +395 | -79 | 400 | 284 | 510 | 406 |
| 2 | +205 | +113 | +35 | +55 | +46 | +47 | 98 | 68 | 103 | 125 |
| 3 | +153 | +97 | -261 | +99 | -237 | +132 | 272 | 136 | 355 | 324 |
| 4 | +159 | +108 | -397 | +114 | -368 | +167 | 404 | 218 | 503 | 492 |
| 5 | +167 | +118 | -391 | +108 | -363 | +160 | 397 | 206 | 453 | 532 |
| 6 | +125 | +95 | -311 | +96 | -287 | +137 | 319 | 176 | 333 | 446 |
| 7 | +43 | +55 | -237 | +85 | -216 | +115 | 247 | 180 | 250 | 312 |
| 8 | -22 | +4 | -191 | +74 | -173 | +98 | 201 | 207 | 217 | 181 |
| 9 | -115 | -49 | -168 | +59 | -153 | +81 | 174 | 208 | 194 | 120 |
| 10 | -138 | -74 | -135 | +40 | -125 | +58 | 138 | 155 | 149 | 111 |
| 11 | -136 | -70 | -84 | +18 | -79 | +29 | 89 | 64 | 95 | 107 |
|Midnight| -147 | -80 | -43 | -2 | -43 | +4 | 91 | 42 | 119 | 111 |
+--------+------+------+--------+-------+------+------+-----+-------+--------+-------+

It was found that the average current derived from a number of undisturbed days on either line might be regarded as made up of a "constant part" plus a regular diurnal inequality, the constant part representing the algebraic mean value of the 24 hourly readings. In both lines the constant part showed a decided alteration during the third year--changing sign in one line--in consequence, it is believed, of alterations made in the earth plates. The constant part was regarded as a plate effect, and was omitted from further consideration. Table I. shows in terms of an arbitrary unit--whose relation to that employed for Greenwich data is unknown--the diurnal inequality in the currents along the two lines, and the inequalities thence calculated for ideal lines in and perpendicular to the _geographical_ meridian. Currents are regarded as positive when directed from Berlin to Dresden and from north to south, the opposite point of view to that adopted by Weinstein. The table also shows the mean _numerical_ value of the resultant current (the "constant" part being omitted) for each hour of the day, for the year as a whole, and for winter (November to February), equinox (March, April, September, October) and summer (May to August). There is a marked double period in both the N.-S. and E.-W. currents. In both cases the numerically largest currents occur from 10 A.M. to noon, the directions then being from north to south and from west to east. The currents tend to die out and change sign about 2 P.M., the numerical magnitude then rising again rapidly to 4 or 5 P.M. The current in the meridian is notably the larger. The numerical values assigned to the resultant current are arithmetic means from the several months composing the season in question.

7. The mean of the 24 hourly numerical values of the resultant current for each month of the year a deducible from Weinstein's data--the unit being the same as before--are given in Table II.

TABLE II.--_Mean Numerical Value of Resultant Current._

Jan. Feb. March April May June July Aug. Sep. Oct. Nov. Dec.
152 211 293 328 313 314 337 300 258 235 165 132

There is thus a conspicuous minimum at mid-winter, and but little difference between the monthly means from April to August. This is closely analogous to what is seen in the daily range of the magnetic elements in similar latitudes (see MAGNETISM, TERRESTRIAL). There is also considerable resemblance between the curve whose ordinates represent the diurnal inequality in the current passing from north to south, and the curve showing the hourly change in the westerly component of the horizontal magnetic force in similar European latitudes.

8. _Relations with Sun-spots, Auroras and Magnetic Storms._--Weinstein gives curves representing the mean diurnal inequality for separate years. In both lines the diurnal amplitudes were notably smaller in the later years which were near sun-spot minimum. This raises a presumption that the regular diurnal earth currents, like the ranges of the magnetic elements, follow the 11-year sun-spot period. When we pass to the large and irregular earth currents, which are of practical interest in telegraphy, there is every reason to suppose that the sun-spot period applies. These currents are always accompanied by magnetic disturbances, and when specially striking by brilliant aurora. One most conspicuous example of this occurred in the end of August and beginning of September 1859. The magnetic disturbances recorded were of almost unexampled size and rapidity, the accompanying aurora was extraordinarily brilliant, and E.M.F.'s of 700 and 800 volts are said to have been reached on telegraph lines 500 to 600 km. long. It is doubtful whether the disturbances of 1859 have been equalled since, but earth current voltages of the order of 0.5 volts per mile have been recorded by various authorities, e.g. Sir W.H. Preece (10).

It was the practice for several years to publish in the _Ann. du bureau central meteorologique_ synchronous magnetic and earth current curves from Parc Saint Maur corresponding to the chief disturbances of the year. In most cases there is a marked similarity between the curve of magnetic declination and that of the north-south earth current. At times there is also a distinct resemblance between the horizontal force magnetic curve and that of the east-west earth current, but exceptions to this are not infrequent. Similar phenomena appear in synchronous Greenwich records published by Airy in 1868; these show a close accordance between the horizontal force curves and those of the currents from magnetic east to west. Originally it was supposed by Airy that whilst rapid movements in the declination and north-south current curves sometimes occurred simultaneously, there was a distinct tendency for the latter to precede the former. More recent examinations of the Greenwich records by W. Ellis (11), and of the Parc St Maur curves by Moureaux, have not confirmed this result, and it is now believed that the two phenomena are practically simultaneous.

There has also been a conflict of views as to the connexion between magnetic and earth current disturbances. Airy's observations tended to suggest that the earth current was the primary cause, and the magnetic disturbance in considerable part at least its effect. Others, on the contrary, have supposed earth currents to be a direct effect of changes in the earth's magnetic field. The prevailing view now is that both the magnetic and the earth current disturbances are due to electric currents in the upper atmosphere, these upper currents becoming visible at times as aurora.

9. There seems some evidence that earth currents can be called into existence by purely local causes, notably difference of level. Thus K.A. Brander (12) has observed a current flowing constantly for a good many days from Airolo (height 1160 metres) to the Hospice St Gotthard (height 2094 metres). In an 8-km. line from Resina to the top of Vesuvius L. Palmieri (13)--observing in 1889 at three-hour intervals from 9 A.M. to 9 P.M.--always found a current running uphill so long as the mountain was quiet. On a long line from Vienna to Graz A. Baumgartner (14) found that the current generally flowed from both ends towards intervening higher ground during the day, but in the opposite directions at night. During a fortnight in September and October 1885 hourly readings were taken of the current in the telegraph cable from Fort-William to Ben Nevis Observatory, and the results were discussed by H.N. Dickson (15), who found a marked preponderance of currents up the line to the summit. The recorded mean data, otherwise regarded, represent a "constant" current, equal to 29 in the arbitrary units employed by Dickson, flowing up the line, together with the following diurnal inequality, + denoting current towards Fort-William (i.e. down the hill, and nearly east to west).

Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| | | | | | | | | | | | |
A.M. | -21 | -41 | +13 | +23 | +55 | -3 | +25 | -32 | -59 | -62 | -46 | +6 |
P.M. | +24 | +18 |+115 | +18 | +75 | -5 | +50 | -9 | -56 | -37 | -28 | -34 |

There is thus a diurnal inequality, which is by no means very irregular considering the limited number of days, and it bears at least a general resemblance to that shown by Weinstein's figures for an east-west line in Germany. This will serve to illustrate the uncertainties affecting these and analogous observations. A constant current in one direction may arise in whole or part from plate E.M.F.'s; a current showing a diurnal inequality will naturally arise between _any_ two places some distance apart whether they be at different levels or not. Finally, when records are taken only for a short time, doubts must arise as to the generality of the results. During the Ben Nevis observations, for instance, we are told that the summit was almost constantly enveloped in fog or mist. By having three earth plates in the same vertical plane, one at the top of a mountain, the others at opposite sides of it, and then observing the currents between the summit and each of the base stations, as well as directly between the base stations--during an adequate number of days representative of different seasons of the year and different climatic conditions--many uncertainties would soon be removed.

10. _Artificial Currents._--The great extension in the applications of electricity to lighting, traction and power transmission, characteristic of the end of the 19th century, has led to the existence of large artificial earth currents, which exert a disturbing influence on galvanometers and magnetic instruments, and also tend to destroy metal pipes. In the former case, whilst the disturbance is generally loosely assigned to stray or "vagabond" earth currents, this is only partly correct. The currents used for traction are large, and even if there were a perfectly insulated return there would be a considerable resultant magnetic field at distances from the track which were not largely in excess of the distance apart of the direct and return currents (16). At a distance of half a mile or more from an electric tram line the disturbance is usually largest in magnetographs recording the vertical component of the earth's field. The magnets are slightly displaced from the position they would occupy if undisturbed, and are kept in continuous oscillation whilst the trams are running (17). The extent of the oscillation depends on the damping of the magnets.

The distance from an electric tram line where the disturbance ceases to be felt varies with the system adopted. It also depends on the length of the line and its subdivision into sections, on the strength of the currents supplied, the amount of leakage, the absence or presence of "boosters," and finally on the sensitiveness of the magnetic instruments. At the U.S. Coast and Geodetic Survey's observatory at Cheltenham the effect of the Washington electric trams has been detected by highly sensitive magnetographs, though the nearest point of the line is 12 m. away (18). Amongst the magnetic observatories which have suffered severely from this cause are those at Toronto, Washington (Naval Observatory), Kew, Paris (Parc St Maur), Perpignan, Nice, Lisbon, Vienna, Rome, Bombay (Colaba) and Batavia. In some cases magnetic observations have been wholly suspended, in others new observatories have been built on more remote sites.

As regards damage to underground pipes, mainly gas and water pipes, numerous observations have been made, especially in Germany and the United States. When electric tramways have uninsulated returns, and the potential of the rails is allowed to differ considerably from that of the earth, very considerable currents are found in neighbouring pipes. Under these conditions, if the joints between contiguous pipes forming a main present appreciable resistance, whilst the surrounding earth through moisture or any other cause is a fair conductor, current passes locally from the pipes to the earth causing electrolytic corrosion of the pipes. Owing to the diversity of interests concerned, the extent of the damage thus caused has been very variously estimated. In some instances it has been so considerable as to be the alleged cause of the ultimate failure of water pipes to stand the pressure they are exposed to.

BIBLIOGRAPHY.--See Svante August Arrhenius, _Lehrbuch der kosmischen
Physik_ (Leipzig, 1903), pp. 984-990. For lists of references see J.E.
Burbank, _Terrestrial Magnetism_, vol. 10 (1905), p. 23, and P.
Bachmetjew (8). For papers descriptive of corrosion of pipes, &c., by
artificial currents see _Science Abstracts_ (in recent years in the
volumes devoted to engineering) under the heading "Traction, Electric;
Electrolysis." The following are the references in the text:--(1)
_Phil. Trans. R.S._ for 1849, pt. i. p. 61; (2) _Phil. Trans. R.S._
vol. 151 (1861), p. 89, and vol. 152 (1862), p. 203; (3) _Etude des
courants telluriques_ (Paris, 1884); (4) _Die Erdstroeme im deutschen
Reichstelegraphengebiet_ (Braunschweig, 1900); (5) _Phil. Trans. R.S._
vol. 158 (1868), p. 465, and vol. 160 (1870), p. 215; (6) _Mem. de
l'Academie St-Petersbourg_, t. 31, No. 12 (1883); (7) T. Moureaux,
_Ann. du Bureau Central Met._ (Annee 1893), 1 Mem. p. B 23; (8) P.
Bachmetjew, _Mem. de l'Academie St-Petersbourg_, vol. 12, No. 3
(1901); (9) _Terrestrial Magnetism_, vol. 3 (1898), p. 130; (10)
_Journal Tel. Engineers_ (1881); (11) _Proc. R.S._ vol. 52 (1892), p.
191; (12) _Akad. Abhandlung_ (Helsingfors, 1888); (13) _Acad. Napoli
Rend._ (1890), and _Atti_ (1894, 1895); (14) _Pogg. Ann._ vol. 76, p.
135; (15) _Proc. R.S.E._ vol. 13, p. 530; (16) A. Ruecker, _Phil. Mag._
1 (1901), p. 423, and R.T. Glazebrook, ibid. p. 432; (17) J. Edler,
_Elektrotech. Zeit._ vol. 20 (1899); (18) L.A. Bauer, _Terrestrial
Magnetism_, vol. 11 (1906), p. 53. (C. Ch.)

EARTH-NUT, the English name for a plant known botanically as _Conopodium denudatum_ (or _Bunium flexuosum_), a member of the natural order Umbelliferae, which has a brown tuber-like root-stock the size of a chestnut. It grows in woods and fields, has a slender flexuous smooth stem 2 to 3 ft. high, much-divided leaves, and small white flowers in many-rayed terminal compound umbels. Boswell Syme, in _English Botany_, iv. 114, says: "The common names of this plant in England are various. It is known as earth-nut, pig-nut, ar-nut, kipper-nut, hawk-nut, jar-nut, earth-chestnut and ground-nut. Though really excellent in taste and unobjectionable as food, it is disregarded in England by all but pigs and children, both of whom appreciate it and seek eagerly for it." Dr Withering describes the roots as little inferior to chestnuts. In Holland and elsewhere on the continent of Europe they are more generally eaten.

EARTH PILLAR, a pillar of soft rock, or earth, capped by some harder material that has protected it from denudation. The "bad lands" of western North America furnish numerous examples. Here "the formations are often beds of sandstone or shale alternating with unindurated beds of clay. A semi-arid climate where the precipitation is much concentrated seems to be most favourable to the development of this type of formation." The country round the Dead Sea, where loose friable sandy clay is capped by harder rock, produces "bad-land" topography. The cap of hard rock gives way at the joints, and the water making its way downwards washes away the softer material directly under the cracks, which become wider, leaving isolated columns of clay capped with hard sandstone or limestone. These become smaller and fewer as denudation proceeds, the pillars standing a great height at times, until finally they all disappear.

EARTHQUAKE. Although the terrible effects which often accompany earthquakes have in all ages forced themselves upon the attention of man, the exact investigation of seismic phenomena dates only from the middle of the 19th century. A new science has been thus established under the name of _seismology_ (Gr. [Greek: seismos], an earthquake).