Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/630

608 time there are portions of the work still incomplete. On the part of England the triangulation was, in, carried through France into Belgium ; and the difference of longitude of Greenwich and Valentia was determined by the Astronomer Royal by means of electric telegraph signals. Although in theory the determination of differences of longitude by electric telegraph signals may appear extremely simple, yet practically there are very many sources of error which have to be sought out and eliminated by a proper arrangement of the observations. The system has now been brought to such perfection that the astronomical amplitude of arcs of longitude can be determined with nearly as much accuracy as those of latitude, and in a few- years the data of the problem of the figure of the earth will thus receive many additions. As an example of the precision arrived at, the difference of longitude of Green wich Observatory and Harvard Observatory, U.S.A., has been three times determined with the following results:—

h. m. s. 1866 by Anglo-American Cable 4 44 31 00 1870 by French Cable to Duxbury 4 44 3099 1872 by French Cable to St Pierre 4 44 30 96

But the different determinations of the velocity of transmission of signals present great anomalies.

Pendulum Observations.

In Clairaut s theorem we have seen that if g be gravity in the latitude of cf&amp;gt;, g its value at the equator, then g = g( +q sin 2 &amp;lt;). If the same pendulum be swung in different latitudes then the square of the number of vibrations will be proportional to gravity. Hence, if N be the number of vibrations of an invariable pendulum per diem at the equator, N the number in latitude &amp;lt;, then N 2 = N 2 (l + q sin 2 &amp;lt;). Thus q can be obtained by observa tions on the same pendulum in different latitudes, and since q = %m-e and m is known, e will at once follow. The pendulum which makes 86400 oscillations per diem in London is observed to lose 136 vibrations at the equator and gain 79 at Spitzbergen. The limits of space at our disposal here prevent our going into the subject of pendulum experiments, and it seems unnecessary to repeat the investigations that have already been based upon the older pendulum observations. See Airy s Figure of the Earth, Baily s paper in the Memoirs of the Royal Astronomical Society, General Sabine s Account of Experiments to determine the Figure of the Earth l&amp;gt;y means of the Pendulum vibrating seconds in Different Latitudes, 1825, and a valuable paper in the Cambridge Philosophical Transactions,, by Professor Stokes. The pendulum gives an ellipticity certainly some what greater than that resulting from arcs of meridian, viz., -ij-g^-.-g-. An immense number of pendulum observations are now being made at the astronomical stations of geodesical surveys in Germany, Russia, and India, which, when fully published, will throw light more perhaps upon the local variations of gravity than on the figure of the earth. The observations made at the various stations of the Indian meridian arc bring to light a physical fact of the very highest importance and interest, namely, that the density of the strata of the earth s crust under and in the vicinity of the Himalayan Mountains is less than that under the plains to the south, the deficiency increasing as the stations of observation approach the Himalayas, and being a maximum when they are situated on the range itself. This accounts for the non-appearance of the large deflections which the Himalayas, according to Archdeacon Pratt s calculations, ought to produce. The Indian pendulum observations also throw some light on the relative variations of gravity at continental, coast, and island stations, showing that, without a single exception, gravity at the coast stations is greater than at the corresponding continental stations, and greater at island stations than at coast stations. The ellipticity of the earth has also been deduced from the motion of the moon, the quantity e m entering as a coefficient^in the expression for the moon s latitude. The resulting value of the ellipticity is Tj-i^th (Airy s Tracts, p. 188). A value of the ellipticity may also be derived from the precession of the equinoxes, but as this depends on the assumed law of density in the interior of the earth it is not of much importance.

Elements of the Figure as a Solid of Revolution.

If p be the radius of curvature of the meridian in latitude &amp;lt;p, p that perpendicular to the meridian, D the length of a degree of the meridian, D the length of a degree of longitude, r the radius drawn from the centre of the earth, V the angle of the vertical, then

Feet. p =20890606-6 -106411 5 cos 2&amp;lt;p + 225 8 cos 40 p =20961607-3 - 35590-9 cos 20 + 45 2 cos 40 D= 364609-87 1857 14 cos 20 + 3 94 cos 40 D = 365538-48 cos 0- 31017 cos 30 + 39 cos 50 Log - =9-9992645 + 0007374 cos 20 - 0000019 cos 4* a V =700&quot; 44 sin 20- 1&quot; 19 sin 40.  EARTHQUAKE. Although the terrible effects which are often produced by earthquakes have in all ages forced themselves upon the attention of man, it is nevertheless only within the last thirty years that the phenomena have been subjected to exact investigation. A new science has been thus established under the name of seismology (0-6107x05, an earthquake). This branch of knowledge, how ever, has hitherto attracted but few students, and its development in England has been almost exclusively due to the researches of MrRobert Mallet. References to his principal works will be given at the end of this article. Accounts of earthquakes are to be found scattered through the writings of many ancient authors, but they are, for the most part, of little value to the seismologist. There is a natural tendency to exaggeration in describing such phenomena, sometimes indeed to the extent of importing a supernatural element into the description. It is true that attempts were made by some ancient writers on natural philosophy to offer a rational explanation of earthquake phenomena, but the hypotheses which their explanations involved are, as a rule, too fanciful to be worth reproducing at the present day. It is therefore unnecessary to dwell upon the references to seismic phenomena which have come down to us in the writings of such historians and philosophers as Thucydides, Aristotle, and Strabo, Seneca, Livy, and Pliny. Nor is much to be gleaned from the pages of medieval and later writers on earthquakes, of whom the most notable are Fromondi, Maggio , and Travagini. In this country, the earliest work worthy of mention is DrRobert Hooke s Discourse on Earthquakes, written in, and read at a later date before the Royal Society. This discourse, though contain ing many passages of considerable merit, tended but little to a correct interpretation of the phenomena in question. Equally unsatisfactory were the attempts of Priestley and some other scientific writers of the last century to connect the cause of earthquakes with electrical phenomena. The great earthquake of Lisbon in led the Rev. John Michell, professor of mineralogy at Cambridge, to turn his attention to the subject; and in he published in the Philosophical Transactions a remarkable essay on the Cause and Phenomena of Earthquakes. Regarding the earth as having a liquid interior covered by a comparatively thin crust, he conceived that waves might be generated in this subterranean liquid, and that such waves by shaking the flexible crust would produce the shocks of an earthquake. 