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period de-fined in the following way:—If we put C=the moment of momentum of the spheroid around the axis of figure, and A= the corresponding moment around an axis passing through the See also:

EQUATOR (Late Lat. aequator, from aequare, to make equal)

equator EQ, then, calling one See also:

day the R i period of rotation of the Pd spheroid, the axis RR will make a revolution around PP in a number of days represented by the fraction C/(C—A). In the See also:

case of the See also:

earth, this ratio is 1/0.0032813 or 305. It follows that the period in question is 305 days. Up to 1890 the most careful observations and researches failed to establish the periodicity of such a rotation, though there was strong See also:

EVIDENCE (Lat. evidentia, evideri, to appear clearly)

evidence of a variation of See also:

LATITUDE (Lat. latitudo, latus, broad)

latitude. Then S. C. See also:

Chandler, from an elaborate discussion of a See also:

GREAT

great number of observations, showed that there was really a variation of the latitude of the points of observation; but, instead of the period being 305 days, it was about 428 days. At first sight this period seemed to be inconsistent with dynamical theory. But a defect was soon found in the latter, the correction of which reconciled the divergence. In deriving a period of 305 days the earth is regarded as an absolutely rigid See also:

BODY

body, and no See also:

account is taken either of its See also:

ELASTICITY

elasticity or of the mobility of the ocean. A study of the figure will show that the centrifugal force round the axis RR will See also:

ACT (Lat. actus, actum)

act on the See also:

EQUATORIAL

equatorial protuberance of the rotating earth so as to make it tend in the direction of the arrows. A slight deformation of the earth will thus result; and the axis of figure of the distorted spheroid will no longer be PP, but a See also:

LINE

line P'P' between PP and RR.

As the latter moves round, P'P' will continually follow it through the incessant See also:

CHANGE (derived through the Fr. from the Late Lat. cambium, cambiare, to barter; the ultimate derivation is probably from the root which appears in the Gr. «a urmu', to bend)

change of figure produced by the change in the direction of the centrifugal force. Now the See also:

RATE

rate of See also:

motion of RR is determined by the actual figure at the moment. It is therefore less than the motion in an absolutely rigid spheroid in the proportion RP': RP. It is found that, even though the earth were no more elastic than See also:

STEEL, FLORA ANNIE (1847– )

steel, its yielding combined with the mobility of the ocean would make this ratio about 2 : 3, resulting in an increase of the period by one-See also:

HALF

half, making it about 457 days. Thus this small flexibility is even of known See also:

COMPRESSION

compression, and is the See also:

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle which the normal to this spheroid makes with the equator. It differs from the astronomical latitude only in being corrected for See also:

LOCAL

local deviation of greater than that necessary to the reconciliation of observation with theory, and the earth is shown to be more rigid than steel—a conclusion See also:

long since announced by See also:

KELVIN, WILLIAM THOMSON, BARON (1824-1907)

Kelvin for other reasons. Chandler afterwards made an important addition to the subject by showing that the motion was represented by the superposition of two See also:

HARMONIC

harmonic terms, the first having a period of about 430 days, the other of one See also:

YEAR

year. The result of this superposition is a seven-year period, which makes 6 periods of the 428-day See also:

TERM

term (428'X6=2568"=7 years, nearly), and 7 periods of the See also:

ANNUAL

annual term. Near one phase of this combined period the two component motions nearly annul each other, so that the variation is then small, while at the opposite phase, 3 to 4 years later, the two motions are in the same direction and the range of variation is at its maximum. The coefficient of the 428-day term seems to be between O'12" and o.16"; that of the annual term between o•o6" and o• 11 ". See also:

RECENT

Recent observations give smaller values of both than those made between 1890 and 1900, and there is no See also:

REASON (Lat. ratio, through French raison)

reason to suppose either to be See also:

CONSTANT, BENJAMIN (1845-1902)

constant. The See also:

PRESENT

present See also:

state of the theory maybe summed up as follows: he 1.

The fourteen-See also:

month term is an immediate result of the fact that the axes of rotation and figure of the earth do not strictly coincide, but make with each other a small angle of which the mean value is about 0.15". If the earth remained invariable, without any motion of See also:

MATTER

matter on its See also:

SURFACE

surface, the result of this non-coincidence would be the revolution of the one See also:

pole round the other in a circle of See also:

RADIUS

radius 0.15", or about 15 ft., in a period of about 429 days. This revolution is called the Eulerian motion, after the mathematician who discovered it. But owing to meteorological causes the motion in question is subject to annual changes. These changes arise from two causes—the one statical, the other dynamical. 2. The statical causes are deposits of See also:

SNOW (in O. Eng. sndw; a common Indo-European word; cf. in Teutonic languages, Ger. Schnee, Du. sneeuw; in Slavonic snieg', Lith. snegas; Gr. vi4a, Lat. nix, nivis, whence the Romanic forms, Ital. neve, Fr. neige, &c.; Ir. and Gael. sneachd; the original

snow or See also:

ICE (a word common to Teutonic languages; cf. Ger. Eis)

ice slowly changing the position of the pole of figure of the earth. For example, a See also:

DEPOSIT (Lat. depositurn, from deponere, to lay down, to put in the care of)

deposit of snow in See also:

SIBERIA

Siberia would bring the equator of figure of the earth a little nearer to Siberia and throw the pole a little way from it, while a deposit on the See also:

AMERICAN

American See also:

CONTINENT (from Lat. continere, "to hold together "; hence " connected," " continuous ")

continent would have the opposite effect. Owing to the approximate symmetry of the American and See also:

ASIATIC

Asiatic continents it does not seem likely that the inequality of snowfall would produce an appreciable effect. 3. The dynamical causes are atmospheric and oceanic currents. Were these currents invariable their only effect would be that the Eulerian motion would not take See also:

PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place exactly round the mean pole of figure, but round a point slightly separated from it.

But, as a matter of fact, they are subject to an annual variation. Hence the motion of the pole of rotation is also subject to a similar variation. The annual term in the latitude is thus accounted for. Besides Chandler, Albrecht of See also:

Berlin has investigated the motion of the pole P. The methods of the two astronomers are in some points different. Chandler has constructed empirical formulae representing the motion, with the results already given, while Albrecht has determined the motion of the pole from observation simply, without trying to represent it either by a See also:

formula or by theory. It is noteworthy that the difference between Albrecht's numerical results and Chandler's formulae is generally less than 0.05". When the fluctuation in the position of the pole was fully confirmed, its importance in See also:

ASTRONOMY (from Gr. &arpov, a star, and v ,usiv, to classify or arrange)

astronomy and See also:

GEODESY (from the Gr. y, the earth, and SatEty, to divide)

geodesy led the See also:

INTERNATIONAL, THE

International See also:

GEODETIC

Geodetic Association to establish a See also:

SERIES (a Latin word from serere, to join)

series of stations round the globe, as nearly as possible on the same parallel of latitude, for the purpose of observing the fluctuation with a greater degree of precision than could be attained by the See also:

MISCELLANEOUS

miscellaneous observations before available. The same stars were to be observed from month to month at each station with See also:

ZENITH (from the Arabic)

zenith-telescopes of similar approved construction. This secures a See also:

double observation of each component of the polar motion, from which most of the systematic errors are eliminated. The See also:

PRINCIPAL

principal stations are: See also:

CARLOFORTE

Carloforte, See also:

Italy; Mizusawa, See also:

JAPAN

Japan; Gaithersburg, See also:

MARYLAND

Maryland; and Ukiah, See also:

California, all nearly on the same parallel of latitude, 390 8'. The fluctuations derived from this international See also:

WORK

work duringthe last seven years deviate but slightly from Chandler's formulae though they show a markedly smaller value of the annual term.

In consequence, the change in the See also:

AMPLITUDE (from Lat. amplus, large)

amplitude of the fluctuation through the seven-year period is not so well marked as before 1900. Chandler's investigations are found in a series of papers published in the Astronomical See also:

Journal, vols. xi. to xv. and xviii. See also:

NEWCOMB, SIMON (1835-1909)

Newcomb's explanation of the lengthening of the Eulerian period is found in the Monthly Notices of the Royal Astronomical Society for See also:

March 1892. Later volumes of the Astronomical Journal contain discussions of the causes which may produce the annual fluctuation. An elaborate mathematical discussion of the theory is by Vito See also:

VOLTERRA (anc. Volaterrae)

Volterra: " See also:

SULLA, LUCIUS CORNELIUS (138–78 B.C.)

Sulla teoria dei movimenti del See also:

Polo terrestre " in the Astronomische Nachrichten, vol. 138; also, more fully in his memoir " Sur la theorie See also:

des See also:

variations des latitudes," Acta Mathematica, vol. xxii. The results of the international observations are discussed from time to time by Albrecht in the publications of the International Geodetic Association, and in the Astronomische Nachrichten (see also EARTH, FIGURE OF). (S.

End of Article: POR

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