See also:

• MOON (a common Teutonic word, cf. Ger. Mond, Du. maan, Dan. maane, &c., and cognate with such Indo-Germanic forms as Gr. µlip, Sans. ma's, Irish mi, &c.; Lat. uses luna, i.e. lucna, the shining one, lucere, to shine, for the moon, but preserves the word i
• MOON, SIR RICHARD, 1ST BARONET (1814-1899)

MOON (a See also:

• COMMON

common See also:

• TEUTONIC
• TEUTONIC (GERMANIC) LANGUAGES

Teutonic word, cf. Ger. See also:

• MOND, LUDWIG (1839-1909)

Mond, Du. maan, See also:

• DAN

Dan. maane, &c., and cognate with such Indo-Germanic forms as Gr. µSee also:

• LIP (a word common in various forms, to Teutonic languages, cf Ger. Lippe, Dan. laebe; Lat. labium is cognate)

lip, Sans. ma's, Irish mi, &c.; See also:

• LAT

Lat. uses See also:

• LUNA (mod. Luni)
• LUNA, ALVARO DE (d. 1453)

luna, i.e. lucna, the shining one, lucere, to shine, for the moon, but preserves the word i  n mensis, See also:

• MONTH
• MONTH (a common Teutonic word, cf. Ger. Mond, Du. maand, Dan. maaned, &c., and cognate with Lat. mensis, Gr. µi7v, &c., in other branches of the Indo-Germanic family; all ultimately from the root seen in the word for the moon in nearly all those languages

month; the ultimate See also:

• ROOT (late O.E. rot, adopted from Scand., cf. Norw. and Swed. rot, Dan. rod; the true O.E. word was wyrt, plant, represented in Ger. Wurz or Wurzel; the ultimate root is the same in both words, and is seen in Lat. radix)
• ROOT, ELIHU (1845– )

root for "See also:

• MOON (a common Teutonic word, cf. Ger. Mond, Du. maan, Dan. maane, &c., and cognate with such Indo-Germanic forms as Gr. µlip, Sans. ma's, Irish mi, &c.; Lat. uses luna, i.e. lucna, the shining one, lucere, to shine, for the moon, but preserves the word i
• MOON, SIR RICHARD, 1ST BARONET (1814-1899)

moon" and "month " is usually taken to be me-, to measure, the moon being a measurer of See also:

• TIME (0. Eng. Lima, cf. Icel. timi, Swed. timme, hour, Dan. time; from the root also seen in " tide," properly the time of between the flow and ebb of the sea, cf. O. Eng. getidan, to happen, " even-tide," &c.; it is not directly related to Lat. tempus)
• TIME, MEASUREMENT OF
• TIME, STANDARD

time), in See also:

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

astronomy, the name given to the See also:

• SATELLITE (from the Lat. satelles, an attendant)

satellite of any See also:

• PLANET (Gr. ssXavirrns, a wanderer)

planet, specifically to the only satellite of the See also:

• EARTH
• EARTH (a word common to Teutonic languages, cf. Ger. Erde, Dutch aarde, Swed. and Dan. jord; outside Teutonic it appears only in the Gr. 'pq'e, on the ground; it has been connected by some etymologists with the Aryan root ar-, to plough, which is seen in
• EARTH, FIGURE OF
• EARTH, FIGURE OF THE

earth . The subject of the moon may be treated as twofold, one See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch being concerned with the aspects, phases and constitution of the moon; the other with the mathematical theory of its See also:

• MOTION (Lat. motio, from movere, to move)
• MOTION, LAWS OF

motion . As the varying phenomena presented by the moon grow out of its orbital motion, the See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general See also:

• CHARACTER (Gr. xapareri7p, from xap&crew, to scratch)

character of the latter will be set forth in advance . A luminous See also:

• IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea of the geometrical relations of the moon, See also:

• MONZONITE

Monzonite, Monzoni . 54.20 15.73 3.67 5.40 3.40 8.50 4.42 3.07 Yogoite, Yogo See also:

• PEAK, THE

Peak . 54.42 14.28 3.32 4.13 6.12 7.72 4.22 3.44 Kentallenite,See also:

• ARGYLLSHIRE

Argyllshire 52.09 11.93 1.84 7.11 12.48 7.8t 3.01 2.04 . S . F.) earth and See also:

• SUN
• SUN (0. Eng. sonne, Ger. sonne. Fr. soleil, Lat. sol, Gr. ijXior, from which comes helio- in various English compounds)

sun will be gained from the figure, by imagining the sun to be moved towards the See also:

• LEFT

left, and placed at a distance of 20 ft. from the position of the earth, as represented at the right-See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand end of the figure . We have here eight positions of the moon, MI, M2, &c., as it moves See also:

• ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

round the earth E . The general See also:

• AVERAGE

average distance of the sun is somewhat less than four See also:

• HUNDRED

hundred times that of the moon . We have next to conceive that, as the earth performs its See also:

• ANNUAL

annual revolution round the sun in an See also:

• ORBIT (from Lat. orbita, a track, orbis, a wheel)

orbit whose See also:

• DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, as represented on the See also:

• DIAGRAM

diagram, is nearly 40 ft., it carries the orbit of the moon with it . Conceiving the See also:

• PLANE

plane of the earth's motion, which is that of the See also:

• ECLIPTIC

ecliptic, to be represented by the See also:

• SURFACE

surface of the See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper, the orbit of the moon makes a small 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 of a little more than 5° with this plane .

Conceiving the See also:

• LINE

line NN' to be that of the nodes at any time, and the earth and lunar orbit to be moving in the direction of the straight arrows, the earth will be on one See also:

• SIDE
• SIDE (mod. Eski Adalia)

side of the ecliptic from M2 to Mb, and on the other side from M6 to MI, intersecting it at the nodes . The See also:

• ABSOLUTE (Lat. absolvere, to loose, set free)

absolute direction of the line of nodes changes but slowly as the earth and moon revolve; consequently, in the See also:

• CASE
• CASE, JOHN (d. 1600)

case shown in the figure, the line a of nodes will pass through the sun after the earth has passed through an arc nearly equal to the angle MI N . Six months later the direction of the opposite See also:

• NODE (Lat. nodus, a loop)

node will pass through the sun . Actually, the line of nodes is in motion in a See also:

• RETROGRADE (from the Lat. retro, backwards, gradiri, to go)

retrograde direction, the opposite of that of the arrows, by 19'3° per See also:

• YEAR

year, thus making a revolution in 18.6 years, or 6,793'39 days . (See See also:

• ECLIPSE (Gr. €uheo,tis, falling out of place, failing)

ECLIPSE.) The varying phases of the moon, due to the different aspects presented by an opaque globe illuminated by the sun, are too See also:

• FAMILIAR (through the Fr. familier, from Lat. familiaris, of or belonging to the familia, family)

familiar to require explanation . We shall merely See also:

• NOTE
• NOTE (Lat. nota, mark, sign, from noscere, to know)

note some points which are frequently overlooked: (I) the See also:

• CRESCENT (Lat. crescens, growing)

crescent phase of the moon is shown only when the moon is less than 9o° from the sun; (2) the See also:

• BRIGHT, JOHN (1811-188g)
• BRIGHT, SIR CHARLES TILSTON

bright See also:

• CONVEX

convex outline of the crescent is then on the side toward the sun, and that the moon is seen full only when in opposition to the sun, and therefore rising about the time of sunset . In consequence of the orbital motion the moon rises, crosses the See also:

• MERIDIAN
• MERIDIAN (from the Lat. meridianus, pertaining to the south or mid-day)

meridian, and sets, about 48 m. later every successive See also:

• DAY (O. Eng. dreg, Ger. Tag; according to the New English Dictionary, " in no way related to the Lat. dies")
• DAY, JOHN (1574-1640?)
• DAY, THOMAS (1748-1789)

day . This excess is, however, subject to wide variation, owing to the obliquity of the ecliptic and of the lunar orbit to the See also:

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

equator, and therefore to the See also:

• HORIZON (Gr. 6pfTwv, dividing)

horizon . The smaller the angle which the orbit of the moon, when near the point of rising, makes with the horizon the less will be the retardation . Near the autumnal See also:

• EQUINOX (from the Lat. aequus, equal, and nox, night)

equinox this angle is at a minimum; hence the phenomenon of the " See also:

• HARVEST (A.S. hcerfest " autumn," O.H. Ger. herbist, possibly through an old Teutonic root representing Lat. car pere, " to pluck ")

harvest moon," when for several successive days the difference of times of rising on one day and the next may be only from 15 to 20 minutes . Near the vernal equinox the case is reversed, the See also:

• INTERVAL

interval between two risings of the nearly full moon being at its maximum, and between two settings at its minimum . Generally, when the rising is accelerated the setting is retarded, and See also:

• VICE

vice versa .

The moon always presents nearly the same See also:

• FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face to the earth, from which it follows that, when referred to a fixed direction in space, it revolves on its See also:

• AXIS (Lat. for " axle ")

axis in the same time in which it performs its revolution . Relatively to the direction of the earth there is really no rotation . The See also:

• RATE

rate of actual rotation is substantially See also:

• UNIFORM

uniform, while the arc through which the moon moves from day to day varies . Consequently, the face which the moon presents to the earth is subject to a corresponding variation, the globe as we see it slightly oscillating in a See also:

• PERIOD
• PERIOD (Gr. irepioSos, a going or way round, circuit, aepi, round, and &Sis, way, road)

period nearly that of revolution . This apparent oscillation is called See also:

• LIBRATION (Lat. libra, a balance)

libration, and its amount on each side of the mean is commonly between 6° and 7° . There is also a libration in See also:

• LATITUDE (Lat. latitudo, latus, broad)

latitude, arising from the fact that the axis of rotation of the moon is not precisely perpendicular to the plane of her orbit . This libration is more See also:

• REGULAR

regular than that in See also:

• LONGITUDE (from Lat. longitudo, " length ")

longitude, its amount being about 6° 44' on each side of the mean . The other side of the moon is therefore invisible from the earth, but in consequence of the libration about six-tenths of the lunar surface may be seen at one time or another, while the remaining four-tenths are for ever hidden from our view . It is found that the direction of the moon's equator remains nearly invariable. with respect to the plane of the orbit, and therefore revolves with that plane in a nodal period of 18.6 years . This shows that the side of the moon presented to us is held in position as it were by the earth, from which it also follows that the lunar globe is more or less elliptical, the longer axis being directed toward the earth . The amount of the See also:

• ELLIPTICITY

ellipticity is, however, very small . Two phenomena presented by the moon are See also:

• PLAIN (O. Fr. plain, from Lat. plenum)

plain to the naked See also:

• EYE
• EYE (O. Eng. edge, Ger. Auge; derived from an Indo-European root also seen in Lat. oc-ulus, the organ of vision (q.v.)

eye .

One is the existence of dark and bright regions, irregular in See also:

• FORM (Lat. forma)

form, on its surface; the other is the See also:

• COMPLETE

complete See also:

• ILLUMINATION

illumination of the lunar disk when seen as a crescent, a faint See also:

• LIGHT

light revealing the dark hemisphere . This is due to the light falling from the sun on the earth and being reflected back to the moon . To an observer on the moon our earth would See also:

• PRESENT

present a surface more than ten times as large as the moon presents to us, consequently this earth-light is more than ten times brighter than our moonlight, thus enabling the lunar surface to be seen by us . The surface of the moon has been a subject of careful telescopic study from the time of Galileo . The See also:

• EARLY
• EARLY, JUBAL ANDERSON (1816-1894)

early observers seem to have been under the impression that the dark regions might be oceans; but this impression must have been corrected as soon as the See also:

• TELESCOPE

telescope began to be improved, when the whole visible surface was found to be rough and mountainous . The See also:

• WORK

work of See also:

• DRAWING

drawing up a detailed description of the lunar surface, and laying its features down on maps, has from time to time occupied telescopic observers . The earliest work of this See also:

• KIND (O. E. ge-cynde, from the same root as is seen in " kin," supra)

kind, and one of the most elaborate, is the Selenographia of See also:

• HEVELIUS [HEVEL or H6WELCKE], JOHANN (1611—1687)

Hevelius, a magnificent See also:

• FOLIO (properly the ablative case of the Lat. folium, leaf, but also frequently an adaptation of the Ital. foglio)

folio See also:

• VOLUME

volume . This contains the first complete See also:

• MAP
• MAP (or MAPES), WALTER (d. c. 1208/9)

map of the moon . Names borrowed from See also:

• GEOGRAPHY (Gr. yil, earth, and ypiickty, to write)

geography and classical See also:

• MYTHOLOGY

mythology are assigned to the regions and features . A See also:

• SYSTEM

system was introduced by Riccioli in his Almagestum novum of designating the more conspicuous smaller features by the names of eminent astronomers and philosophers, while the See also:

• GREAT

great dark regions were designated as oceans, with quite fanciful names: See also:

• MARE

Mare imbrium, See also:

• OCEANUS (Gr. 'Slrceavts)

Oceanus procellarum, &c . More than a See also:

• CENTURY (from Lat. centuria, a division of a hundred men)

century elapsed from the time of . Hevelius and Riccioli when J .

H . See also:

• SCHROTER, JOHANN HIERONYMUS (1745-1816)

Schroter of Lilienthal produced another profusely illustrated description of lunar See also:

• TOPOGRAPHY
• TOPOGRAPHY (Gr. Toros, place, -partied', to write)

topography . The See also:

• STANDARD
• STANDARD, BATTLE OF THE

standard work on this subject during the 19th century was See also:

• LONG, GEORGE (1800-1879)
• LONG, JOHN DAVIS (1838– )

long the well-executed description and map of W . See also:

• BEER

Beer and J . H . Madler, published in 1836 . It was the result of several years' careful study and micrometric measurement of the features shown by the moon . The volume of See also:

• TEXT (Lat. textum, woven fabric, from texere, to weave)

text gives descriptive details and measurement of the spots and heights of the mountains . In See also:

• RECENT

recent times See also:

• PHOTOGRAPHY (Gr. bias, light, and ypa w, to write)
• PHOTOGRAPHY, CELESTIAL

photography has been so successfully applied to the mapping of our satellites as nearly to supersede visual observation . The first photograph of the moon was a daguerreotype, made by Dr J . W . See also:

• DRAPER
• DRAPER, JOHN WILLIAM (1811-1882)

Draper of New See also:

• YORK
• YORK (HOUSE OF)
• YORK, EDMUND OF LANGLEY, DUKE OF (1341-1402)
• YORK, EDWARD
• YORK, FREDERICK AUGUSTUS, DUKE OF (1763-1827)
• YORK, RICHARD, DUKE

York in 184o; but it was not possible to do much in this direction until the more sensitive See also:

• PROCESS

process of photographing on See also:

• GLASS
• GLASS (O.E. glees, cf. Ger. Glas, perhaps derived from an old Teutonic root gla-, a variant of glo-, having the general sense of shining, cf. " glare," " glow ")
• GLASS, STAINED

glass was introduced instead of the daguerreotype .

The taking of photographs of the moon then excited much See also:

• INTEREST

interest among astronomical observers of various countries . See also:

• BOND
• BOND, SIR EDWARD AUGUSTUS (1815-1898)

Bond at the Harvard See also:

• OBSERVATORY

observatory, De la See also:

• RUE (Fr. rue, Lat. ruta, from Gr. pur)

Rue in See also:

• ENGLAND
• ENGLAND, THE CHURCH OF

England, and See also:

• RUTHERFORD, MARK
• RUTHERFORD, WILLIAM GUNION (1853–1907)

Rutherford in New York, produced lunar photographs of remarkable accuracy and beauty . The See also:

• FINE

fine See also:

• ATMOSPHERE (Gr. fir µ6r, vapour; orkaipa, a sphere)

atmosphere of the Lick observatory was well adapted to this work, and a complete photographic map of the moon on a large See also:

• SCALE
• SCALE (1) A

scale was prepared which exceeded in precision of detail any before produced . The most extended and elaborate work of this sort yet undertaken is that of See also:

• MAURICE (1521–1553)
• MAURICE (MAURICIUS FLAVIUS TIBERIUS) (c. 539–602)
• MAURICE [or MAURITIUS], ST (d. c. 286)
• MAURICE, JOHN FREDERICK DENISON (1805-1872)

Maurice Loewy (1833—1907) and See also:

• PIERRE

Pierre Puiseux at the See also:

• PARIS
• PARIS (also called ALEXANDROS)
• PARIS, ALEXIS PAULIN (1800-x881)
• PARIS, BRUNO PAULIN GASTON (1839-1903)
• PARIS, FRANCOIS DE (169o-1727)
• PARIS, LOUIS PHILIPPE ALBERT
• PARIS, TREATIES OF (1814-1815)

Paris observatory, of which the first See also:

• PART

part was published in 1895 . The broken and irregular character of the surface is most evident near the boundary between the dark and illuminated portions, about the time of first See also:

• QUARTER (through Fr. from Lat. quartarius, fourth part)

quarter . The most remarkable Het . In te,oenea a space calla( to M about 190 those the distance Id, H . 8o4 . feature of the surface comprises the craters, which are scattered everywhere, and generally surrounded by an approximately circular elevated See also:

• RING (O.E. hring; a word common to Teutonic languages; and probably cognate with the Lat. circus, Gr. KtpKOS or KpLKOS, Skt'. chakra, wheel, circle, cf. also " harangue "); in art, a band of circular shape of varying sizes, made of any material and used f

ring . Yet another remarkable feature comprises bright streaks, branching out in various directions and through long distances from a few central points, especially that known as Tycho . The height of the lunar mountains is a subject of interest . It cannot be stated with the same definiteness that we can assign heights to our terrestrial mountains, because there is no fixed See also:

• SEA (in O. Eng. sae, a common Teutonic word; cf. Ger. See, Dutch Zee, &c.; the ultimate source is uncertain)
• SEA, COMMAND OF THE

sea-level on the moon to which elevations can be referred .

The only determination that can be made on the moon is that of the height above some neighbouring hollow, See also:

• CRATER

crater or plain . The most detailed See also:

• MEASURES

measures of this sort were made by Beer and Madler, who give a great number of such heights . These generally range between 500 and 3000 toises, or 3000 and 20,000 See also:

• ENGLISH

English feet . The highest which they measured was See also:

• NEWTON
• NEWTON, ALFRED (1829–1907)
• NEWTON, JOHN (1725-1807)
• NEWTON, JOHN (1823-1895)
• NEWTON, SIR CHARLES THOMAS (1816-1894)
• NEWTON, SIR ISAAC (1642-1727)

Newton, 3727 toises, or 24,000 ft . The general trend of lunar investigation has been against the view that there is any resemblance between the surfaces of the moon and of the earth, except in the general features already mentioned . No See also:

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

evidence has yet been found that the moon has either See also:

• WATER

water or See also:

• AIR (from an Indo-European root meaning " breathe," " blow ")
• AIR, or ASBEN

air . The former, if it existed at all, could be found only in the more depressed portions; and even here it would evaporate under the See also:

• INFLUENCE (Late Lat. influentia, from influere, to flow in)

influence of the sun's rays, forming a vapour which, if it existed in considerable quantity, would in some way make itself known to our See also:

• SCRUTINY (Fr. scrutin, Late Lat. scrulinium, from scrutari, to search or examine thoroughly)

scrutiny . The most delicate indication of an atmosphere would be through the See also:

• REFRACTION
• REFRACTION (Lat. refringere, to break open or apart)

refraction of the light of a See also:

• STAR

star when seen coincident with the See also:

• LIMB

limb of the moon . Not the slightest 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 in the direction of such a star when in this position has ever been detected, and it is certain that if any occurs it can be but a See also:

• MINUTE
• MINUTE (Lat. minutes, small; minuere, to make less)

minute fraction of a second of arc . As an Atmosphere equal to ours in See also:

• DENSITY (Lat. densus, thick)

density would produce a deviation of an important fraction of a degree, it may be said that the moon can have no atmosphere exceeding in density the bti that of the earth . Devoid of air and atmosphere, the causes of meteorological phenomena on the earth are non-existent on the moon . The only active cause of such changes is the varying temperature produced by the presence or See also:

• ABSENCE (Lat. absentia)

absence of the sun's rays .

The range of temperature must be vastly wider than on the earth, owing-to the absence of an atmosphere to make it equable . Elaborate observations of the See also:

• HEAT (0. E. haktu, which like " hot," Old Eng. hat, is from the Teutonic type haita, hit, to be hot; cf. Ger. hitze, heiss; Dutch, hitte, heet, &c.)

heat coming from the moon at its various phases were made and discussed in 1871–1872 by See also:

• LORD
• LORD (O. Eng. hldford, i.e. hldfweard, the warder or keeper of bread, hlIf, loaf; the word is not represented in any other Teutonic language)
• LORD, JOHN (1810-1894)

Lord See also:

• ROSSE, EARL OF
• ROSSE, WILLIAM PARSONS, 3RD EARL

Rosse . Among his results was that during the progressive phases from before the first quarter till the full moon the heat received increases in a much greater proportion than the light, from which it followed that the former was composed mainly of heat radiated from the moon itself in consequence of the temperature which it assumed under the sun's rays . So far as could be determined, 86% of the heat radiated was by the moon itself, and 14% reflected See also:

• SOLAR, SOLLER (Lat. solarium, Fr.• galetas, Ital. solaio)

solar heat . But it seems probable that this disproportion may be somewhat too great . Rosse's determinations, like those of his predecessors, were made with the thermopile . After S . P . See also:

• LANGLEY, SAMUEL PIERPONT (1834-1906)

Langley devised his bolometer, which was a much more sensitive See also:

• INSTRUMENT (Lat. instrumentum, from insincere, to build up, furnish, arrange, prepare)

instrument than the thermopile, he, in See also:

• CONJUNCTION (from Lat. conjungere, to join together)

conjunction with F . W . Very, applied it to determine the moon's See also:

• RADIATION, THEORY OF

radiation at the See also:

• ALLEGHENY

Allegheny observatory . His results for the ratio of the See also:

• TOTAL

total radiation of the full moon to that of the sun ranged from I : 70,000 to I : 110,000, which were in substantial agreement with those of Rosse, who found 1: 82,000 .

When Langley published his work the See also:

• LAW
• LAW (0. Eng. lagu, M. Eng. lawe; from an old Teutonic root lag, " lie," what lies fixed or evenly; cf. Lat. lex, Fr. loi)
• LAW, JOHN (1671—1729)
• LAW, WILLIAM (1686-1761)

law of radiation as a See also:

• FUNCTION

function of the temperature was not yet established . He therefore wrongly concluded that the highest temperature reached by the moon approximated to the freezing-point of water . Stefan's law of radiation, on the other hand, shows that the temperature must have been about the boiling-point in See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order that the observed amount of heat might be radiated . This is in See also:

• FAIR

fair agreement with the computed temperature due to the sun's radiation upon a perpendicular absorbing surface when no temperature is lost through See also:

• CONDUCTION, ELECTRIC

conduction to the interior . The agreement thus brought about between the results deduced from the law of radiation and the most delicate observa-tions of the quantity of heat radiated is of great interest, as showing that the theory of cosmicai temperature now rests upon a See also:

• SOUND
• SOUND, THE (Danish Oresund)

sound basis . There is; however, still See also:

• ROOM

room for improved determinations of the moon's heat by the use of the bolometer in its latest form . Possibility of Changes on the Moon.—No evidence of See also:

• LIFE

life on the moon has ever been brought out by the minutest telescopic scrutiny, nor does life seem possible in the absence of air and water . Some bright spots are visible by the earth-light when the moon is a thin crescent, which were supposed by See also:

• HERSCHEL, CAROLINE LUCRETIA (1750-1848)
• HERSCHEL, SIR F
• HERSCHEL, SIR FREDERICK WILLIAM (1738-1822)
• HERSCHEL, SIR JOHN FREDERICK WILLIAM, BART

Herschel to be volcanoes in eruption . But these are now known to be nothing more than spots of unusual whiteness, and if any active See also:

• VOLCANO

volcano exists it is yet to be discovered . Still, the question whether everything on the moon's surface is absolutely unchangeable is as yet an open one, with the general trend of See also:

• OPINION (Lat. opinio, from opinari, to think)

opinion toward the affirmative, so far as any actual See also:

• PROOF (in M. Eng. preove, proeve, preve, &°c., from O. Fr . prueve, proeve, &c., mod. preuve, Late. Lat. proba, probate, to prove, to test the goodness of anything, probus, good)

proof from observation is concerned . The spot which has most frequently exhibited changes in See also:

• APPEARANCE (from Lat. apparere, to appear)

appearance is near the centre of the visible disk, marked on Beer and Madler's map as Linne . This has been found to present an aspect quite different from that depicted on the map, and one which varies at different times .

But the question still remains open whether these See also:

• VARIATIONS
• VARIATIONS, CALCULUS
• VARIATIONS, CALCULUS OF

variations may not be due wholly to the different phases of illumination by the sunlight as the latter strikes the region from various directions . Intensity of Moonlight.—An interesting and important quantity is the ratio of moonlight to sunlight . This has been measured for the full moon by various investigators, but the results are not as accordant as could be desired . The most reliable determinations were made by G . P . Bond at Harvard and F . See also:

• ZOLLNER, JOHANN KARL FRIEDRICH (1834-1882)

Zollner at See also:

• LEIPZIG

Leipzig, in i86o and 1864 . The mean result of these two determinations is the ratio 1 : 570,000 . We may therefore say that the intensity of sunlight is somewhat more than See also:

• HALF

half a million times that of full moonlight . A remarkable feature of the reflecting See also:

• POWER [WILLIAM GRATTAN] TYRONE (1797-1841)

power of the moon, which was made known by Miner's observations, is that the proportion of light reflected by a region on the moon is much greater when the light falls perpendicularly, which. is the case near the time of full moon, and rapidly becomes less as the light is more oblique . This result was traced by See also:

• MILNER, ALFRED MILNER, VISCOUNT (1854– )
• MILNER, JOSEPH (1744-1797)

Milner to the general irregularity of the lunar surface, and the inference was See also:

• DRAWN

drawn that the average slope of the lunar See also:

• ELEVATION

elevation amounts to 470 Motion of the Moon.—The orbit of the moon around the earth, though not a fixed See also:

• CURVE (Lat. curvus, bent)

curve of any class, is elliptical in form, and may be represented by an See also:

• ELLIPSE (adapted from Gr. EXkei 'tc, a deficiency, iXXeirely, to fall behind)

ellipse which is constantly changing its form and position, and has the earth in one of its foci . The eccentricity of the ellipse is in the general average about 0.055, whence the moon is commonly more than 3lofurther from the earth at apogee than at See also:

• PERIGEE (Gr. zrepi, near, 'A', the earth)

perigee .

The line of apsides is in continual motion, generally See also:

• DIRECT

direct, and performs a revolution in about 12 years . The inclination to the ecliptic is a little more than 50, and the line of nodes performs a revolution in the retrograde direction in 18.6 years . The See also:

• PARALLAX (Gr. aapa?X6, alternately)

parallax of the moon is determined by observation from two widely separated points; the most accurate measures are those made at See also:

• GREENWICH

Greenwich and at the Cape of See also:

• GOOD, JOHN MASON (1764-1827)

Good See also:

• HOPE, ANTHONY
• HOPE, THOMAS (c. 1770-1831)

Hope . The distance of the moon can also be computed from the law of gravity, the problem being to determine the distance at which a See also:

• BODY

body having the moon's See also:

• MASS (O.E. maesse; Fr. messe; Ger. Messe; Ital. messa; from eccl. Lat. missa)
• MASS, IN

mass would revolve around the earth in the observed period . The measures of parallax agree perfectly with the computed distance in showing a mean parallax of 57' 2.8", and a mean distance of 238,800 See also:

• MILES, NELSON APPLETON (1839— )

miles . The period of revolution, or the lunar month, depends upon the point to which the revolution is referred . Any one of five such directions may be chosen, that of the sun, the fixed stars, the equinox, the perigee, or the node . The terms synodical, sidereal, tropical, anomalistic, nodical, are applied respectively to these months, of which the lengths are as follow: Synodic month Length . Deviation from 29.53059 days. sidereal month . +2.20893 days . Sidereal month . 27.32166 „ 0.00000 „ Tropical month .

27.32156 „ —o•o00I0 Anomalistic month 27.55460 „ -+•23294 Nodical month . 27.2I222 „ -0.10944 „ Other numerical particulars See also:

• RELATING

relating to the moon are: . 60.2634 Mean distance from the earth (earth's See also:

• RADIUS

radius as i) . Mean apparent diameter . . 31' 5I•5 Diameter in miles . . 2159.6 Moon's surface in square miles . . . . 14,600,000 Diameter (earth's See also:

• EQUATORIAL

equatorial diameter as 1) . . 0.2725 Surface (earth's as 1) . . 0.0742 Volume (earth's as 1) . 0.0202 Ratio of mass to earth's mass i . . .

. 1: 81.53 ' •047 Density (earth's as I) . . . . . . 0.60736 Density (water's as 1, and earth's assumed as 5) • • . 3.46 Ratio of gravity to gravity at the earth's surface . . . 1:6 Inclination of axis of rotation to ecliptic . . . . 1° 30' 11.3" The Lunar Theory . The mathematical theory of the moon's motion does not yet form a well-defined body of reasoning and See also:

• DOCTRINE

doctrine, like other branches of mathematical See also:

• SCIENCE (Lat. scientia, from scire; to learn, know)

science, but consists of a See also:

• SERIES (a Latin word from serere, to join)

series of researches, extending through twenty centuries or more, and not easily welded into a unified whole . Before Newton the problem was that of devising empirical curves to formally represent the observed inequalities in the motion of the moon around the earth . After the See also:

• ESTABLISHMENT (0. Fr. establissement, Fr. etablissement, late Norm. Fr. establishement, from O. Fr. establir, Fr. etablir, Lat. stabilire, to make stable)

establishment of universal See also:

• GRAVITATION (from Lat. gravis, heavy)

gravitation as the See also:

• PRIMARY

primary law of the See also:

• CELESTIAL, OR STELLAR

celestial motions, the problem was reduced to that of integrating the See also:

• DIFFERENTIAL

differential equations of the moon's motion, and testing the completeness of the results by comparison with observation .

Although the precision of the mathematical See also:

• SOLUTION (from Lat. solvere, to loosen, dissolve)

solution has been placed beyond serious doubt, the problem of completely reconciling this solution with the observed motions of the moon is not yet completely solved . Under these circumstances the See also:

• HISTORICAL

historical treatment is that best adopted to give a clear idea of the progress and results of See also:

• RESEARCH (O. Fr. recerche, from recercher, re- and cercer, mod. chercher, to search; Late Lat. circare, to go round in a circle, to explore)

research in this See also:

• FIELD (a word common to many West German languages, cf. Ger. Feld, Dutch veld, possibly cognate with O.E. f olde, the earth, and ultimately with root of the Gr. irAaror, broad)
• FIELD, CYRUS WEST (1819-1892)
• FIELD, DAVID DUDLEY (18o5-1894)
• FIELD, EUGENE (1850-1895)
• FIELD, FREDERICK (18o1—1885)
• FIELD, HENRY MARTYN (1822-1907)
• FIELD, JOHN (1782—1837)
• FIELD, MARSHALL (183 1906)
• FIELD, NATHAN (1587—1633)
• FIELD, STEPHEN JOHNSON (1816-1899)
• FIELD, WILLIAM VENTRIS FIELD, BARON (1813-1907)

field . See also:

• MODERN

Modern researches were See also:

• DEVELOPED

developed o naturally from the results of the ancients that we shall begin with a brief mention of the work of the latter . It is in the investigation of the moon's motion that the merits of the See also:

• ANCIENT
• ANCIENT (also spelt ANTIENT; derived, through the Fr. ancien, old, from the late Lat. antianum, from ante, before)

ancient astronomy are seen to the best See also:

• ADVANTAGE

advantage . In the hands of See also:

• HIPPARCHUS (fl. 146-126 B.c.)

Hipparchus the theory was brought to a degree of precision which is really marvellous when we compare it either with other branches of See also:

• PHYSICAL

physical science in that See also:

• AGE (Fr. age, through late Lat. aetaticum, from aetas)

age or with the views of contemporary non-scientific writers . The discoveries of Hipparchus were: I . The Eccentricity of the Moon's Orbit.—He found that the moon moved most rapidly near a certain point of its orbit, and most slowly near the opposite point . The law of this motion was such that the phenomena could be represented by supposing the motion to be actually circular and uniform, the apparent variations being explained by the See also:

• HYPOTHESIS (from Gr. inrorcOivat, to put under; cf. Lat. suppositio, from sub-ponere)

hypothesis that the earth was not situated in the centre of the orbit, but was displaced by an amount about equal to one-twentieth of the radius of the orbit . Then, by an obvious law of See also:

• KINEMATICS (from Gr. rciVI La, a motion)

kinematics, the angular motion round the earth would be most rapid at the point nearest the earth, that is at perigee, and slowest at the point most distant from the earth, that is at apogee . Thus the apogee and perigee became two definite points of the orbit, indicated by the variations in the angular motion of the moon . These points are at the ends of that diameter of the orbit which passes through the eccentrically situated earth, or, in other words, they are on that line which passes through the centre of the earth and the centre of the orbit . This line was called the line of apsides .

On comparing observations made at different times it was found that the line of apsides was not fixed, but made a complete revolution in the heavens, in the order of the signs of the See also:

• ZODIAC (o i'w&arcds rvKcXor, from d,&ov, " a little animal ")

zodiac, in about nine years . 2 . The Numerical Determination of the Elements, of the Moon's Motion.—In order that the two See also:

• CAPITAL (i.e. capital stock or fund)
• CAPITAL (Lat. caput, head)

capital discoveries just mentioned should have the highest scientific value, it was essential that the numerical values of the elements involved in these complicated motions should be fixed with precision . This Hipparchus was enabled to do by lunar eclipses . Each eclipse gave a moment at which the longitude of the moon was 1800 different from that of the sun . The latter admitted of ready calculation . Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities—the mean longitude at a given See also:

• EPOCH (Gr. E7roxij, holding in suspense, a pause, from E1rxav, to hold up, to stop)

epoch, the eccentricity, and the position of the perigee . By taking three eclipses separated at See also:

• SHORT, FRANCIS JOB (1857– )

short intervals, both the mean motion and the motion of the perigee would be known beforehand, from other data, with sufficient accuracy to reduce all the observations to the same epoch, and thus to leave only the three elements already mentioned unknown . The same three elements being again determined from a second triplet of eclipses at as remote an epo ; as possible, the difference in the i A . R . Hinks, " Mass of the Moon, from Observations of See also:

• EROS

Eros; 1900-1901," M . N .

See also:

• ROY, WILLIAM (1726-1790)

Roy . See also:

• ASTI (anc. Hasta)

Asti See also:

• SOC

Soc., 1900, Nov.. p . 73.longitude of the perigee at the two epochs gave the annual motion of that See also:

• ELEMENT (Lat. elementum)

element, and the difference of mean longitudes gave the mean motion . The eccentricity determined in this way is more than a degree in See also:

• ERROR (Lat. error, from errare, to wander, to err)

error, owing to the effect of the erection, which was unknown to Hipparchus . The result of the latter inequality is brought out when it is sought to determine the eccentricity of the orbit from the observations near the time of the first and last quarter . It was thus found by See also:

• PTOLEMY (CLAUDIUS PTOLEMAEUS)

Ptolemy that an additional inequality existed in the motion, which is now known as the See also:

• EVECTION (Latin for " carrying away ")

evection . The relations of the quantities involved may be shown by See also:

• SIMPLE

simple trigonometric formulae . If we put g for the moon's See also:

• ANOMALY (from Gr. lwvw)

anomaly or distance from the perigee, and D for its See also:

• ELONGATION

elongation from the sun, the inequalities in question as now known are 6.29° See also:

• SIN
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

sin g (See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation of centre) +1.27° sin (2D–g) (evection) . During a lunar eclipse we always have D =18o°, very nearly, and 2D=36o° . Hence the evection is then — 1.2° sin g, and consequently has the same See also:

• ARGUMENT

argument g as the equation of centre, so that it is confounded with it . The value of the equation of centre derived from eclipses is thus 6.29° sin g—1.27° sin g=5.02° sing . Therefore the eccentricity found by Hipparchus was only 5°, and was more than a degree less than its true value .

At first quarter we have D =90° and 2D =18o° . Substituting this value of 2D in the last See also:

• TERM

term of the above equation, we see that the combined equation of the centre and evection are, at See also:

• QUADRATURE (from Lat. quadratura, a making square)

quadrature 6.29° sin g+1.27° sin g=7.56° sin g . Thus, in consequence of the evection, the equation of the centre comes out 2° 30' larger from observations at the moon's quarters than during eclipses . The next forward step was due to Tycho See also:

• BRAHE, PER, COUNT (1602-1680)
• BRAHE, TYCHO (1546-1601)

Brahe . He found that, although the two inequalities found by Hipparchus and Ptolemy correctly represented the moon's longitude near See also:

• CON

con-junction and opposition, and also at the quadratures, it left a large outstanding error at the octants, that is when the moon was 45 or 135° on either side of the sun . This inequality, which reaches the magnitude of nearly 1 °, is known as the variation . Although Tycho Brahe was an See also:

• ORIGINAL

original discoverer of this inequality, through whom it became known, See also:

• JOSEPH
• JOSEPH, COMTE DE (1785-1870)
• JOSEPH, FATHER (FRANCOIS LECLERC DU TREMBLAY) (1577-1638)

Joseph See also:

• BERTRAND, HENRI GRATIEN, COMTE (1773-1844)

Bertrand of Paris claimed the See also:

• DISCOVERY

discovery for See also:

• ABU

Abu 'l-Wefa, an Arabian astronomer, and made it appear that the latter really detected inequalities in the moon's motion which we now know to have been the variation . But he has not shown, on the part of the Arabian, any such exact description of the inequality as is necessary to make clear his claim to the discovery . We may conclude the ancient See also:

• HISTORY

history of the lunar theory by saying that the only real progress from Hipparchus to Newton consisted in the more exact determination of the mean motions of the moon, its perigee and its line of nodes, and in the discovery of three inequalities, the See also:

• REPRESENTATION

representation of which required geometrical constructions increasing in complexity with every step . The modern lunar theory began with Newton, and consists in determining the motion of the moon deductively from the theory of gravitation . But the great. founder of celestial See also:

• MECHANICS

mechanics employed a geometrical method, See also:

• ILL

ill-adapted to See also:

• LEAD
• LEAD (pronounced iced)

lead to the desired result; and hence his efforts to construct a lunar theory are of more interest as illustrations of his wonderful power and correctness in mathematical reasoning than as germs of new methods of research . The See also:

• ANALYTIC (the adjective of " analysis," q.v.)

analytic method sought to See also:

• EXPRESS (through the French from the past participle of the Lat. exprimere, to press out, by transference used of representing objects in painting or sculpture, or of thoughts, &c. in words)

express the moon's motion by integrating the differential equations of the dynamical theory .

The methods may be divided into three classes: I . See also:

• LAPLACE, PIERRE SIMON, MARQUIS DE (1749—1827)

Laplace and his immediate successors, especially G . A A . Plana (1781-1864), effected the integration by expressing the time in terms of the moon's true longitude . Then, by inverting the series, the longitude was expressed in terms of the time . 2 . By the second general method the moon's co-ordinates are obtained in terms of the time by the direct integration of the differential equations of motion, retaining as algebraic symbols the values of the various elements . Most of the elements are small numerical fractions: e, the eccentricity of the moon's orbit, about 0.055; e', the eccentricity of the earth's orbit, about 0'017* ry, the sine of half the inclination of the moon's orbit, about 0.046; m, the ratio of the mean motions of the moon and earth, about 0.075 . The expressions for the longitude, latitude and parallax appear as an See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite trigonometric series, in which the coefficients of the sines and cosines are themselves infinite series proceeding according to the See also:

• POWERS, HIRAM (1805-1873)

powers of the above small See also:

• NUMBERS, BOOK OF
• NUMBERS, PARTITION OF

numbers . This method was applied with success by Pontecoulant and See also:

• SIR

Sir See also:

• JOHN
• JOHN (1167–1216)
• JOHN (1290-c. 1320)
• JOHN (1296-1346)
• JOHN (1371–1419)
• JOHN (1468-1532)
• JOHN (1801-1873)
• JOHN (Heb. llni')
• JOHN (ZAPOLYA) (1487-1540)
• JOHN, 4TH MARQUESS OF TWEEDDALE (c. 1695-1762)
• JOHN, DON (1545-1578)
• JOHN, DON (1629–1679)
• JOHN, GOSPEL OF ST
• JOHN, or HAYS (1513–1571)
• JOHN, THE APOSTLE
• JOHN, THE EPISTLES OF

John W . Lubbock, and after-wards by See also:

• DELAUNAY, ELIE (1828-1891)
• DELAUNAY, LOUIS ARSENE (1826-1903)

Delaunay . By these methods the series converge so slowly, and the final expressions for the moon's longitude are so long and complicated, that the series has never been carried far enough to ensure the accuracy of all the terms .

This is especially the case with the development in powers of m, the convergence of which has often been questioned . 3 . The third method seeks to avoid the difficulty by using the numerical values of the elements instead of their algebraic symbols, This method has the advantage of leading to a more rapid and certain determination of the numerical quantities required . It has the disadvantage of giving the solution of the problem only for a particular case, and of being inapplicable in researches in which the general equations of See also:

• DYNAMICS
• DYNAMICS (from Gr. bbvayts, strength)

dynamics have to be applied . It has been employed by Damoiseau, See also:

• HANSEN, PETER ANDREAS (1795-1874)

Hansen and See also:

• AIRY, SIR GEORGE BIDDELL (1801-1892)

Airy . The methods of the second general class are those most worthy of study . Among these we must assign the first See also:

• RANK (O.Fr. rant or rent, mod. rang, generally connected with the O.E. and O.H.G. bring, a ring)

rank to the method of C . E . Delaunay, developed in his Theorie du mouvement de la Lune (2 vols., 186o, 1867), because it contains a germ which may yet develop into the great desideratum of a general method in celestial mechanics . Among applications of the third or numerical method, the most successful yet completed is that of P . A . Hansen .

His first work, Fundamenta nova, appeared in 1838, and contained an exposition of his ingenious and See also:

• PECULIAR

peculiar methods of computation . During the twenty years following he devoted a large part of his energies to the numerical computation of the lunar inequalities, the redetermination of the elements of motion, and the preparation of new tables for computing the moon's position . In the latter branch of the work he received material aid from the See also:

• BRITISH

British See also:

• GOVERNMENT
• GOVERNMENT (0. Fr. governement, mod. gouvernement, O. Fr. governer, mod. gouverner, from Lat. gubernare, to steer a ship, guide, rule; cf. Gr. xv(3epvav)

government, which published his tables on their completion in 1857 . The computations of Hansen were published some seven years later by the Royal Saxon Society of Sciences . It was found on comparing the results of Hansen and Delaunay that there are some outstanding discrepancies which are of sufficient magnitude to demand the See also:

• ATTENTION (from Lat. ad-tendo, await, expect; the condition of being " stretched " or " tense ")

attention of those interested in the mathematical theory of the subject . It was therefore necessary that the numerical inequalities should be again determined by an entirely different method . This has been done by Ernest W . See also:

• BROWN
• BROWN, CHARLES BROCKDEN (1771-181o)
• BROWN, FORD MADOX (1821-1893)
• BROWN, FRANCIS (1849- )
• BROWN, GEORGE (1818-188o)
• BROWN, HENRY KIRKE (1814-1886)
• BROWN, JACOB (1775–1828)
• BROWN, JOHN (1715–1766)
• BROWN, JOHN (1722-1787)
• BROWN, JOHN (1735–1788)
• BROWN, JOHN (1784–1858)
• BROWN, JOHN (1800-1859)
• BROWN, JOHN (1810—1882)
• BROWN, JOHN GEORGE (1831— )
• BROWN, ROBERT (1773-1858)
• BROWN, SAMUEL MORISON (1817—1856)
• BROWN, SIR GEORGE (1790-1865)
• BROWN, SIR JOHN (1816-1896)
• BROWN, SIR WILLIAM, BART
• BROWN, THOMAS (1663-1704)
• BROWN, THOMAS (1778-1820)
• BROWN, THOMAS EDWARD (1830-1897)
• BROWN, WILLIAM LAURENCE (1755–1830)

Brown, whose work may be regarded not only as the last word on the subject, but as embodying a seemingly complete and satisfactory solution of a problem which has absorbed an important part of the energies of mathematical astronomers since the time of Hipparchus . We shall try to convey an idea of this solution . We have just mentioned the four small quantities e, e', -y and m, in terms of the powers and See also:

• PRO

pro-ducts of which the moon's co-ordinates have to be expressed . See also:

• EULER, LEONHARD (1707-1783)

Euler conceived the idea of starting with a preliminary solution of the problem in which the orbit of the moon should be supposed to See also:

• LIE, JONAS LAURITZ EDEMIL (1833—1908)
• LIE, MARIUS SOPHUS (1842–1899)

lie in the ecliptic, and to have no eccentricity, while that of the sun was circular . This solution being reached, the additional terms were found, which were multiplied by the first power of the several eccentricities and of the inclination .

Then the terms of the second order were found, and so on to any extent . In a series of remark-able papers published in 1877–1888 See also:

• HILL
• HILL (0. Eng. hyll; cf. Low Ger. hull, Mid. Dutch hul, allied to Lat. celsus, high, collis, hill, &c.)
• HILL, A
• HILL, AARON (1685-175o)
• HILL, AMBROSE POWELL
• HILL, DANIEL HARVEY (1821-1889)
• HILL, DAVID BENNETT (1843–1910)
• HILL, GEORGE BIRKBECK NORMAN (1835-1903)
• HILL, JAMES J
• HILL, JOHN (c. 1716-1775)
• HILL, MATTHEW DAVENPORT (1792-1872)
• HILL, OCTAVIA (1838– )
• HILL, ROWLAND (1744–1833)
• HILL, SIR ROWLAND (1795-1879)

Hill improved Euler's method, and worked it out with much more rigour and fullness than Euler had been able to do . His most important contribution to the subject consisted in working out by extremely elegant mathematical processes the method of determining the motion of the perigee . John See also:

• COUCH, DARIUS NASH (1822-1897)

Couch See also:

• ADAMS
• ADAMS, ANDREW LEITH (1827-1882)
• ADAMS, CHARLES FRANCIS (1807-1886)
• ADAMS, HENRY (1838— )
• ADAMS, HENRY CARTER (1852— )
• ADAMS, HERBERT (i858— )
• ADAMS, HERBERT BAXTER (1850—1901)
• ADAMS, JOHN (1735–1826)
• ADAMS, JOHN QUINCY (1767-1848)
• ADAMS, SAMUEL (1722-1803)
• ADAMS, THOMAS (d. c. 1655)
• ADAMS, WILLIAM (d. 162o)

Adams afterwards determined the motion of the node in a similar way . The numerical computations were worked out by Hill only for the first approximation . The subject was then taken up by Brown, who in a series of researches published in the See also:

• MEMOIRS

Memoirs of the Royal Astronomical Society and in the Transactions of the See also:

• AMERICAN

American Mathematical Society extended Hill's method so as to form a practically complete solution of the entire problem . The See also:

• PRINCIPAL

principal feature of his work was that the quantity m, which is regarded as See also:

• CONSTANT, BENJAMIN (1845-1902)

constant, appears only in a numerical form, so that the uncertainties arising from development in a series accruing to its powers is done away with . The solution of the See also:

• MAIN (from the Aryan root which appears in " may " and " might," and Lat. magnus, great)
• MAIN (Lat. Moenus)

main mathematical problem thus reached is that of the motion of three bodies only—the sun, earth and moon . The mean motion of the moon round the earth is then invariable, the longitude containing no inequalities of longer period than that of the moon's node, 18.6 y . But See also:

• EDMUND
• EDMUND, or EADMUND (c. 980-1016)
• EDMUND, SAINT [EDMUND RICE] (d. 1240)

Edmund See also:

• HALLEY, EDMUND (1656–1742)

Halley found, by a comparison of ancient eclipses with modern observations, that the mean motion had been accelerated . This was confirmed by See also:

• RICHARD
• RICHARD (d. 1184)
• RICHARD, FRANCOIS MARIE BENJAMIN (18,9-1908)
• RICHARD, HENRY (1812-1888)
• RICHARD, ST

Richard Dunthorne (1711–1775) . Corresponding to this observed fact was the inference that the See also:

• ACTION

action of the See also:

• PLANETS, MINOR

planets might in some way influence the moon's motion .

Thus a new branch of the lunar theory was suggested—the determination by theory of the effect of planetary action . The first step in constructing this theory was taken by Laplace, who showed that the See also:

• SECULAR (Lat. saecularis, of or belonging to an age or generation, saeculum)

secular See also:

• ACCELERATION (from Lat. accelerare, to hasten, celer, quick)

acceleration was produced by the secular diminution of the earth's orbit . He computed the amount as about to" per century, which agreed with the results derived by Dunthorne from ancient eclipses . Laplace's immediate successors, among whom were Hansen, Plana and Pontecoulant, found a larger value, Hansen increasing it to 12.5", which he introduced into his tables . This value was found by himself and Airy to represent fairly well several ancient eclipses of the sun, notably the supposed one of Thales . But Adams in 18531 showed that the previous computations of the acceleration were only a See also:

• RUDE, FRANCOIS (1784–1855)

rude first approximation, and that a more rigorous computation reduced the result to about one-half . This diminution was soon fully con-firmed by others, especially Delaunay, although for some time Pontecoulant stoutly maintained the correctness of the older result . But the demonstration of See also:

• ADAM
• ADAM (or ADAN) DE LE HALE (died c. 1288)
• ADAM, ALEXANDER (1741–1809)
• ADAM, JULIETTE (1836– )
• ADAM, LAMBERT SIGISBERT (1700-1759)
• ADAM, MELCHIOR (d. 1622)
• ADAM, PAUL (1862– )
• ADAM, ROBERT (1728—1792)
• ADAM, SIR FREDERICK (1781-1853)
• ADAM, WILLIAM (1751-1839)

Adam's result was soon made 1 Philosophical Transactions, 1853 . conclusive, and a value which may be regarded as definitive has been derived by Brown . With the latest accepted diminution of the eccentricity, the coefficient is 5.91" . The question now arose of the origin of the discrepancy between the smaller values by theory, and the supposed values of 12" derived from ancient eclipses . In 1856 See also:

• WILLIAM
• WILLIAM (1143-1214)
• WILLIAM (1227-1256)
• WILLIAM (1J33-1584)
• WILLIAM (A.S. Wilhelm, O. Norse Vilhidlmr; O. H. Ger. Willahelm, Willahalm, M. H. Ger. Willehelm, Willehalm, Mod.Ger. Wilhelm; Du. Willem; O. Fr. Villalme, Mod. Fr. Guillaume; from " will," Goth. vilja, and " helm," Goth. hilms, Old Norse hidlmr, meaning
• WILLIAM (c. 1130-C. 1190)
• WILLIAM, 13TH

William Ferrel showed that the action of the moon on the ocean tidal waves would result in a retardation of the earth's rotation, a result, at first unnoticed, which was independently reached a few years later by Delaunay .

The amount of retardation does not admit of accurate computation, owing to the uncertainty both as to the amount of the oceanic See also:

• FRICTION (from Lat. fricare, to rub)

friction from which it arises and of the exact height and form of the tidal See also:

• WAVE

wave, the action of the moon on which produces the effect . But any rough estimate that can be made shows that it might well be supposed much larger than is necessary to produce the observed See also:

• DIFFERENCES, CALCULUS OF (Theory of Finite Differences)

differences of 6" per century . It was therefore surprising when, in 1877, See also:

• SIMON, ABRAHAM (1622-1692)
• SIMON, JULES FRANCOIS (1814–1896)
• SIMON, RICHARD (1638–1712)
• SIMON, SIR JOHN (1816–1904)
• SIMON, THOMAS (c. 1623-1665)

Simon See also:

• NEWCOMB, SIMON (1835-1909)

Newcomb found, by a study of the lunar eclipses handed down by Ptolemy and those observed by the Arabians—data much more reliable than the vague accounts of ancient solar eclipses —that the actual apparent acceleration was only about 8-3" . This is only 2.4" larger than the theoretical value, and it seems difficult to suppose that the effect of the tidal retardation can be as small as this . This suggests that the retardation may be in great part compensated by some accelerating cause, the existence of which is not yet well established . The following is a See also:

• SUMMARY

summary of the present See also:

• STATE
• STATE, GREAT OFFICERS OF

state of the question: The theoretical value of the acceleration,- assuming the day to be constant, is . . . 5.91" Hansen's value in his Tables de la Lune is . . . . 12.19 Hansen's revised, but still theoretically erroneous, result is 12.56 The value which best represents the supposed eclipses —(1) of Thales, (2) at See also:

• LARISSA (Turk. Yeni Shehr, " new town ")

Larissa, (3) at Stikkelstad —is about . . . 11.7 The result from purely astronomical observation is 8.3 • Inequalities of Long Period.—Combined with the question of secular acceleration is another which is still not entirely settled-that of inequalities of long period in the mean motion of the moon round the earth .

Laplace first showed that modern observations of the moon indicated that its mean motion was really less during the second half of the 18th century than during the first half, and hence inferred the existence of an inequality having a period of more than a century . The existence of one or more such inequalities has been fully confirmed by all the observations, both early and recent, that have become available since the time of Laplace . It is also found by computation from theory that the planets do produce several appreciable inequalities of long period, as well as a great number of short period, in the motion of the moon . But the former do not correspond to the observed inequalities, and the explanation of the outstanding differences may be regarded to-day as the most perplexing See also:

• ENIGMA (Gr. aTvcyµa)

enigma in astronomy . The most plausible explanation is that, like the discrepancy in the secular acceleration, the observed deviation is only apparent, and arises from slow fluctuations in the earth's rotation, and therefore in our measure of time pro, duced by the motion of great masses of polar See also:

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

ice and the variability of the amount of snowfall on the great continents . Were this the case a similar inequality should be found in the observed times of the transits of See also:

• MERCURY
• MERCURY (MERCU1uus)
• MERCURY (symbol Hg, atomic weight = 2oo)

Mercury . But the latter do not certainly show any deviation in the measure of time, and seem to preclude a deviation so large as that derived from observations of the moon . This suggests that inequalities in the action of the planets may have been still overlooked, the subject being the most intricate with which celestial mechanics has to See also:

• DEAL

deal . But this action has been recently worked up with such completeness of detail by Radau, Newcomb and Brown, that the possibility of any unknown term seems out of the question . ,The enigma therefore still defies solution . On the subject of lunar See also:

• GEOLOGY (from Gr. yp7, the earth, and Abyor, science)

geology, see N . S .

Shales in Smithsonian Contributions to Knowledge, vol. xxxiv . No . 1438, and P . Puiseux, " Recherches sur 1'origine probable See also:

• DES

des formations lunaires," in Annales de l'observatoire de Paris, Memoires, tome xxii . The following are among the See also:

• WORKS

works relating to the motion of the moon, which are of historic importance or present interest to the student: Clairaut, Theorie de la tune (2nd ed., Paris, 1765); L . Euler, Theoria motuum lunae nova methodo pertractata (See also:

• PETROPOLIS

Petropolis, 1772) ; G . Plana, Theorie du mouvement de la line (3 vols., See also:

• TURIN

Turin, 1832) ; P . A . Hansen, Fundamenta nova investigations orbitae verae quam tuna perlustrat (See also:

• GOTHA

Gotha, 1838) ; Darlegung der theoretischen Berechnung der sn den Mondtafeln angewandten Storungen (Leipzig, 1862); C . Delaunay, Theorie du mouvement de la line (2 vols., Paris, 186o—1867); F . F . See also:

• TISSERAND, FRANCOIS FELIX (1845-1896)

Tisserand, Traite de mecanique See also:

• CELESTE, MADAME (1815–1882)

celeste, tome iii., Expose de l'ensemble des theories relatives au mouvement de la line (Paris, 1894) ; E .

W . Brown, " Theory of the Motion of the Moon," Memoirs of the Royal Astronomical Society, various vols . ; also Transactions of the American Mathematical Society, vols. iv. and vi . ; E . W . Brown, See also:

• INTRODUCTORY

Introductory See also:

• TREATISE

Treatise on the Lunar Theory (See also:

• CAM (CAO), DIOGO (fl. 1480-1486)

Cam-See also:

• BRIDGE

bridge University See also:

• PRESS (through Fr. presse from Lat. pressare, frequentative of premere, to crush, squeeze, press)

Press, 1896) ; Hansen, Tables de la lune (See also:

• LONDON

London, 1857) (See also:

• ADMIRALTY, HIGH COURT OF

Admiralty publication) ; W . Ferrel, " On the Effect of the Sun and Moon on the Rotary Motion of the Earth," Astron . Jour., vol. iii . (1854) ; S . Newcomb, " Researches on the Motion of the Moon " (Appendix to See also:

• WASHINGTON
• WASHINGTON (or WASHINGTON COURT HOUSE)
• WASHINGTON, BOOKER TALIAFERRO (c. 1859– )
• WASHINGTON, BUSHROD (1762-1829)
• WASHINGTON, GEORGE (1732-1799)

Washington Observations for 1875, discussion of the moon's mean motion) ; S . Newcomb, " Transformation of Hansen's Lunar Theory," See also:

• AST, GEORG ANTON FRIEDRICH (1778-1841)

Ast . Papers of the Amer .

See also:

• EPHEMERIS (Greek for a " diary ")

Ephemeris, vol. i . ; R . Radau, " Inegalites planetaires du mouvement de la lune " (Annales, Paris Observatory, vol. xxi.) ; S . Newcomb, " Action of the Planets on the Moon," Ast . Papers of the Amer . Ephemeris, vol. v., pt . 3 (1896) . Also, Publication 72 of the See also:

• CARNEGIE
• CARNEGIE, ANDREW (1837– )

Carnegie Institution of -Washington (1907) ; E . W . Brown, Inequalities in the Moon's Motion produced by the Action of the Planets (the Adams See also:

• PRIZE, or PRIZE OF WAR (Fr. prise, from prendre, to take)

prize See also:

• ESSAY, ESSAYIST (Fr. essai, Late Lat. exagium, a weighing or balance; exigere, to examine; the term in general meaning any trial or effort)

essay for 1907) . (S .