[1] W. E. H. Lecky, _Leaders of Public Opinion in Ireland_, i. 127
(enlarged edition, 2 vols., 1903).
[2] _Ibid._ i. 204.
[3] _Ibid._ i. 241.
[4] _Grattan's Speeches_, iv. 23.
[5] W. E. H. Lecky, _History of England in the Eighteenth Century_,
viii. 491. Cf. _Cornwallis Correspondence_, iii. 250.
[6] W. E. H. Lecky, _Leaders of Public Opinion in Ireland_, i. 270.
[7] Sydney Smith's _Works_, ii. 166-167.
GRATTIUS [FALISCUS], Roman poet, of the age of Augustus, author of a
poem on hunting (_Cynegetica_), of which 541 hexameters remain. He was
possibly a native of Falerii. The only reference to him in any ancient
writer is incidental (Ovid, _Ex Ponto_, iv. 16. 33). He describes
various kinds of game, methods of hunting, the best breeds of horses and
dogs.
There are editions by R. Stern (1832); E. Bahrens in _Poetae Latini
Minores_ (i., 1879) and G. G. Curcio in _Poeti Latini Minori_ (i.,
1902), with bibliography; see also H. Schenkl, _Zur Kritik des G._
(1898). There is a translation by Christopher Wase (1654).
GRAUDENZ (Polish _Grudziadz_), a town in the kingdom of Prussia,
province of West Prussia, on the right bank of the Vistula, 18 m. S.S.W.
of Marienwerder and 37 m. by rail N.N.E. of Thorn. Pop. (1885) 17,336,
(1905) 35,988. It has two Protestant and three Roman Catholic churches,
and a synagogue. It is a place of considerable manufacturing activity.
The town possesses a museum and a monument to Guillaume Rene Courbiere
(1733-1811), the defender of the town in 1807. It has fine promenades
along the bank of the Vistula. Graudenz is an important place in the
German system of fortifications, and has a garrison of considerable
size.
Graudenz was founded about 1250, and received civic rights in 1291. At
the peace of Thorn in 1466 it came under the lordship of Poland. From
1665 to 1759 it was held by Sweden, and in 1772 it came into the
possession of Prussia. The fortress of Graudenz, which since 1873 has
been used as a barracks and a military depot and prison, is situated on
a steep eminence about 1-1/2 m. north of the town and outside its
limits. It was completed by Frederick the Great in 1776, and was
rendered famous through its defence by Courbiere against the French in
1807.
GRAUN, CARL HEINRICH (1701-1759), German musical composer, the youngest
of three brothers, all more or less musical, was born on the 7th of May
1701 at Wahrenbruck in Saxony. His father held a small government post
and he gave his children a careful education. Graun's beautiful soprano
voice secured him an appointment in the choir at Dresden. At an early
age he composed a number of sacred cantatas and other pieces for the
church service. He completed his studies under Johann Christoph Schmidt
(1664-1728), and profited much by the Italian operas which were
performed at Dresden under the composer Lotti. After his voice had
changed to a tenor, he made his debut at the opera of Brunswick, in a
work by Schurmann, an inferior composer of the day; but not being
satisfied with the arias assigned him he re-wrote them, so much to the
satisfaction of the court that he was commissioned to write an opera for
the next season. This work, _Polydorus_ (1726), and five other operas
written for Brunswick, spread his fame all over Germany. Other works,
mostly of a sacred character, including two settings of the _Passion_,
also belong to the Brunswick period. Frederick the Great, at that time
crown prince of Prussia, heard the singer in Brunswick in 1735, and
immediately engaged him for his private chapel at Rheinsberg. There
Graun remained for five years, and wrote a number of cantatas, mostly to
words written by Frederick himself in French, and translated into
Italian by Boltarelli. On his accession to the throne in 1740, Frederick
sent Graun to Italy to engage singers for a new opera to be established
at Berlin. Graun remained a year on his travels, earning universal
applause as a singer in the chief cities of Italy. After his return to
Berlin he was appointed conductor of the royal orchestra
(_Kapellmeister_) with a salary of 2000 thalers (L300). In this capacity
he wrote twenty-eight operas, all to Italian words, of which the last,
_Merope_ (1756), is perhaps the most perfect. It is probable that Graun
was subjected to considerable humiliation from the arbitrary caprices of
his royal master, who was never tired of praising the operas of Hasse
and abusing those of his _Kapellmeister_. In his oratorio _The Death of
Jesus_ Graun shows his skill as a contrapuntist, and his originality of
melodious invention. In the Italian operas he imitates the florid style
of his time, but even in these the recitatives occasionally show
considerable dramatic power. Graun died on the 8th of August 1759, at
Berlin, in the same house in which, thirty-two years later, Meyerbeer
was born.
GRAVAMEN. (from Lat. _gravare_, to weigh down; _gravis_, heavy), a
complaint or grievance, the ground of a legal action, and particularly
the more serious part of a charge against an accused person. In English
the term is used chiefly in ecclesiastical cases, being the technical
designation of a memorial presented from the Lower to the Upper House of
Convocation, setting forth grievances to be redressed, or calling
attention to breaches in church discipline.
GRAVE. (1) (From a common Teutonic verb, meaning "to dig"; in O. Eng.
_grafan_; cf. Dutch _graven_, Ger. _graben_), a place dug out of the
earth in which a dead body is laid for burial, and hence any place of
burial, not necessarily an excavation (see FUNERAL RITES and BURIAL).
The verb "to grave," meaning properly to dig, is particularly used of
the making of incisions in a hard surface (see ENGRAVING). (2) A title,
now obsolete, of a local administrative official for a township in
certain parts of Yorkshire and Lincolnshire; it also sometimes appears
in the form "grieve," which in Scotland and Northumberland is used for
sheriff (q.v.), and also for a bailiff or under-steward. The origin of
the word is obscure, but it is probably connected with the German
_graf_, count, and thus appears as the second part of many Teutonic
titles, such as landgrave, burgrave and margrave. "Grieve," on the other
hand, seems to be the northern representative of O.E. _gerefa_, reeve;
cf. "sheriff" and "count." (3) (From the Lat. _gravis_, heavy), weighty,
serious, particularly with the idea of dangerous, as applied to diseases
and the like, of character or temperament as opposed to gay. It is also
applied to sound, low or deep, and is thus opposed to "acute." In music
the term is adopted from the French and Italian, and applied to a
movement which is solemn or slow. (4) To clean a ship's bottom in a
specially constructed dock, called a "graving dock." The origin of the
word is obscure; according to the _New English Dictionary_ there is no
foundation for the connexion with "greaves" or "graves," the refuse of
tallow, in candle or soap-making, supposed to be used in "graving" a
ship. It may be connected with an O. Fr. _grave_, mod. _greve_, shore.
GRAVEL, or PEBBLE BEDS, the name given to deposits of rounded,
subangular, water-worn stones, mingled with finer material such as sand
and clay. The word "gravel" is adapted from the O. Fr. _gravele_, mod.
_gravelle_, dim. of _grave_, coarse sand, sea-shore, Mod. Fr. _greve_.
The deposits are produced by the attrition of rock fragments by moving
water, the waves and tides of the sea and the flow of rivers. Extensive
beds of gravel are forming at the present time on many parts of the
British coasts where suitable rocks are exposed to the attack of the
atmosphere and of the sea waves during storms. The flint gravels of the
coast of the Channel, Norfolk, &c., are excellent examples. When the sea
is rough the lesser stones are washed up and down the beach by each
wave, and in this way are rounded, worn down and finally reduced to
sand. These gravels are constantly in movement, being urged forward by
the shore currents especially during storms. Large banks of gravel may
be swept away in a single night, and in this way the coast is laid bare
to the erosive action of the sea. Moreover, the movement of the gravel
itself wears down the subjacent rocks. Hence in many places barriers
have been erected to prevent the drift of the pebbles and preserve the
land, while often it has been found necessary to protect the shores by
masonry or cement work. Where the pebbles are swept along to a
projecting cape they may be carried onwards and form a long spit or
submarine bank, which is constantly reduced in size by the currents and
tides which flow across it (e.g. Spurn Head at the mouth of the Humber).
The Chesil Bank is the best instance in Britain of a great accumulation
of pebbles constantly urged forward by storms in a definite direction.
In the shallower parts of the North Sea considerable areas are covered
with coarse sand and pebbles. In deeper water, however, as in the
Atlantic, beyond the 100 fathom line pebbles are very rare, and those
which are found are mostly erratics carried southward by floating
icebergs, or volcanic rocks ejected by submarine volcanoes.
In many parts of Britain, Scandinavia and North America there are marine
gravels, in every essential resembling those of the sea-shore, at
levels considerably above high tide. These gravels often lie In
flat-topped terraces which may be traced for great distances along the
coast. They are indications that the sea at one time stood higher than
it does at present, and are known to geologists as "raised beaches." In
Scotland such beaches are known 25, 50 and 100 ft. above the present
shores. In exposed situations they have old shore cliffs behind them;
although their deposits are mainly gravelly there is much fine sand and
silt in the raised beaches of sheltered estuaries and near river mouths.
River gravels occur most commonly in the middle and upper parts of
streams where the currents in times of flood are strong enough to
transport fairly large stones. In deltas and the lower portions of large
rivers gravel deposits are comparatively rare and indicate periods when
the volume of the stream was temporarily greatly increased. In the
higher torrents also, gravels are rare because transport is so effective
that no considerable accumulations can form. In most countries where the
drainage is of a mature type, river gravels occur in the lower parts of
the courses of the rivers as banks or terraces which lie some distance
above the stream level. Individual terraces usually do not persist for a
long space but are represented by a series of benches at about the same
altitude. These were once continuous, and have been separated by the
stream cutting away the intervening portions as it deepened and
broadened its channel. Terraces of this kind often occur in successive
series at different heights, and the highest are the oldest because they
were laid down at a time when the stream flowed at their level and mark
the various stages by which the valley has been eroded. While marine
terraces are nearly always horizontal, stream terraces slope downwards
along the course of the river.
The extensive deposits of river gravels in many parts of England,
France, Switzerland, North America, &c., would indicate that at some
former time the rivers flowed in greater volume than at the present day.
This is believed to be connected with the glacial epoch and the
augmentation of the streams during those periods when the ice was
melting away. Many changes in drainage have taken place since then;
consequently wide sheets of glacial and fluvio-glacial gravel lie spread
out where at present there is no stream. Often they are commingled with
sand, and where there were temporary post-glacial lakes deposits of
silt, brick clay and mud have been formed. These may be compared to the
similar deposits now forming in Greenland, Spitzbergen and other
countries which are at present in a glacial condition.
As a rule gravels consist mainly of the harder kinds of stone because
these alone can resist attrition. Thus the gravels formed from chalk
consist almost entirely of flint, which is so hard that the chalk is
ground to powder and washed away, while the flint remains little
affected. Other hard rocks such as chert, quartzite, felsite, granite,
sandstone and volcanic rocks very frequently are largely represented in
gravels, while coal, limestone and shale are far less common. The size
of the pebbles varies from a fraction of an inch to several feet; it
depends partly on the fissility of the original rocks and partly on the
strength of the currents of water; coarse gravels indicate the action of
powerful eroding agents. In the Tertiary systems gravels occur on many
horizons, e.g. the Woolwich and Reading beds, Oldhaven beds and Bagshot
beds of the Eocene of the London basin. They do not essentially differ
from recent gravel deposits. But in course of time the action of
percolating water assisted by pressure tends to convert gravels into
firm masses of conglomerate by depositing carbonate of lime, silica and
other substances in their interstices. Gravels are not usually so
fossiliferous as finer deposits of the same age, partly because their
porous texture enables organic remains to be dissolved away by water,
and partly because shells and other fossils are comparatively fragile
and would be broken up during the accumulation of the pebbles. The rock
fragments in conglomerates, however, sometimes contain fossils which
have not been found elsewhere. (J. S. F.)
GRAVELINES (Flem. _Gravelinghe_), a fortified seaport town of northern
France, in the department of Nord and arrondissement of Dunkirk, 15 m.
S.W. of Dunkirk on the railway to Calais. Pop. (1906) town, 1858;
commune, 6284. Gravelines is situated on the Aa, 1-1/4 m. from its mouth
in the North Sea. It is surrounded by a double circuit of ramparts and
by a tidal moat. The river is canalized and opens out beneath the
fortifications into a floating basin. The situation of the port is one
of the best in France on the North Sea, though its trade has suffered
owing to the nearness of Calais and Dunkirk and the silting up of the
channel to the sea. It is a centre for the cod and herring fisheries.
Imports consist chiefly of timber from Northern Europe and coal from
England, to which eggs and fruit are exported. Gravelines has
paper-manufactories, sugar-works, fish-curing works, salt-refineries,
chicory-roasting factories, a cannery for preserved peas and other
vegetables and an important timber-yard. The harbour is accessible to
vessels drawing 18 ft. at high tides. The greater part of the population
of the commune of Gravelines dwells in the maritime quarter of
Petit-Fort-Philippe at the mouth of the Aa, and in the village of Les
Huttes (to the east of the town), which is inhabited by the fisher-folk.
The canalization of the Aa by a count of Flanders about the middle of
the 12th century led to the foundation of Gravelines (_grave-linghe_,
meaning "count's canal."). In 1558 it was the scene of the signal
victory of the Spaniards under the count of Egmont over the French. It
finally passed from the Spaniards to the French by the treaty of the
Pyrenees in 1659.
GRAVELOTTE, a village of Lorraine between Metz and the French frontier,
famous as the scene of the battle of the 18th of August 1870 between the
Germans under King William of Prussia and the French under Marshal
Bazaine (see METZ and FRANCO-GERMAN WAR). The battlefield extends from
the woods which border the Moselle above Metz to Roncourt, near the
river Orne. Other villages which played an important part in the battle
of Gravelotte were Saint Privat, Amanweiler or Amanvillers and
Sainte-Marie-aux-Chenes, all lying to the N. of Gravelotte.
GRAVES, ALFRED PERCEVAL (1846- ), Irish writer, was born in Dublin,
the son of the bishop of Limerick. He was educated at Windermere
College, and took high honours at Dublin University. In 1869 he entered
the Civil Service as clerk in the Home Office, where he remained until
he became in 1874 an inspector of schools. He was a constant contributor
of prose and verse to the _Spectator_, _The Athenaeum_, _John Bull_, and
_Punch_, and took a leading part in the revival of Irish letters. He was
for several years president of the Irish Literary Society, and is the
author of the famous ballad of "Father O'Flynn" and many other songs and
ballads. In collaboration with Sir C. V. Stanford he published _Songs of
Old Ireland_ (1882), _Irish Songs and Ballads_ (1893), the airs of which
are taken from the Petrie MSS.; the airs of his _Irish Folk-Songs_
(1897) were arranged by Charles Wood, with whom he also collaborated in
_Songs of Erin_ (1901).
His brother, Charles L. Graves (b. 1856), educated at Marlborough and at
Christ Church, Oxford, also became well known as a journalist, author of
two volumes of parodies, _The Hawarden Horace_ (1894) and _More Hawarden
Horace_ (1896), and of skits in prose and verse. An admirable musical
critic, his _Life and Letters of Sir George Grove_ (1903) is a model
biography.
GRAVESEND, a municipal and parliamentary borough, river-port and market
town of Kent, England, on the right bank of the Thames opposite Tilbury
Fort, 22 m. E. by S. of London by the South-Eastern & Chatham railway.
Pop. (1901) 27,196. It extends about 2 m. along the river bank,
occupying a slight acclivity which reaches its summit at Windmill Hill,
whence extensive views are obtained of the river, with its windings and
shipping. The older and lower part of the town is irregularly built,
with narrow and inconvenient streets, but the upper and newer portion
contains several handsome streets and terraces. Among several piers are
the town pier, erected in 1832, and the terrace pier, built in 1845, at
a time when local river-traffic by steamboat was specially prosperous.
Gravesend is a favourite resort of the inhabitants of London, both for
excursions and as a summer residence; it is also a favourite yachting
centre. The principal buildings are the town-hall, the parish church of
Gravesend, erected on the site of an ancient building destroyed by fire
in 1727; Milton parish church, a Decorated and Perpendicular building
erected in the time of Edward II.; and the county courts. Milton Mount
College is a large institution for the daughters of Congregational
ministers. East of the town are the earthworks designed to assist
Tilbury Fort in obstructing the passage up river of an enemy's force.
They were originally constructed on Vauban's system in the reign of
Charles II. Rosherville Gardens, a popular resort, are in the western
suburb of Rosherville, a residential quarter named after James Rosher,
an owner of lime works. They were founded in 1843 by George Jones.
Gravesend, which is within the Port of London, has some import trade in
coal and timber, and fishing, especially of shrimps, is carried on
extensively. The principal other industries are boat-building,
ironfounding, brewing and soap-boiling. Fruit and vegetables are largely
grown in the neighbourhood for the London market. Since 1867 Gravesend
has returned a member to parliament, the borough including Northfleet to
the west. The town is governed by a mayor, 6 aldermen and 18
councillors. Area, 1259 acres.
In the Domesday Survey "Gravesham" is entered among the bishop of
Bayeux's lands, and a "hythe" or landing-place is mentioned. In 1401
Henry IV. granted the men of Gravesend the sole right of conveying in
their own vessels all persons travelling between London and Gravesend,
and this right was confirmed by Edward IV. in 1462. In 1562 the town was
granted a charter of incorporation by Elizabeth, which vested the
government in 2 portreeves and 12 jurats, but by a later charter of 1568
one portreeve was substituted for the two. Charles I. incorporated the
town anew under the title of the mayor, jurats and inhabitants of
Gravesend, and a further charter of liberties was granted by James II.
in 1687. A Thursday market and fair on the 13th of October were granted
to the men of Gravesend by Edward III. in 1367; Elizabeth's charters
gave them a Wednesday market and fairs on the 24th of June and the 13th
of October, with a court of pie-powder; by the charter of Charles I.
Thursday and Saturday were made the market days, and these were changed
again to Wednesday and Saturday by a charter of 1694, which also granted
a fair on the 23rd of April; the fairs on these dates have died out, but
the Saturday market is still held.
From the beginning of the 17th century Gravesend was the chief station
for East Indiamen; most of the ships outward bound from London stopped
here to victual. A customs house was built in 1782. Queen Elizabeth
established Gravesend as the point where the corporation of London
should welcome in state eminent foreign visitors arriving by water.
State processions by water from Gravesend to London had previously taken
place, as in 1522, when Henry VIII. escorted the emperor Charles V. A
similar practice was maintained until modern times; as when, on the 7th
of March 1863, the princess Alexandra was received here by the prince of
Wales (King Edward VII.) three days before their marriage. Gravesend
parish church contains memorials to "Princess" Pocahontas, who died when
preparing to return home from a visit to England in 1617, and was buried
in the old church. A memorial pulpit from the state of Indiana, U.S.A.,
made of Virginian wood, was provided in 1904, and a fund was raised for
a stained-glass window by ladies of the state of Virginia.
GRAVINA, GIOVANNI VINCENZO (1664-1718), Italian litterateur and
jurisconsult, was born at Roggiano, a small town near Cosenza, in
Calabria, on the 20th of January 1664. He was descended from a
distinguished family, and under the direction of his maternal uncle,
Gregorio Caloprese, who possessed some reputation as a poet and
philosopher, received a learned education, after which he studied at
Naples civil and canon law. In 1689 he came to Rome, where in 1695 he
united with several others of literary tastes in forming the Academy of
Arcadians. A schism occurred in the academy in 1711, and Gravina and his
followers founded in opposition to it the Academy of Quirina. From
Innocent XII. Gravina received the offer of various ecclesiastical
honours, but declined them from a disinclination to enter the clerical
profession. In 1699 he was appointed to the chair of civil law in the
college of La Sapienza, and in 1703 he was transferred to the chair of
canon law. He died at Rome on the 6th of January 1718. He was the
adoptive father of Metastasio.
Gravina is the author of a number of works of great erudition, the
principal being his _Origines juris civilis_, completed in 3 vols.
(1713) and his _De Romano imperio_ (1712). A French translation of the
former appeared in 1775, of which a second edition was published in
1822. His collected works were published at Leipzig in 1737, and at
Naples, with notes by Mascovius, in 1756.
GRAVINA, a town and episcopal see of Apulia, Italy, in the province of
Bari, from which it is 63 m. S.W. by rail (29 m. direct), 1148 ft. above
sea-level. Pop. (1901) 18,197. The town is probably of medieval origin,
though some conjecture that it occupies the site of the ancient Blera, a
post station on the Via Appia. The cathedral is a basilica of the 15th
century. The town is surrounded with walls and towers, and a castle of
the emperor Frederick II. rises above the town, which later belonged to
the Orsini, dukes of Gravina; just outside it are dwellings and a church
(S. Michele) all hewn in the rock, and now abandoned.
Prehistoric remains in the district (remains of ancient settlements,
_tumuli_, &c.) are described by V. di Cicco in _Notizie degli scavi_
(1901), p. 217.
GRAVITATION (from Lat. _gravis_, heavy), in physical science, that
mutual action between masses of matter by virtue of which every such
mass tends toward every other with a force varying directly as the
product of the masses and inversely as the square of their distances
apart. Although the law was first clearly and rigorously formulated by
Sir Isaac Newton, the fact of the action indicated by it was more or
less clearly seen by others. Even Ptolemy had a vague conception of a
force tending toward the centre of the earth which not only kept bodies
upon its surface, but in some way upheld the order of the universe. John
Kepler inferred that the planets move in their orbits under some
influence or force exerted by the sun; but the laws of motion were not
then sufficiently developed, nor were Kepler's ideas of force
sufficiently clear, to admit of a precise statement of the nature of the
force. C. Huygens and R. Hooke, contemporaries of Newton, saw that
Kepler's third law implied a force tending toward the sun which, acting
on the several planets, varied inversely as the square of the distance.
But two requirements necessary to generalize the theory were still
wanting. One was to show that the law of the inverse square not only
represented Kepler's third law, but his first two laws also. The other
was to show that the gravitation of the earth, following one and the
same law with that of the sun, extended to the moon. Newton's researches
showed that the attraction of the earth on the moon was the same as that
for bodies at the earth's surface, only reduced in the inverse square of
the moon's distance from the earth's centre. He also showed that the
total gravitation of the earth, assumed as spherical, on external
bodies, would be the same as if the earth's mass were concentrated in
the centre. This led at once to the statement of the law in its most
general form.
The law of gravitation is unique among the laws of nature, not only in
its wide generality, taking the whole universe in its scope, but in the
fact that, so far as yet known, it is absolutely unmodified by any
condition or cause whatever. All other forms of action between masses of
matter, vary with circumstances. The mutual action of electrified
bodies, for example, is affected by their relative or absolute motion.
But no conditions to which matter has ever been subjected, or under
which it has ever been observed, have been found to influence its
gravitation in the slightest degree. We might conceive the rapid motions
of the heavenly bodies to result in some change either in the direction
or amount of their gravitation towards each other at each moment; but
such is not the case, even in the most rapidly moving bodies of the
solar system. The question has also been raised whether the action of
gravitation is absolutely instantaneous. If not, the action would not be
exactly in the line adjoining the two bodies at the instant, but would
be affected by the motion of the line joining them during the time
required by the force to pass from one body to the other. The result of
this would be seen in the motions of the planets around the sun; but the
most refined observations show no such effect. It is also conceivable
that bodies might gravitate differently at different temperatures. But
the most careful researches have failed to show any apparent
modification produced in this way except what might be attributed to the
surrounding conditions. The most recent and exhaustive experiment was
that of J. H. Poynting and P. Phillips (_Proc. Roy. Soc._, 76A, p. 445).
The result was that the change, if any, was less than 1/10 of the force
for one degree change of temperature, a result too minute to be
established by any measures.
Another cause which might be supposed to modify the action of
gravitation between two bodies would be the interposition of masses of
matter between them, a cause which materially modifies the action of
electrified bodies. The question whether this cause modifies gravitation
admits of an easy test from observation. If it did, then a portion of
the earth's mass or of that of any other planet turned away from the sun
would not be subjected to the same action of the sun as if directly
exposed to that action. Great masses, as those of the great planets,
would not be attracted with a force proportional to the mass because of
the hindrance or other effect of the interposed portions. But not the
slightest modification due to this cause is shown. The general
conclusion from everything we see is that a mass of matter in Australia
attracts a mass in London precisely as it would if the earth were not
interposed between the two masses.
We must therefore regard the law in question as the broadest and most
fundamental one which nature makes known to us.
It is not yet experimentally proved that variation as the inverse square
is absolutely true at all distances. Astronomical observations extend
over too brief a period of time to show any attraction between different
stars except those in each other's neighbourhood. But this proves
nothing because, in the case of distances so great, centuries or even
thousands of years of accurate observation will be required to show any
action. On the other hand the enigmatical motion of the perihelion of
Mercury has not yet found any plausible explanation except on the
hypothesis that the gravitation of the sun diminishes at a rate slightly
greater than that of the inverse square--the most simple modification
being to suppose that instead of the exponent of the distance being
exactly -2, it is -2.000 000 161 2.
The argument is extremely simple in form. It is certain that, in the
general average, year after year, the force with which Mercury is drawn
toward the sun does vary from the exact inverse square of its distance
from the sun. The most plausible explanation of this is that one or more
masses of matter move around the sun, whose action, whether they are
inside or outside the orbit of Mercury, would produce the required
modification in the force. From an investigation of all the observations
upon Mercury and the other three interior planets, Simon Newcomb found
it almost out of the question that any such mass of matter could exist
without changing either the figure of the sun itself or the motion of
the planes of the orbits of either Mercury or Venus. The qualification
"almost" is necessary because so complex a system of actions comes into
play, and accurate observations have extended through so short a period,
that the proof cannot be regarded as absolute. But the fact that careful
and repeated search for a mass of matter sufficient to produce the
desired effect has been in vain, affords additional evidence of its
non-existence. The most obvious test of the reality of the required
modifications would be afforded by two other bodies, the motions of
whose pericentres should be similarly affected. These are Mars and the
moon. Newcomb found an excess of motions in the perihelion of Mars
amounting to about 5' per century. But the combination of observations
and theory on which this is based is not sufficient fully to establish
so slight a motion. In the case of the motion of the moon around the
earth, assuming the gravitation of the latter to be subject to the
modification in question, the annual motion of the moon's perigee
should be greater by 1.5' than the theoretical motion. E. W. Brown is
the first investigator to determine the theoretical motions with this
degree of precision; and he finds that there is no such divergence
between the actual and the computed motion. There is therefore as yet no
ground for regarding any deviation from the law of inverse square as
more than a possibility. (S. N.)