Hence our instrument draws a curve which gives the integral (1) in the form

y = 2/[pi] [Integral,0:[pi]] f(x)cos((n/[pi])[theta]x) dx

as a function of [theta]. But this integral becomes the coefficient a_m in

the cosine expansion if we make

[theta]n/[pi] = m or [theta] = m[pi]/n.

The ordinates of the curve at the values [theta] = [pi]/n, 2[pi]/n, ...

give therefore all coefficients up to m = 80. The curve shows at a glance

which and how many of the coefficients are of importance.

The instrument is described in _Phil. Mag._, vol. xlv., 1898. A number of

curves drawn by it are given, and also examples of the analysis of curves

for which the coefficients a_m are known. These indicate that a remarkable

accuracy is obtained.

(O. H.)

[1] For a fuller description of the manner in which a mere addition machine

can be used for multiplication and division, and even for the extraction of

square roots, see an article by C.V. Boys in _Nature_, 11th July 1901.

CALCUTTA, the capital of British India and also of the province of Bengal.

It is situated in 22° 34' N. and 88° 24' E., on the left or east bank of

the Hugli, about 80 m. from the sea. Including its suburbs it covers an

area of 27,267 acres, and contains a population (1901) of 949,144. Calcutta

and Bombay have long contested the position of the premier city of India in

population and trade; but during the decade 1891-1901 the prevalence of

plague in Bombay gave a considerable advantage to Calcutta, which was

comparatively free from that disease. Calcutta lies only some 20 ft. above

sea-level, and extends about 6 m. along the Hugli, and is bounded elsewhere

by the Circular Canal and the Salt Lakes, and by suburbs which form

separate municipalities. Fort William stands in its centre.

_Public Buildings._--Though Calcutta was called by Macaulay "the city of

palaces," its modern public buildings cannot compare with those of Bombay.

Its chief glory is the Maidan or park, which is large enough to embrace the

area of Fort William and a racecourse. Many monuments find a place on the

Maidan, among them being modern equestrian statues of Lord Roberts and Lord

Lansdowne, which face one another on each side of the Red Road, where the

rank and [v.04 p.0982] fashion of Calcutta take their evening drive. In the

north-eastern corner of the Maidan the Indian memorial to Queen Victoria,

consisting of a marble hall, with a statue and historical relics, was

opened by the prince of Wales in January 1906. The government acquired

Metcalfe Hall, in order to convert it into a public library and

reading-room worthy of the capital of India; and also the country-house of

Warren Hastings at Alipur, for the entertainment of Indian princes. Lord

Curzon restored, at his own cost, the monument which formerly commemorated

the massacre of the Black Hole, and a tablet let into the wall of the

general post office indicates the position of the Black Hole in the

north-east bastion of Fort William, now occupied by the roadway. Government

House, which is situated near the Maidan and Eden Gardens, is the residence

of the viceroy; it was built by Lord Wellesley in 1799, and is a fine pile

situated in grounds covering six acres, and modelled upon Kedleston Hall in

Derbyshire, one of the Adam buildings. Belvedere House, the official

residence of the lieutenant-governor of Bengal, is situated close to the

botanical gardens in Alipur, the southern suburb of Calcutta. Facing the

Maidan for a couple of miles is the Chowringhee, one of the famous streets

of the world, once a row of palatial residences, but now given up almost

entirely to hotels, clubs and shops.

_Commerce._--Calcutta owes its commercial prosperity to the fact that it is

situated near the mouth of the two great river systems of the Ganges and

Brahmaputra. It thus receives the produce of these fertile river valleys,

while the rivers afford a cheaper mode of conveyance than any railway. In

addition Calcutta is situated midway between Europe and the Far East and

thus forms a meeting-place for the commerce and peoples of the Eastern and

Western worlds. The port of Calcutta is one of the busiest in the world,

and the banks of the Hugli rival the port of London in their show of

shipping. The total number of arrivals and departures during 1904-1905 was

3027 vessels with an average tonnage of 3734. But though the city is such a

busy commercial centre, most of its industries are carried on outside

municipal limits. Howrah, on the opposite side of the Hugli, is the

terminus of three great railway systems, and also the headquarters of the

jute industry and other large factories. It is connected with Calcutta by

an immense floating bridge, 1530 ft. in length, which was constructed in

1874. Other railways have their terminus at Sealdah, an eastern suburb. The

docks lie outside Calcutta, at Kidderpur, on the south; and at Alipur are

the zoological gardens, the residence of the lieutenant-governor of Bengal,

cantonments for a native infantry regiment, the central gaol and a

government reformatory. The port of Calcutta stretches about 10 m. along

the river. It is under the control of a port trust, whose jurisdiction

extends to the mouth of the Hugli and also over the floating bridge. New

docks were opened in 1892, which cost upwards of two millions sterling. The

figures for the sea-borne trade of Calcutta are included in those of

Bengal. Its inland trade is carried on by country boat, inland steamer,

rail and road, and amounted in 1904-1905 to about four and three quarter

millions sterling. More than half the total is carried by the East Indian

railway, which serves the United Provinces. Country boats hold their own

against inland steamers, especially in imports.

_Municipality._--The municipal government of Calcutta was reconstituted by

an act of the Bengal legislature, passed in 1899. Previously, the governing

body consisted of seventy-five commissioners, of whom fifty were elected.

Under the new system modelled upon that of the Bombay municipality, this

body, styled the corporation, remains comparatively unaltered; but a large

portion of their powers is transferred to a general committee, composed of

twelve members, of whom one-third are elected by the corporation, one-third

by certain public bodies and one-third are nominated by the government. At

the same time, the authority of the chairman, as supreme executive officer,

is considerably strengthened. The two most important works undertaken by

the old municipality were the provision of a supply of filtered water and

the construction of a main drainage system. The water-supply is derived

from the river Hugli, about 16 m. above Calcutta, where there are large

pumping-stations and settling-tanks. The drainage-system consists of

underground sewers, which are discharged by a pumping-station into a

natural depression to the eastward, called the Salt Lake. Refuse is also

removed to the Salt Lake by means of a municipal railway.

_Education._--The Calcutta University was constituted in 1857, as an

examining body, on the model of the university of London. The chief

educational institutions are the Government Presidency College; three aided

missionary colleges, and four unaided native colleges; the Sanskrit College

and the Mahommedan Madrasah; the government medical college, the government

engineering college at Sibpur, on the opposite bank of the Hugli, the

government school of art, high schools for boys, the Bethune College and

high schools for girls.

_Population._--The population of Calcutta in 1710 was estimated at 12,000,

from which figure it rose to about 117,000 in 1752. In the census of 1831

it was 187,000, in 1839 it had become 229,000 and in 1901, 949,144. Thus in

the century between 1801 and 1901 it increased sixfold, while during the

same period London only increased fivefold. Out of the total population of

town and suburbs in 1901, 615,000 were Hindus, 286,000 Mahommedans and

38,000 Christians.

_Climate and Health._--The climate of the city was originally very

unhealthy, but it has improved greatly of recent years with modern

sanitation and drainage. The climate is hot and damp, but has a pleasant

cold season from November to March. April, May and June are hot; and the

monsoon months from June to October are distinguished by damp heat and

malaria. The mean annual temperature is 79° F., with a range from 85° in

the hot season and 83° in the rains to 72° in the cool season, a mean

maximum of 102° in May and a mean minimum of 48° in January. Calcutta has

been comparatively fortunate in escaping the plague. The disease manifested

itself in a sporadic form in April 1898, but disappeared by September of

that year. Many of the Marwari traders fled the city, and some trouble was

experienced in shortage of labour in the factories and at the docks. The

plague returned in 1899 and caused a heavy mortality during the early

months of the following year; but the population was not demoralized, nor

was trade interfered with. A yet more serious outbreak occurred in the

early months of 1901, the number of deaths being 7884. For three following

years the totals were (1902-1903) 7284; (1903-1904) 8223; and (1904-1905)

4689; but these numbers compared very favourably with the condition of

Bombay at the same time.

_History._--The history of Calcutta practically dates from the 24th of

August 1690, when it was founded by Job Charnock (_q.v._) of the English

East India Company. In 1596 it had obtained a brief entry as a rent-paying

village in the survey of Bengal executed by command of the emperor Akbar.

But it was not till ninety years later that it emerged into history. In

1686 the English merchants at Hugli under Charnock's leadership, finding

themselves compelled to quit their factory in consequence of a rupture with

the Mogul authorities, retreated about 26 m. down the river to Sutanati, a

village on the banks of the Hugli, now within the boundaries of Calcutta.

They occupied Sutanati temporarily in December 1686, again in November 1687

and permanently on the 24th of August 1690. It was thus only at the third

attempt that Charnock was able to obtain the future capital of India for

his centre and the subsequent prosperity of Calcutta is due entirely to his

tenacity of purpose. The new settlement soon extended itself along the

river bank to the then village of Kalikata, and by degrees the cluster of

neighbouring hamlets grew into the present town. In 1696 the English built

the original Fort William by permission of the nawab, and in 1698 they

formally purchased the three villages of Sutanati, Kalikata and Govindpur

from Prince Azim, son of the emperor Aurangzeb.

The site thus chosen had an excellent anchorage and was defended by the

river from the Mahrattas, who harried the districts on the other side. The

fort, subsequently rebuilt on the Vauban principle, and a moat, designed to

form a semicircle [v.04 p.0983] round the town, and to be connected at both

ends with the river, but never completed, combined with the natural

position of Calcutta to render it one of the safest places for trade in

India during the expiring struggles of the Mogul empire. It grew up without

any fixed plan, and with little regard to the sanitary arrangements

required for a town. Some parts of it lay below high-water mark on the

Hugli, and its low level throughout rendered its drainage a most difficult

problem. Until far on in the 18th century the malarial jungle and paddy

fields closely hemmed in the European mansions; the vast plain (_maidán_),

now covered with gardens and promenades, was then a swamp during three

months of each year; the spacious quadrangle known as Wellington Square was

built upon a filthy creek. A legend relates how one-fourth of the European

inhabitants perished in twelve months, and during seventy years the

mortality was so great that the name of Calcutta, derived from the village

of Kalikata, was identified by mariners with Golgotha, the place of a

skull.

The chief event in the history of Calcutta is the sack of the town, and the

capture of Fort William in 1756, by Suraj-ud-Dowlah, the nawab of Bengal.

The majority of the English officials took ship and fled to the mouth of

the Hugli river. The Europeans, under John Zephaniah Holwell, who remained

were compelled, after a short resistance, to surrender themselves to the

mercies of the young prince. The prisoners, numbering 146 persons, were

forced into the guard-room, a chamber measuring only 18 ft. by 14 ft. 10

in., with but two small windows, where they were left for the night. It was

the 20th of June; the heat was intense; and next morning only 23 were taken

out alive, among them Holwell, who left an account of the awful sufferings

endured in the "Black Hole." The site of the Black Hole is now covered with

a black marble slab, and the incident is commemorated by a monument erected

by Lord Curzon in 1902. The Mahommedans retained possession of Calcutta for

about seven months, and during this brief period the name of the town was

changed in official documents to Alinagar. In January 1757 the expedition

despatched from Madras, under the command of Admiral Watson and Colonel

Clive, regained possession of the city. They found many of the houses of

the English residents demolished and others damaged by fire. The old church

of St John lay in ruins. The native portion of the town had also suffered

much. Everything of value had been swept away, except the merchandise of

the Company within the fort, which had been reserved for the nawab. The

battle of Plassey was fought on the 23rd of June 1757, exactly twelve

months after the capture of Calcutta. Mir Jafar, the nominee of the

English, was created nawab of Bengal, and by the treaty which raised him to

this position he agreed to make restitution to the Calcutta merchants for

their losses. The English received £500,000, the Hindus and Mahommedans

£200,000, and the Armenians £70,000. By another clause in this treaty the

Company was permitted to establish a mint, the visible sign in India of

territorial sovereignty, and the first coin, still bearing the name of the

Delhi emperor, was issued on the 19th of August 1757. The restitution money

was divided among the sufferers by a committee of the most respectable

inhabitants. Commerce rapidly revived and the ruined city was rebuilt.

Modern Calcutta dates from 1757. The old fort was abandoned, and its site

devoted to the custom-house and other government offices. A new fort, the

present Fort William, was begun by Clive a short distance lower down the

river, and is thus the second of that name. It was not finished till 1773,

and is said to have cost two millions sterling. At this time also the

_maidán_, the park of Calcutta, was formed; and the healthiness of its

position induced the European inhabitants gradually to shift their

dwellings eastward, and to occupy what is now the Chowringhee quarter.

Up to 1707, when Calcutta was first declared a presidency, it had been

dependent upon the older English settlement at Madras. From 1707 to 1773

the presidencies were maintained on a footing of equality; but in the

latter year the act of parliament was passed, which provided that the

presidency of Bengal should exercise a control over the other possessions

of the Company; that the chief of that presidency should be styled

governor-general; and that a supreme court of judicature should be

established at Calcutta. In the previous year, 1772, Warren Hastings had

taken under the immediate management of the Company's servants the general

administration of Bengal, which had hitherto been left in the hands of the

old Mahommedan officials, and had removed the treasury from Murshidabad to

Calcutta. The latter town thus became the capital of Bengal and the seat of

the supreme government in India. In 1834 the governor-general of Bengal was

created governor-general of India, and was permitted to appoint a

deputy-governor to manage the affairs of Lower Bengal during his occasional

absence. It was not until 1854 that a separate head was appointed for

Bengal, who, under the style of lieutenant-governor, exercises the same

powers in civil matters as those vested in the governors in council of

Madras or Bombay, although subject to closer supervision by the supreme

government. Calcutta is thus at present the seat both of the supreme and

the local government, each with an independent set of offices. (See

BENGAL.)

See A.K. Ray, _A Short History of Calcutta_ (Indian Census, 1901); H.B.

Hyde, _Parochial Annals of Bengal_ (1901); K. Blechynden, _Calcutta, Past

and Present_ (1905); H.E. Busteed, _Echoes from Old Calcutta_ (1897); G.W.

Forrest, _Cities of India_ (1903); C.R. Wilson, _Early Annals of the

English in Bengal_ (1895); and _Old Fort William in Bengal_ (1906);

_Imperial Gazetteer of India_ (Oxford, 1908), _s.v._ "Calcutta."

CALDANI, LEOPOLDO MARCO ANTONIO (1725-1813), Italian anatomist and

physician, was born at Bologna in 1725. After studying under G.B. Morgagni

at Padua, he began to teach practical medicine at Bologna, but in

consequence of the intrigues of which he was the object he returned to

Padua, where in 1771 he succeeded Morgagni in the chair of anatomy. He

continued to lecture until 1805 and died at Padua in 1813. His works

include _Institutiones pathologicae_ (1772), _Institutiones physiologicae_

(1773) and _Icones anatomicae_ (1801-1813).

His brother, PETRONIO MARIA CALDANI (1735-1808), was professor of

mathematics at Bologna, and was described by J. le R. D'Alembert as the

"first geometer and algebraist of Italy."

CALDECOTT, RANDOLPH (1846-1886), English artist and illustrator, was born

at Chester on the 22nd of March 1846. From 1861 to 1872 he was a bank

clerk, first at Whitchurch in Shropshire, afterwards at Manchester; but

devoted all his spare time to the cultivation of a remarkable artistic

faculty. In 1872 he migrated to London, became a student at the Slade

School and finally adopted the artist's profession. He gained immediately a

wide reputation as a prolific and original illustrator, gifted with a

genial, humorous faculty, and he succeeded also, though in less degree, as

a painter and sculptor. His health gave way in 1876, and after prolonged

suffering he died in Florida on the 12th of February 1886. His chief book

illustrations are as follows:--_Old Christmas_ (1876) and _Bracebridge

Hall_ (1877), both by Washington Irving; _North Italian Folk_ (1877), by

Mrs Comyns Carr; _The Harz Mountains_ (1883); _Breton Folk_ (1879), by

Henry Blackburn; picture-books (_John Gilpin, The House that Jack Built_,

and other children's favourites) from 1878 onwards; _Some Aesop's Fables

with Modern Instances, &c._ (1883). He held a roving commission for the

_Graphic_, and was an occasional contributor to _Punch_. He was a member of

the Royal Institute of Painters in Water-colours.

See Henry Blackburn, _Randolph Caldecott, Personal Memoir of his Early

Life_ (London, 1886).

CALDER, SIR ROBERT, Bart. (1745-1818), British admiral, was born at Elgin,

in Scotland, on the 2nd of July 1745 (o.s.). He belonged to a very ancient

family of Morayshire, and was the second son of Sir Thomas Calder of

Muirton. He was educated at the grammar school of Elgin, and at the age of

fourteen entered the British navy as midshipman. In 1766 he was serving as

lieutenant of the "Essex," under Captain the Hon. George Faulkner, in the

West Indies. Promotion came slowly, and it was not till 1782 that he

attained the rank of post-captain. He acquitted himself honourably in the

various services to which he was called, but for a long time had no

opportunity [v.04 p.0984] of distinguishing himself. In 1796 he was named

captain of the fleet by Sir John Jervis, and took part in the great battle

off Cape St Vincent (February 14, 1797). He was selected as bearer of the

despatches announcing the victory, and on that occasion was knighted by

George III. He also received the thanks of parliament, and in the following

year was created a baronet. In 1799 he became rear-admiral; and in 1801 he

was despatched with a small squadron in pursuit of a French force, under

Admiral Gantheaume, conveying supplies to the French in Egypt. In this

pursuit he was not successful, and returning home at the peace he struck

his flag. When the war again broke out he was recalled to service, was

promoted vice-admiral in 1804, and was employed in the following year in

the blockade of the ports of Ferrol and Corunna, in which (amongst other

ports) ships were preparing for the invasion of England by Napoleon I. He

held his position with a force greatly inferior to that of the enemy, and

refused to be enticed out to sea. On its becoming known that the first

movement directed by Napoleon was the raising of the blockade of Ferrol,

Rear-Admiral Stirling was ordered to join Sir R. Calder and cruise with him

to intercept the fleets of France and Spain on their passage to Brest. The

approach of the enemy was concealed by a fog; but on the 22nd of July 1805

their fleet came in sight. It still outnumbered the British force; but Sir

Robert entered into action. After a combat of four hours, during which he

captured two Spanish ships, he gave orders to discontinue the action. He

offered battle again on the two following days, but the challenge was not

accepted. The French admiral Villeneuve, however, did not pursue his

voyage, but took refuge in Ferrol. In the judgment of Napoleon, his scheme

of invasion was baffled by this day's action; but much indignation was felt

in England at the failure of Calder to win a complete victory. In

consequence of the strong feeling against him at home he demanded a

court-martial. This was held on the 23rd of December, and resulted in a

severe reprimand of the vice-admiral for not having done his utmost to

renew the engagement, at the same time acquitting him of both cowardice and

disaffection. False expectations had been raised in England by the

mutilation of his despatches, and of this he indignantly complained in his

defence. The tide of feeling, however, turned again; and in 1815, by way of

public testimony to his services, and of acquittal of the charge made

against him, he was appointed commander of Portsmouth. He died at Holt,

near Bishop's Waltham, in Hampshire, on the 31st of August 1818.

See _Naval Chronicle_, xvii.; James, _Naval History_, iii. 356-379 (1860).

CALDER, an ancient district of Midlothian, Scotland. It has been divided

into the parishes of Mid-Calder (pop. in 1901 3132) and West-Calder (pop.

8092), East-Calder belonging to the parish of Kirknewton (pop. 3221). The

whole locality owes much of its commercial importance and prosperity to the

enormous development of the mineral oil industry. Coal-mining is also

extensively pursued, sandstone and limestone are worked, and paper-mills

flourish. Mid-Calder, a town on the Almond (pop. 703), has an ancient

church, and John Spottiswood (1510-1585), the Scottish reformer, was for

many years minister. His sons--John, archbishop of St Andrews, and James

(1567-1645), bishop of Clogher--were both born at Mid-Calder. West-Calder

is situated on Breich Water, an affluent of the Almond, 15½ m. S.W. of

Edinburgh by the Caledonian railway, and is the chief centre of the

district. Pop. (1901) 2652. At Addiewell, about 1½ m. S.W., the manufacture

of ammonia, naphtha, paraffin oil and candles is carried on, the village

practically dating from 1866, and having in 1901 a population of 1591. The

Highland and Agricultural Society have an experimental farm at Pumpherston

(pop. 1462). The district contains several tumuli, old ruined castles and a

Roman camp in fair preservation.

CALDERÓN, RODRIGO (d. 1621), COUNT OF OLIVA AND MARQUES DE LAS SIETE

IGLESIAS, Spanish favourite and adventurer, was born at Antwerp. His

father, Francisco Calderón, a member of a family ennobled by Charles V.,

was a captain in the army who became afterwards _comendador mayor_ of

Aragon, presumably by the help of his son. The mother was a Fleming, said

by Calderón to have been a lady by birth and called by him Maria Sandelin.

She is said by others to have been first the mistress and then the wife of

Francisco Calderón. Rodrigo is said to have been born out of wedlock. In

1598 he entered the service of the duke of Lerma as secretary. The

accession of Philip III. in that year made Lerma, who had unbounded

influence over the king, master of Spain. Calderón, who was active and

unscrupulous, made himself the trusted agent of Lerma. In the general

scramble for wealth among the worthless intriguers who governed in the name

of Philip III., Calderón was conspicuous for greed, audacity and insolence.

He was created count of Oliva, a knight of Santiago, commendador of Ocaña

in the order, secretary to the king (_secretario de cámara_), was loaded

with plunder, and made an advantageous marriage with Ines de Vargas. As an

insolent upstart he was peculiarly odious to the enemies of Lerma. Two

religious persons, Juan de Santa Mariá, a Franciscan, and Mariana de San

José, prioress of La Encarnacion, worked on the queen Margarita, by whose

influence Calderón was removed from the secretaryship in 1611. He, however,

retained the favour of Lerma, an indolent man to whom Calderón's activity

was indispensable. In 1612 he was sent on a special mission to Flanders,

and on his return was made marques de las Siete Iglesias in 1614. When the

queen Margarita died in that year in childbirth, Calderón was accused of

having used witchcraft against her. Soon after it became generally known

that he had ordered the murder of one Francisco de Juaras. When Lerma was

driven from court in 1618 by the intrigues of his own son, the duke of

Uceda, and the king's confessor, the Dominican Aliaga, Calderón was seized

upon as an expiatory victim to satisfy public clamour. He was arrested,

despoiled, and on the 7th of January 1620 was savagely tortured to make him

confess to the several charges of murder and witchcraft brought against

him. Calderón confessed to the murder of Juaras, saying that the man was a

pander, and adding that he gave the particular reason by word of mouth

since it was more fit to be spoken than written. He steadfastly denied all

the other charges of murder and the witchcraft. Some hope of pardon seems

to have remained in his mind till he heard the bells tolling for Philip

III. in March 1621. "He is dead, and I too am dead" was his resigned

comment. One of the first measures of the new reign was to order his

execution. Calderón met his fate firmly and with a show of piety on the

21st of October 1621, and this bearing, together with his broken and

prematurely aged appearance, turned public sentiment in his favour. The

magnificent devotion of his wife helped materially to placate the hatred he

had aroused. Lord Lytton made Rodrigo Calderón the hero of his story

_Calderon the Courtier_.

See Modests de la Fuente, _Historia General España_ (Madrid, 1850-1867),

vol. xv. pp. 452 et seq.; Quevedo, _Obras_ (Madrid, 1794), vol.

x.--_Grandes Anales de Quince Dias_. A curious contemporary French pamphlet

on him, _Histoire admirable et declin pitoyable advenue en la personne

d'unfawory de la Cour d'Espagne,_ is reprinted by M.E. Fournier in

_Variétés historiques_ (Paris, 1855), vol. i.

(D. H.)

CALDERÓN DE LA BARCA, PEDRO (1600-1681), Spanish dramatist and poet, was

born at Madrid on the 17th of January 1600. His mother, who was of Flemish

descent, died in 1610; his father, who was secretary to the treasury, died

in 1615. Calderón was educated at the Jesuit College in Madrid with a view

to taking orders and accepting a family living; abandoning this project, he

studied law at Salamanca, and competed with success at the literary fêtes

held in honour of St Isaidore at Madrid (1620-1632). According to his

biographer, Vera Tassis, Calderón served with the Spanish army in Italy and

Flanders between 1625 and 1635; but this statement is contradicted by

numerous legal documents which prove that Calderón resided at Madrid during

these years. Early in 1629 his brother Diego was stabbed by an actor who

took sanctuary in the convent of the Trinitarian nuns; Calderón and his

friends broke into the cloister and attempted to seize the offender. This

violation was denounced by the fashionable preacher, Hortensio Félix

Paravicino (_q.v._), in a sermon preached before Philip IV.; [v.04 p.0985]

Calderón retorted by introducing into _El Príncipe constante_ a mocking

reference (afterwards cancelled) to Paravicino's gongoristic verbiage, and

was committed to prison. He was soon released, grew rapidly in reputation

as a playwright, and, on the death of Lope de Vega in 1635, was recognized

as the foremost Spanish dramatist of the age. A volume of his plays, edited

by his brother José in 1636, contains such celebrated and diverse

productions as _La Vida es sueño, El Purgatorío de San Patricia, La

Devoción de la cruz, La Dama duende_ and _Peor está que estaba_. In

1636-1637 he was made a knight of the order of Santiago by Philip IV., who

had already commissioned from him a series of spectacular plays for the

royal theatre in the Buen Retiro. Calderón was almost as popular with the

general public as Lope de Vega had been in his zenith; he was, moreover, in

high favour at court, but this royal patronage did not help to develop the

finer elements of his genius. On the 28th of May 1640 he joined a company

of mounted cuirassiers recently raised by Olivares, took part in the

Catalonian campaign, and distinguished himself by his gallantry at

Tarragona; his health failing, he retired from the army in November 1642,

and three years later was awarded a special military pension in recognition

of his services in the field. The history of his life during the next few

years is obscure. He appears to have been profoundly affected by the death

of his mistress--the mother of his son Pedro José--about the year

1648-1649; his long connexion with the theatre had led him into

temptations, but it had not diminished his instinctive spirit of devotion,

and he now sought consolation in religion. He became a tertiary of the

order of St Francis in 1650, and finally reverted to his original intention

of joining the priesthood. He was ordained in 1651, was presented to a

living in the parish of San Salvador at Madrid, and, according to his

statement made a year or two later, determined to give up writing for the

stage. He did not adhere to this resolution after his preferment to a

prebend at Toledo in 1653, though he confined himself as much as possible

to the composition of _autos sacramentales_--allegorical pieces in which

the mystery of the Eucharist was illustrated dramatically, and which were

performed with great pomp on the feast of Corpus Christi and during the

weeks immediately ensuing. In 1662 two of Calderón's _autos_--_Las órdenes

militares_ and _Místicay real Babilonia_--were the subjects of an inquiry

by the Inquisition; the former was censured, the manuscript copies were

confiscated, and the condemnation was not rescinded till 1671. Calderón was

appointed honorary chaplain to Philip IV, in 1663, and the royal favour was

continued to him in the next reign. In his eighty-first year he wrote his

last secular play, _Hado y Divisa de Leonido y Marfisa_, in honour of

Charles II.'s marriage to Marie-Louise de Bourbon. Notwithstanding his

position at court and his universal popularity throughout Spain, his

closing years seem to have been passed in poverty. He died on the 25th of

May 1681.

Like most Spanish dramatists, Calderón wrote too much and too speedily, and

he was too often content to recast the productions of his predecessors. His

_Saber del mal y del bien_ is an adaptation of Lope de Vega's play, _Las

Mudanzas de la fortuna y sucesos de Don Beltran de Aragón_; his _Selva

confusa_ is also adapted from a play of Lope's which bears the same title;

his _Encanto sin encanto_ derives from Tirso de Molina's _Amar par señas_,

and, to take an extreme instance, the second act of his _Cabellos de

Absalón _is transferred almost bodily from the third act of Tirso's

_Venganza de Tamar_. It would be easy to add other examples of Calderón's

lax methods, but it is simple justice to point out that he committed no

offence against the prevailing code of literary morality. Many of his

contemporaries plagiarized with equal audacity, but with far less success.

Sometimes, as in _El Alcalde de Zalamea_, the bold procedure is completely

justified by the result; in this case by his individual treatment he

transforms one of Lope de Vega's rapid improvisations into a finished

masterpiece. It was not given to him to initiate a great dramatic movement;

he came at the end of a literary revolution, was compelled to accept the

conventions which Lope de Vega had imposed on the Spanish stage, and he

accepted them all the more readily since they were peculiarly suitable to

the display of his splendid and varied gifts. Not a master of observation

nor an expert in invention, he showed an unexampled skill in contriving

ingenious variants on existing themes; he had a keen dramatic sense, an

unrivalled dexterity in manipulating the mechanical resources of the stage,

and in addition to these minor indispensable talents he was endowed with a

lofty philosophic imagination and a wealth of poetic diction. Naturally, he

had the defects of his great qualities; his ingenuity is apt to degenerate

into futile embellishment; his employment of theatrical devices is the

subject of his own good-humoured satire in _No hay burlas con el amor_; his

philosophic intellect is more interested in theological mysteries than in

human passions; and the delicate beauty of his style is tinged with a

wilful preciosity. Excelling Lope de Vega at many points, Calderón falls

below his great predecessor in the delineation of character. Yet in almost

every department of dramatic art Calderón has obtained a series of

triumphs. In the symbolic drama he is best represented by _El Principe

constante_, by _El Mágico prodigioso_ (familiar to English readers in

Shelley's free translation), and by _La Vida es sueño_, perhaps the most

profound and original of his works. His tragedies are more remarkable for

their acting qualities than for their convincing truth, and the fact that

in _La Niña de Gomez Arias_ he interpolates an entire act borrowed from

Velez de Guevara's play of the same title seems to indicate that this kind

of composition awakened no great interest in him; but in _El Médico de sa

honra_ and _El Mayor monstruo los celos_ the theme of jealousy is handled

with sombre power, while _El Alcalde de Zalamea_ is one of the greatest

tragedies in Spanish literature. Calderón is seen to much less advantage in

the spectacular plays--_dramas de tramoya_--which he wrote at the command

of Philip IV.; the dramatist is subordinated to the stage-carpenter, but

the graceful fancy of the poet preserves even such a mediocre piece as _Los

Tres Mayores prodigies_ (which won him his knighthood) from complete

oblivion. A greater opportunity is afforded in the more animated _comedias

palaciegas_, or melodramatic pieces destined to be played before courtly

audiences in the royal palace: _La Banda y la flor_ and _El Galán fantasma_

are charming illustrations of Calderón's genial conception and refined

artistry. His historical plays (_La Gran Cenobia, Las armas de la

hermosura_, &c.) are the weakest of all his formal dramatic productions;

_El Golfo de la sirenas_ and _La Púrpura de la rosa_ are typical

_zarzuelas_, to be judged by the standard of operatic libretti, and the

_entremeses_ are lacking in the lively humour which should characterize

these dramatic interludes. On the other hand, Calderón's faculty of

ingenious stagecraft is seen at its best in his "cloak-and-sword" plays

(_comedias de capa y espada_) which are invaluable pictures of contemporary

society. They are conventional, no doubt, in the sense that all

representations of a specially artificial society must be conventional; but

they are true to life, and are still as interesting as when they first

appeared. In this kind _No siempre lo peor es cierto, La Dama duende, Una

casa con dos puertas mala es de guardar_ and _Guárdate del agua mansa_ are

almost unsurpassed. But it is as a writer of _autos sacramentales_ that

Calderón defies rivalry: his intense devotion, his subtle intelligence, his

sublime lyrism all combine to produce such marvels of allegorical poetry as

_La Cena del rey Baltasar, La Viña del Senor_ and _La Serpiente de metal_.

The _autos_ lingered on in Spain till 1765, but they may be said to have

died with Calderón, for his successors merely imitated him with a tedious

fidelity. Almost alone among Spanish poets, Calderón had the good fortune

to be printed in a fairly correct and readable edition (1682-1691), thanks

to the enlightened zeal of his admirer, Juan de Vera Tassis y Villaroel,

and owing to this happy accident he came to be regarded generally as the

first of Spanish dramatists. The publication of the plays of Lope de Vega

and of Tirso de Molina has affected the critical estimate of Calderón's

work; he is seen to be inferior to Lope de Vega in creative power, and

inferior to Tirso de Molina in variety of conception. But, setting aside

the extravagances of his admirers, he is admittedly an exquisite poet, an

expert in the dramatic form, and a typical representative of the [v.04

p.0986] devout, chivalrous, patriotic and artificial society in which he

moved.

BIBLIOGRAPHY.--H. Breymann, _Calderon-Studien_ (München and Berlin, 1905),

i. Teil, contains a fairly exhaustive list of editions, translations and

arrangements; _Autos sacramentales_ (Madrid, 1759-1760, 6 vols.), edited by

Juan Fernandez de Apontes; _Comedias_ (Madrid, 1848-1850, 4 vols.), edited

by Juan Eugenio Hartzenbuch; Max Krenkel, _Klassische Buhnendichtungen der

Spanier_, containing _La Vida es sueño, El mágico prodigioso_ and _El

Alcalde de Zalamca_ (Leipzig, 1881-1887, 3 vols.); _Teatro selecto_

(Madrid, 1884, 4 vols.), edited by M. Menéndez y Pelayo; _El Mágico

prodigioso_ (Heilbronn, 1877), edited by Alfred Morel-Fatio; _Select Plays

of Calderón_ (London, 1888), edited by Norman MacColl; F.W.V. Schmidt, _Die

Schauspiele Calderon's_ (Elberfeld, 1857); E. Günthner, _Calderon und seine

Werke_ (Freiburg i. B., 1888, 2 vols.); Felipe Picatoste y Rodriguez,

_Biografia de Don Pedro Calderón de la Barca_ in _Homenage á Calderón_

(Madrid, 1881); Antonio Sánchez Moguel, _Memoria acerca de "El Mágico

prodigioso"_ (Madrid, 1881); M. Menéndez y Pelayo, _Calderón y su teatro_

(Madrid, 1881); Ernest Martinenche, _La Comedia espagnole en France de

Hardy á Racine_ (Paris, 1900).

(J. F.-K.)

CALDERWOOD, DAVID (1575-1650), Scottish divine and historian, was born in

1575. He was educated at Edinburgh, where he took the degree of M.A. in

1593. About 1604 he became minister of Crailing, near Jedburgh, where he

became conspicuous for his resolute opposition to the introduction of

Episcopacy. In 1617, while James was in Scotland, a Remonstrance, which had

been drawn up by the Presbyterian clergy, was placed in Calderwood's hands.

He was summoned to St Andrews and examined before the king, but neither

threats nor promises could make him deliver up the roll of signatures to

the Remonstrance. He was deprived of his charge, committed to prison at St

Andrews and afterwards removed to Edinburgh. The privy council ordered him

to be banished from the kingdom for refusing to acknowledge the sentence of

the High Commission. He lingered in Scotland, publishing a few tracts, till

the 27th of August 1619, when he sailed for Holland. During his residence

in Holland he published his _Altare Damascenum_. Calderwood appears to have

returned to Scotland in 1624, and he was soon afterwards appointed minister

of Pencaitland, in the county of Haddington. He continued to take an active

part in the affairs of the church, and introduced in 1649 the practice, now

confirmed by long usage, of dissenting from the decision of the Assembly,

and requiring the protest to be entered in the record. His last years were

devoted to the preparation of a _History of the Church of Scotland_. In

1648 the General Assembly urged him to complete the work he had designed,

and voted him a yearly pension of £800. He left behind him a historical

work of great extent and of great value as a storehouse of authentic

materials for history. An abridgment, which appears to have been prepared

by himself, was published after his death. An excellent edition of the

complete work was published by the Wodrow Society, 8 vols., 1842-1849. The

manuscript, which belonged to General Calderwood Durham, was presented to

the British Museum. Calderwood died at Jedburgh on the 29th of October

1650.

CALDERWOOD, HENRY (1830-1897), Scottish philosopher and divine, was born at

Peebles on the 10th of May 1830. He was educated at the Royal High school,

and later at the university of Edinburgh. He studied for the ministry of

the United Presbyterian Church, and in 1856 was ordained pastor of the

Greyfriars church, Glasgow. He also examined in mental philosophy for the

university of Glasgow from 1861 to 1864, and from 1866 conducted the moral

philosophy classes at that university, until in 1868 he became professor of

moral philosophy at Edinburgh. He was made LL.D. of Glasgow in 1865. He

died on the 19th of November 1897. His first and most famous work was _The

Philosophy of the Infinite_ (1854), in which he attacked the statement of

Sir William Hamilton that we can have no knowledge of the Infinite.

Calderwood maintained that such knowledge, though imperfect, is real and

ever-increasing; that Faith implies Knowledge. His moral philosophy is in

direct antagonism to Hegelian doctrine, and endeavours to substantiate the

doctrine of divine sanction. Beside the data of experience, the mind has

pure activity of its own whereby it apprehends the fundamental realities of

life and combat. He wrote in addition _A Handbook of Moral Philosophy, On

the Relations of Mind and Brain, Science and Religion, The Evolution of

Man's Place in Nature_. Among his religious works the best-known is his

_Parables of Our Lord_, and just before his death he finished a _Life of

David Hume_ in the "Famous Scots" series. His interests were not confined

to religious and intellectual matters; as the first chairman of the

Edinburgh school board, he worked hard to bring the Education Act into

working order. He published a well-known treatise on education. In the

cause of philanthropy and temperance he was indefatigable. In politics he

was at first a Liberal, but became a Liberal Unionist at the time of the

Home Rule Bill.

A biography of Calderwood was published in 1900 by his son W.C. Calderwood

and the Rev. David Woodside, with a special chapter on his philosophy by

Professor A.S. Pringle-Pattison.

CALEB (Heb. _k[=e]leb_, "dog"), in the Bible, one of the spies sent by

Moses from Kadesh in South Palestine to spy out the land of Canaan. For his

courage and confidence he alone was rewarded by the promise that he and his

seed should obtain a possession in it (Num. xiii. seq.). The later

tradition includes Joshua, the hero of the conquest of the land.

Subsequently Caleb settled in Kirjath-Arba (Hebron), but the account of the

occupation is variously recorded. Thus (_a_) Caleb by himself drove out the

Anakites, giants of Hebron, and promised to give his daughter Achsah to the

hero who could take Kirjath-Sepher (Debir). This was accomplished by

Othniel, the brother of Caleb (Josh. xv. 14-19). Both are "sons" of Kenaz,

and Kenaz is an Edomite clan (Gen. xxxvi. 11, 15, 42). Elsewhere (_b_)

Caleb the Kenizzite reminds Joshua of the promise at Kadesh; he asks that

he may have the "mountain whereof Yahweh spake," and hopes to drive out the

giants from its midst. Joshua blesses him and thus Hebron becomes the

inheritance of Caleb (Josh. xiv. 6-15). Further (_c_) the capture of Hebron

and Debir is ascribed to Judah who gives them to Caleb (Judg. i. 10 seq.

20); and finally (_d_) these cities are taken by Joshua himself in the

course of a great and successful campaign against South Canaan (Josh. x.

36-39). Primarily the clan Caleb was settled in the south of Judah but

formed an independent unit (i Sam. xxv., xxx. 14). Its seat was at Carmel,

and Abigail, the wife of the Calebite Nabal, was taken by David after her

husband's death. Not until later are the small divisions of the south

united under the name Judah, and this result is reflected in the

genealogies where the brothers Caleb and Jerahmeel are called "sons of

Hezron" (the name typifies nomadic life) and become descendants of JUDAH.

Similarly in Num. xiii. 6, xxxiv. 19 (post-exilic), Caleb becomes the

representative of the tribe of Judah, and also in _c_ (above) Caleb's

enterprise was later regarded as the work of the tribe with which it became

incorporated, _b_ and _d_ are explained in accordance with the aim of the

book to ascribe to the initiation or the achievements of one man the

conquest of the whole of Canaan (see JOSHUA). The mount or hill-country in

_b_ appears to be that which the Israelites unsuccessfully attempted to

take (Num. xiv. 41-45), but according to another old fragment Hormah was

the scene of a victory (Num. xxi. 1-3), and it seems probable that Caleb,

at least, was supposed to have pushed his way northward to Hebron. (See

JERAHMEEL, KENITES, SIMEON.)

The genealogical lists place the earliest seats of Caleb in the south of

Judah (1 Chron. ii. 42 sqq.; Hebron, Maon, &c.). Another list numbers the

more northerly towns of Kirjath-jearim, Bethlehem, &c., and adds the

"families of the scribes," and the Kenites (ii. 50 seq.). This second move

is characteristically expressed by the statements that Caleb's first wife

was Az[=u]bah ("abandoned," desert region)--Jer[=i][=o]th ("tent curtains")

appears to have been another--and that after the death of Hezron he united

with Ephrath (p. 24 Bethlehem). On the details in 1 Chron. ii., iv., see

further, J. Wellhausen, _De Gent. et Famil. Judaeorum_ (1869); S. Cook,

_Critical Notes on O.T. History, Index_, s.v.; E. Meyer, _Israeliten_, pp.

400 sqq.; and the commentaries on Chronicles (_q.v._).

(S. A. C.)

CALEDON (1) a town of the Cape Province, 81 m. by rail E.S.E. of Cape Town.

Pop. (1904) 3508. The town is 15 m. N. of the sea at Walker Bay and is

built on a spur of the Zwartberg, 800 ft. high. The streets are lined with

blue gums and oaks. From the early day of Dutch settlement at the Cape

Caledon has been noted for the curative value of its mineral springs, which

yield 150,000 gallons daily. There are seven springs, six with a natural

temperature of 120° F., the seventh [v.04 p.0987] being cold. The district

is rich in flowering heaths and everlasting flowers. The name Caledon was

given to the town and district in honour of the 2nd earl of Caledon,

governor of the Cape 1807-1811. (2) A river of South Africa, tributary to

the Orange (_q.v._), also named after Lord Caledon.

CALEDONIA, the Roman name of North Britain, still used especially in poetry

for Scotland. It occurs first in the poet Lucan (A.D. 64), and then often

in Roman literature. There were (1) a district Caledonia, of which the

southern border must have been on or near the isthmus between the Clyde and

the Forth, (2) a Caledonian Forest (possibly in Perthshire), and (3) a

tribe of Caledones or Calidones, named by the geographer Ptolemy as living

within boundaries which are now unascertainable. The Romans first invaded

Caledonia under Agricola (about A.D. 83). They then fortified the Forth and

Clyde Isthmus with a line of forts, two of which, those at Camelon and

Barhill, have been identified and excavated, penetrated into Perthshire,

and fought the decisive battle of the war (according to Tacitus) on the

slopes of Mons Graupius.[1] The site--quite as hotly contested among

antiquaries as between Roman and Caledonian--may have been near the Roman

encampment of Inchtuthill (in the policies of Delvine, 10 m. N. of Perth

near the union of Tay and Isla), which is the most northerly of the

ascertained Roman encampments in Scotland and seems to belong to the age of

Agricola. Tacitus represents the result as a victory. The home government,

whether averse to expensive conquests of barren hills, or afraid of a

victorious general, abruptly recalled Agricola, and his northern

conquests--all beyond the Tweed, if not all beyond Cheviot--were abandoned.

The next advance followed more than fifty years later. About A.D. 140 the

district up to the Firth of Forth was definitely annexed, and a rampart

with forts along it, the Wall of Antoninus Pius, was drawn from sea to sea

(see BRITAIN: _Roman_; and GRAHAM'S DYKE). At the same time the Roman forts

at Ardoch, north of Dunblane, Carpow near Abernethy, and perhaps one or two

more, were occupied. But the conquest was stubbornly disputed, and after

several risings, the land north of Cheviot seems to have been lost about

A.D. 180-185. About A.D. 208 the emperor Septimius Severus carried out an

extensive punitive expedition against the northern tribes, but while it is

doubtful how far he penetrated, it is certain that after his death the

Roman writ never again ran north of Cheviot. Rome is said, indeed, to have

recovered the whole land up to the Wall of Pius in A.D. 368 and to have

established there a province, Valentia. A province with that name was

certainly organized somewhere. But its site and extent is quite uncertain

and its duration was exceedingly brief. Throughout, Scotland remained

substantially untouched by Roman influences, and its Celtic art, though

perhaps influenced by Irish, remained free from Mediterranean infusion.

Even in the south of Scotland, where Rome ruled for half a century (A.D.

142-180), the occupation was military and produced no civilizing effects.

Of the actual condition of the land during the period of Roman rule in

Britain, we have yet to learn the details by excavation. The curious

carvings and ramparts, at Burghead on the coast of Elgin, and the

underground stone houses locally called "wheems," in which Roman fragments

have been found, may represent the native forms of dwelling, &c., and some

of the "Late Celtic" metal-work may belong to this age. But of the

political divisions, the boundaries and capitals of the tribes, and the

like, we know nothing. Ptolemy gives a list of tribe and place-names. But

hardly one can be identified with any approach to certainty, except in the

extreme south. Nor has any certainty been reached about the ethnological

problems of the population, the Aryan or non-Aryan character of the Picts

and the like. That the Caledonians, like the later Scots, sometimes sought

their fortunes in the south, is proved by a curious tablet of about A.D.

220, found at Colchester, dedicated to an unknown equivalent of Mars,

Medocius, by one "Lossio Veda, nepos [ = kin of] Vepogeni, Caledo." The

name Caledonia is said to survive in the second syllable of Dunkeld and in

the mountain name Schiehallion (Sith-chaillinn).

AUTHORITIES.--Tacitus, _Agricola_; Hist. Augusta, _Vita Severi_; Dio

lxxvi.; F. Haverfield, _The Antonine Wall Report_ (Glasgow, 1899), pp.

154-168; J. Rhys, _Celtic Britain_ (ed. 3). On Burghead, see H.W. Young,

_Proc. of Scottish Antiq._ xxv., xxvii.; J. Macdonald, _Trans. Glasgow

Arch. Society_. The Roman remains of Scotland are described in Rob.

Stuart's _Caled. Romana_ (Edinburgh, 1852), the volumes of the Scottish

Antiq. Society, the _Corpus Inscriptionum Latinarum_, vol. vii., and

elsewhere.

(F. J. H.)

[1] This, not Grampius, is the proper spelling, though Grampius was at one

time commonly accepted and indeed gave rise to the modern name Grampian.

CALEDONIAN CANAL. The chain of fresh-water lakes--Lochs Ness, Oich and

Lochy--which stretch along the line of the Great Glen of Scotland in a S.W.

direction from Inverness early suggested the idea of connecting the east

and west coasts of Scotland by a canal which would save ships about 400 m.

of coasting voyage round the north of Great Britain through the stormy

Pentland Firth. In 1773 James Watt was employed by the government to make a

survey for such a canal, which again was the subject of an official report

by Thomas Telford in 1801. In 1803 an act of parliament was passed

authorizing the construction of the canal, which was begun forthwith under

Telford's direction, and traffic was started in 1822. From the northern

entrance on Beauly Firth to the southern, near Fort William, the total

length is about 60 m., that of the artificial portion being about 22 m. The

number of locks is 28, and their standard dimensions are:--length 160 ft,

breadth 38 ft., water-depth 15 ft. Their lift is in general about 8 ft.,

but some of them are for regulating purposes only. A flight of 8 at

Corpach, with a total lift of 64 ft., is known as "Neptune's Staircase."

The navigation is vested in and managed by the commissioners of the

Caledonian Canal, of whom the speaker of the House of Commons is _ex

officio_ chairman. Usually the income is between £7000 and £8000 annually,

and exceeds the expenditure by a few hundred pounds; but the commissioners

are not entitled to make a profit, and the credit balances, though

sometimes allowed to accumulate, must be expended on renewals and

improvements of the canal. They have not, however, always proved sufficient

for their purposes, and parliament is occasionally called upon to make

special grants. In the commissioners is also vested the Crinan Canal, which

extends from Ardrishaig on Loch Gilp to Crinan on Loch Crinan. This canal

was made by a company incorporated by act of parliament in 1793, and was

opened for traffic in 1801. At various times it received grants of public

money, and ultimately in respect of these it passed into the hands of the

government. In 1848 it was vested by parliament in the commissioners of the

Caledonian Canal (who had in fact administered it for many years

previously); the act contained a proviso that the company might take back

the undertaking on repayment of the debt within 20 years, but the power was

not exercised. The length of the canal is 9 m., and it saves vessels

sailing from the Clyde a distance of about 85 m. as compared with the

alternative route round the Mull of Kintyre. Its highest reach is 64 ft.

above sea level, and its locks, 15 in number, are 96 ft. long, by 24 ft.

wide, the depth of water being such as to admit vessels up to a draught of

9½ ft. The revenue is over £6000 a year, and there is usually a small

credit balance which, as with the Caledonian Canal, must be applied to the

purposes of the undertaking.

CALENBERG, or KALENBERG, the name of a district, including the town of

Hanover, which was formerly part of the duchy of Brunswick. It received its

name from a castle near Schulenburg, and is traversed by the rivers Weser

and Leine, its area being about 1050 sq. m. The district was given to

various cadets of the ruling house of Brunswick, one of these being Ernest

Augustus, afterwards elector of Hanover, and the ancestor of the Hanoverian

kings of Great Britain and Ireland.

CALENDAR, so called from the Roman Calends or Kalends, a method of

distributing time into certain periods adapted to the purposes of civil

life, as hours, days, weeks, months, years, &c.

Of all the periods marked out by the motions of the celestial bodies, the

most conspicuous, and the most intimately connected with the affairs of

mankind, are the _solar day_, which is [v.04 p.0988] distinguished by the

diurnal revolution of the earth and the alternation of light and darkness,

and the _solar year_, which completes the circle of the seasons. But in the

early ages of the world, when mankind were chiefly engaged in rural

occupations, the phases of the moon must have been objects of great

attention and interest,--hence the _month_, and the practice adopted by

many nations of reckoning time by the motions of the moon, as well as the

still more general practice of combining lunar with solar periods. The

solar day, the solar year, and the lunar month, or lunation, may therefore

be called the _natural_ divisions of time. All others, as the hour, the

week, and the civil month, though of the most ancient and general use, are

only arbitrary and conventional.

_Day._--The subdivision of the day (_q.v._) into twenty-four parts, or

hours, has prevailed since the remotest ages, though different nations have

not agreed either with respect to the epoch of its commencement or the

manner of distributing the hours. Europeans in general, like the ancient

Egyptians, place the commencement of the civil day at midnight, and reckon

twelve morning hours from midnight to midday, and twelve evening hours from

midday to midnight. Astronomers, after the example of Ptolemy, regard the

day as commencing with the sun's culmination, or noon, and find it most

convenient for the purposes of computation to reckon through the whole

twenty-four hours. Hipparchus reckoned the twenty-four hours from midnight

to midnight. Some nations, as the ancient Chaldeans and the modern Greeks,

have chosen sunrise for the commencement of the day; others, again, as the

Italians and Bohemians, suppose it to commence at sunset. In all these

cases the beginning of the day varies with the seasons at all places not

under the equator. In the early ages of Rome, and even down to the middle

of the 5th century after the foundation of the city, no other divisions of

the day were known than sunrise, sunset, and midday, which was marked by

the arrival of the sun between the Rostra and a place called Graecostasis,

where ambassadors from Greece and other countries used to stand. The Greeks

divided the natural day and night into twelve equal parts each, and the

hours thus formed were denominated _temporary hours_, from their varying in

length according to the seasons of the year. The hours of the day and night

were of course only equal at the time of the equinoxes. The whole period of

day and night they called [Greek: nuchthêmeron].

_Week._--The week is a period of seven days, having no reference whatever

to the celestial motions,--a circumstance to which it owes its unalterable

uniformity. Although it did not enter into the calendar of the Greeks, and

was not introduced at Rome till after the reign of Theodosius, it has been

employed from time immemorial in almost all eastern countries; and as it

forms neither an aliquot part of the year nor of the lunar month, those who

reject the Mosaic recital will be at a loss, as Delambre remarks, to assign

it to an origin having much semblance of probability. It might have been

suggested by the phases of the moon, or by the number of the planets known

in ancient times, an origin which is rendered more probable from the names

universally given to the different days of which it is composed. In the

Egyptian astronomy, the order of the planets, beginning with the most

remote, is Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon. Now,

the day being divided into twenty-four hours, each hour was consecrated to

a particular planet, namely, one to Saturn, the following to Jupiter, the

third to Mars, and so on according to the above order; and the day received

the name of the planet which presided over its first hour. If, then, the

first hour of a day was consecrated to Saturn, that planet would also have

the 8th, the 15th, and the 22nd hour; the 23rd would fall to Jupiter, the

24th to Mars, and the 25th, or the first hour of the second day, would

belong to the Sun. In like manner the first hour of the 3rd day would fall

to the Moon, the first of the 4th day to Mars, of the 5th to Mercury, of

the 6th to Jupiter, and of the 7th to Venus. The cycle being completed, the

first hour of the 8th day would return to Saturn, and all the others

succeed in the same order. According to Dio Cassius, the Egyptian week

commenced with Saturday. On their flight from Egypt, the Jews, from hatred

to their ancient oppressors, made Saturday the last day of the week.

The English names of the days are derived from the Saxon. The ancient

Saxons had borrowed the week from some Eastern nation, and substituted the

names of their own divinities for those of the gods of Greece. In

legislative and justiciary acts the Latin names are still retained.

Latin. English. Saxon.

Dies Solis. Sunday. Sun's day.

Dies Lunae. Monday. Moon's day.

Dies Martis. Tuesday. Tiw's day.

Dies Mercurii. Wednesday. Woden's day.

Dies Jovis. Thursday. Thor's day.

Dies Veneris. Friday. Frigg's day.

Dies Saturni. Saturday. Seterne's day.

_Month._--Long before the exact length of the year was determined, it must

have been perceived that the synodic revolution of the moon is accomplished

in about 29½ days. Twelve lunations, therefore, form a period of 354 days,

which differs only by about 11¼ days from the solar year. From this

circumstance has arisen the practice, perhaps universal, of dividing the

year into twelve _months_. But in the course of a few years the accumulated

difference between the solar year and twelve lunar months would become

considerable, and have the effect of transporting the commencement of the

year to a different season. The difficulties that arose in attempting to

avoid this inconvenience induced some nations to abandon the moon

altogether, and regulate their year by the course of the sun. The month,

however, being a convenient period of time, has retained its place in the

calendars of all nations; but, instead of denoting a synodic revolution of

the moon, it is usually employed to denote an arbitrary number of days

approaching to the twelfth part of a solar year.

Among the ancient Egyptians the month consisted of thirty days invariably;

and in order to complete the year, five days were added at the end, called

supplementary days. They made use of no intercalation, and by losing a

fourth of a day every year, the commencement of the year went back one day

in every period of four years, and consequently made a revolution of the

seasons in 1461 years. Hence 1461 Egyptian years are equal to 1460 Julian

years of 365¼ days each. This year is called _vague_, by reason of its

commencing sometimes at one season of the year, and sometimes at another.

The Greeks divided the month into three decades, or periods of ten days,--a

practice which was imitated by the French in their unsuccessful attempt to

introduce a new calendar at the period of the Revolution. This division

offers two advantages: the first is, that the period is an exact measure of

the month of thirty days; and the second is, that the number of the day of

the decade is connected with and suggests the number of the day of the

month. For example, the 5th of the decade must necessarily be the 5th, the

15th, or the 25th of the month; so that when the day of the decade is

known, that of the month can scarcely be mistaken. In reckoning by weeks,

it is necessary to keep in mind the day of the week on which each month

begins.

The Romans employed a division of the month and a method of reckoning the

days which appear not a little extraordinary, and must, in practice, have

been exceedingly inconvenient. As frequent allusion is made by classical

writers to this embarrassing method of computation, which is carefully

retained in the ecclesiastical calendar, we here give a table showing the

correspondence of the Roman months with those of modern Europe.

Instead of distinguishing the days by the ordinal numbers first, second,

third, &c., the Romans counted _backwards_ from three fixed epochs, namely,

the _Calends_, the _Nones_ and the _Ides_. The Calends (or Kalends) were

invariably the first day of the month, and were so denominated because it

had been an ancient custom of the pontiffs to call the people together on

that day, to apprize them of the festivals, or days that were to be kept

sacred during the month. The Ides (from an obsolete verb _iduare_, to

divide) were at the middle of the month, either the 13th or the 15th day;

and the Nones were the _ninth_ day before the [v.04 p.0989] Ides, counting

inclusively. From these three terms the days received their denomination in

the following manner:--Those which were comprised between the Calends and

the Nones were called _the days before the Nones_; those between the Nones

and the Ides were called _the days before the Ides_; and, lastly, all the

days after the Ides to the end of the month were called _the days before

the Calends_ of the succeeding month. In the months of March, May, July and

October, the Ides fell on the 15th day, and the Nones consequently on the

7th; so that each of these months had six days named from the Nones. In all

the other months the Ides were on the 13th and the Nones on the 5th;

consequently there were only four days named from the Nones. Every month

had eight days named from the Ides. The number of days receiving their

denomination from the Calends depended on the number of days in the month

and the day on which the Ides fell. For example, if the month contained 31

days and the Ides fell on the 13th, as was the case in January, August and

December, there would remain 18 days after the Ides, which, added to the

first of the following month, made 19 days of Calends. In January,

therefore, the 14th day of the month was called the _nineteenth before the

Calends of February_ (counting inclusively), the 15th was the 18th before

the Calends and so on to the 30th, which was called the third before the

Calend (_tertio Calendas_), the last being the second of the Calends, or

the day before the Calends (_pridie Calendas_).

+-------+------------+------------+------------+------------+

| | March. | | April. | |

|Days of| May. | January. | June. | |

| the | July. | August. | September. | February. |

| Month.| October. | December. | November. | |

+-------+------------+------------+------------+------------+

| 1 | Calendae. | Calendae. | Calendae. | Calendae. |

| 2 | 6 | 4 | 4 | 4 |

| 3 | 5 | 3 | 3 | 3 |

| 4 | 4 |Prid. Nonas.|Prid. Nonas.|Prid. Nonas.|

| 5 | 3 | Nonae. | Nonae. | Nonae. |

| 6 |Prid. Nonas.| 8 | 8 | 8 |

| 7 | Nonae. | 7 | 7 | 7 |

| 8 | 8 | 6 | 6 | 6 |

| 9 | 7 | 5 | 5 | 5 |

| 10 | 6 | 4 | 4 | 4 |

| 11 | 5 | 3 | 3 | 3 |

| 12 | 4 | Prid. Idus.| Prid. Idus.| Prid. Idus.|

| 13 | 3 | Idus. | Idus. | Idus. |

| 14 | Prid. Idus.| 19 | 18 | 16 |

| 15 | Idus. | 18 | 17 | 15 |

| 16 | 17 | 17 | 16 | 14 |

| 17 | 16 | 16 | 15 | 13 |

| 18 | 15 | 15 | 14 | 12 |

| 19 | 14 | 14 | 13 | 11 |

| 20 | 13 | 13 | 12 | 10 |

| 21 | 12 | 12 | 11 | 9 |

| 22 | 11 | 11 | 10 | 8 |

| 23 | 10 | 10 | 9 | 7 |

| 24 | 9 | 9 | 8 | 6 |

| 25 | 8 | 8 | 7 | 5 |

| 26 | 7 | 7 | 6 | 4 |

| 27 | 6 | 6 | 5 | 3 |

| 28 | 5 | 5 | 4 |Prid. Calen.|

| 29 | 4 | 4 | 3 | Mart. |

| 30 | 3 | 3 |Prid. Calen.| |

| 31 |Prid. Calen.|Prid. Calen.| | |

+-------+------------+------------+------------+------------+

YEAR.--The year is either astronomical or civil. The solar astronomical

year is the period of time in which the earth performs a revolution in its

orbit about the sun, or passes from any point of the ecliptic to the same

point again; and consists of 365 days 5 hours 48 min. and 46 sec. of mean

solar time. The civil year is that which is employed in chronology, and

varies among different nations, both in respect of the season at which it

commences and of its subdivisions. When regard is had to the sun's motion

alone, the regulation of the year, and the distribution of the days into

months, may be effected without much trouble; but the difficulty is greatly

increased when it is sought to reconcile solar and lunar periods, or to

make the subdivisions of the year depend on the moon, and at the same time

to preserve the correspondence between the whole year and the seasons.

_Of the Solar Year._--In the arrangement of the civil year, two objects are

sought to be accomplished,--first, the equable distribution of the days

among twelve months; and secondly, the preservation of the beginning of the

year at the same distance from the solstices or equinoxes. Now, as the year

consists of 365 days and a fraction, and 365 is a number not divisible by

12, it is impossible that the months can all be of the same length and at

the same time include all the days of the year. By reason also of the

fractional excess of the length of the year above 365 days, it likewise

happens that the years cannot all contain the same number of days if the

epoch of their commencement remains fixed; for the day and the civil year

must necessarily be considered as beginning at the same instant; and

therefore the extra hours cannot be included in the year till they have

accumulated to a whole day. As soon as this has taken place, an additional

day must be given to the year.

The civil calendar of all European countries has been borrowed from that of

the Romans. Romulus is said to have divided the year into ten months only,

including in all 304 days, and it is not very well known how the remaining

days were disposed of. The ancient Roman year commenced with March, as is

indicated by the names September, October, November, December, which the

last four months still retain. July and August, likewise, were anciently

denominated Quintilis and Sextilis, their present appellations having been

bestowed in compliment to Julius Caesar and Augustus. In the reign of Numa

two months were added to the year, January at the beginning and February at

the end; and this arrangement continued till the year 452 B.C., when the

Decemvirs changed the order of the months, and placed February after

January. The months now consisted of twenty-nine and thirty days

alternately, to correspond with the synodic revolution of the moon, so that

the year contained 354 days; but a day was added to make the number odd,

which was considered more fortunate, and the year therefore consisted of

355 days. This differed from the solar year by ten whole days and a

fraction; but, to restore the coincidence, Numa ordered an additional or

intercalary month to be inserted every second year between the 23rd and

24th of February, consisting of twenty-two and twenty-three days

alternately, so that four years contained 1465 days, and the mean length of

the year was consequently 366¼ days. The additional month was called

_Mercedinus_ or _Mercedonius_, from _merces_, wages, probably because the

wages of workmen and domestics were usually paid at this season of the

year. According to the above arrangement, the year was too long by one day,

which rendered another correction necessary. As the error amounted to

twenty-four days in as many years, it was ordered that every third period

of eight years, instead of containing four intercalary months, amounting in

all to ninety days, should contain only three of those months, consisting

of twenty-two days each. The mean length of the year was thus reduced to

365¼ days; but it is not certain at what time the octennial periods,

borrowed from the Greeks, were introduced into the Roman calendar, or

whether they were at any time strictly followed. It does not even appear

that the length of the intercalary month was regulated by any certain

principle, for a discretionary power was left with the pontiffs, to whom

the care of the calendar was committed, to intercalate more or fewer days

according as the year was found to differ more or less from the celestial

motions. This power was quickly abused to serve political objects, and the

calendar consequently thrown into confusion. By giving a greater or less

number of days to the intercalary month, the pontiffs were enabled to

prolong the term of a magistracy or hasten the annual elections; and so

little care had been taken to regulate the year, that, at the time of

Julius Caesar, the civil equinox differed from the astronomical by three

months, so that the winter months were carried back into autumn and the

autumnal into summer.

In order to put an end to the disorders arising from the negligence or

ignorance of the pontiffs, Caesar abolished the use of the lunar year and

the intercalary month, and regulated the civil year entirely by the sun.

With the advice and assistance of Sosigenes, he fixed the mean length of

the year at 365¼ days, and decreed that every fourth year should have 366

days, the [v.04 p.0990] other years having each 365. In order to restore

the vernal equinox to the 25th of March, the place it occupied in the time

of Numa, he ordered two extraordinary months to be inserted between

November and December in the current year, the first to consist of

thirty-three, and the second of thirty-four days. The intercalary month of

twenty-three days fell into the year of course, so that the ancient year of

355 days received an augmentation of ninety days; and the year on that

occasion contained in all 445 days. This was called the last year of

confusion. The first Julian year commenced with the 1st of January of the

46th before the birth of Christ, and the 708th from the foundation of the

city.

In the distribution of the days through the several months, Caesar adopted

a simpler and more commodious arrangement than that which has since

prevailed. He had ordered that the first, third, fifth, seventh, ninth and

eleventh months, that is January, March, May, July, September and November,

should have each thirty-one days, and the other months thirty, excepting

February, which in common years should have only twenty-nine, but every

fourth year thirty days. This order was interrupted to gratify the vanity

of Augustus, by giving the month bearing his name as many days as July,

which was named after the first Caesar. A day was accordingly taken from

February and given to August; and in order that three months of thirty-one

days might not come together, September and November were reduced to thirty

days, and thirty-one given to October and December. For so frivolous a

reason was the regulation of Caesar abandoned, and a capricious arrangement

introduced, which it requires some attention to remember.

The additional day which occured every fourth year was given to February,

as being the shortest month, and was inserted in the calendar between the

24th and 25th day. February having then twenty-nine days, the 25th was the

6th of the calends of March, _sexto calendas_; the preceding, which was the

additional or intercalary day, was called _bis-sexto calendas_,--hence the

term _bissextile_, which is still employed to distinguish the year of 366

days. The English denomination of _leap-year_ would have been more

appropriate if that year had differed from common years in _defect_, and

contained only 364 days. In the modern calendar the intercalary day is

still added to February, not, however, between the 24th and 25th, but as

the 29th.

The regulations of Caesar were not at first sufficiently understood; and

the pontiffs, by intercalating every third year instead of every fourth, at

the end of thirty-six years had intercalated twelve times, instead of nine.

This mistake having been discovered, Augustus ordered that all the years

from the thirty-seventh of the era to the forty-eighth inclusive should be

common years, by which means the intercalations were reduced to the proper

number of twelve in forty-eight years. No account is taken of this blunder

in chronology; and it is tacitly supposed that the calendar has been

correctly followed from its commencement.

Although the Julian method of intercalation is perhaps the most convenient

that could be adopted, yet, as it supposes the year too long by 11 minutes

14 seconds, it could not without correction very long answer the purpose

for which it was devised, namely, that of preserving always the same

interval of time between the commencement of the year and the equinox.

Sosigenes could scarcely fail to know that this year was too long; for it

had been shown long before, by the observations of Hipparchus, that the

excess of 365¼ days above a true solar year would amount to a day in 300

years. The real error is indeed more than double of this, and amounts to a

day in 128 years; but in the time of Caesar the length of the year was an

astronomical element not very well determined. In the course of a few

centuries, however, the equinox sensibly retrograded towards the beginning

of the year. When the Julian calendar was introduced, the equinox fell on

the 25th of March. At the time of the council of Nice, which was held in

325, it fell on the 21st; and when the reformation of the calendar was made

in 1582, it had retrograded to the 11th. In order to restore the equinox to

its former place, Pope Gregory XIII. directed ten days to be suppressed in

the calendar; and as the error of the Julian intercalation was now found to

amount to three days in 400 years, he ordered the intercalations to be

omitted on all the centenary years excepting those which are multiples of

400. According to the Gregorian rule of intercalation, therefore, every

year of which the number is divisible by four without a remainder is a leap

year, excepting the centurial years, which are only leap years when

divisible by four after omitting the two ciphers. Thus 1600 was a leap

year, but 1700, 1800 and 1900 are common years; 2000 will be a leap year,

and so on.

As the Gregorian method of intercalation has been adopted in all Christian

countries, Russia excepted, it becomes interesting to examine with what

degrees of accuracy it reconciles the civil with the solar year. According

to the best determinations of modern astronomy (Le Verrier's _Solar

Tables_, Paris, 1858, p. 102), the mean geocentric motion of the sun in

longitude, from the mean equinox during a Julian year of 365.25 days, the

same being brought up to the present date, is 360° + 27".685. Thus the mean

length of the solar year is found to be 360°/(360° + 27".685) × 365.25 =

365.2422 days, or 365 days 5 hours 48 min. 46 sec. Now the Gregorian rule

gives 97 intercalations in 400 years; 400 years therefore contain 365 × 400

+ 97, that is, 146,097 days; and consequently one year contains 365.2425

days, or 365 days 5 hours 49 min. 12 sec. This exceeds the true solar year

by 26 seconds, which amount to a day in 3323 years. It is perhaps

unnecessary to make any formal provision against an error which can only

happen after so long a period of time; but as 3323 differs little from

4000, it has been proposed to correct the Gregorian rule by making the year

4000 and all its multiples common years. With this correction the rule of

intercalation is as follows:--

Every year the number of which is divisible by 4 is a leap year, excepting

the last year of each century, which is a leap year only when the number of

the century is divisible by 4; but 4000, and its multiples, 8000, 12,000,

16,000, &c. are common years. Thus the uniformity of the intercalation, by

continuing to depend on the number four, is preserved, and by adopting the

last correction the commencement of the year would not vary more than a day

from its present place in two hundred centuries.

In order to discover whether the coincidence of the civil and solar year

could not be restored in shorter periods by a different method of

intercalation, we may proceed as follows:--The fraction 0.2422, which

expresses the excess of the solar year above a whole number of days, being

converted into a continued fraction, becomes

1

-----

4 + 1

-----

7 + 1

-----

1 + 1

-----

3 + 1

-----

4 + 1

-----

1 +, &c.

which gives the series of approximating fractions,

1/4, 7/29, 8/33, 31/128, 132/545, 163/673, &c.

The first of these, 1/4, gives the Julian intercalation of one day in four

years, and is considerably too great. It supposes the year to contain 365

days 6 hours.

The second, 7/29, gives seven intercalary days in twenty-nine years, and

errs in defect, as it supposes a year of 365 days 5 hours 47 min. 35 sec.

The third, 8/33, gives eight intercalations in thirty-three years or seven

successive intercalations at the end of four years respectively, and the

eighth at the end of five years. This supposes the year to contain 365 days

5 hours 49 min. 5.45 sec.

The fourth fraction, 31/128 = (24 + 7) / (99 + 29) = (3 × 8 + 7) / (3 × 33

+ 29) combines three periods of thirty-three years with one of twenty-nine,

and would consequently be very convenient in application. It supposes the

year to consist of 365 days 5 hours 48 min. 45 sec., and is practically

exact.

The fraction 8/33 offers a convenient and very accurate method of

intercalation. It implies a year differing in excess from the true year

only by 19.45 sec., while the Gregorian year is too long by 26 sec. It

produces a much nearer coincidence between the civil and solar years than

the Gregorian method; and, by reason of its shortness of period, confines

the evagations of the mean equinox from the true within much narrower

limits. It has been stated by Scaliger, Weidler, Montucla, and others, that

the modern Persians actually follow this method, and intercalate eight days

in thirty-three [v.04 p.0991] years. The statement has, however, been

contested on good authority; and it seems proved (see Delambre, _Astronomie

Moderne_, tom. i. p.81) that the Persian intercalation combines the two

periods 7/29 and 8/33. If they follow the combination (7 + 3 × 8) / (29 + 3

× 33) = 31/128 their determination of the length of the tropical year has

been extremely exact. The discovery of the period of thirty-three years is

ascribed to Omar Khayyam, one of the eight astronomers appointed by

Jel[=a]l ud-Din Malik Shah, sultan of Khorasan, to reform or construct a

calendar, about the year 1079 of our era.

If the commencement of the year, instead of being retained at the same

place in the seasons by a uniform method of intercalation, were made to

depend on astronomical phenomena, the intercalations would succeed each

other in an irregular manner, sometimes after four years and sometimes

after five; and it would occasionally, though rarely indeed, happen, that

it would be impossible to determine the day on which the year ought to

begin. In the calendar, for example, which was attempted to be introduced

in France in 1793, the beginning of the year was fixed at midnight

preceding the day in which the true autumnal equinox falls. But supposing

the instant of the sun's entering into the sign Libra to be very near

midnight, the small errors of the solar tables might render it doubtful to

which day the equinox really belonged; and it would be in vain to have

recourse to observation to obviate the difficulty. It is therefore

infinitely more commodious to determine the commencement of the year by a

fixed rule of intercalation; and of the various methods which might be

employed, no one perhaps is on the whole more easy of application, or

better adapted for the purpose of computation, than the Gregorian now in

use. But a system of 31 intercalations in 128 years would be by far the

most perfect as regards mathematical accuracy. Its adoption upon our

present Gregorian calendar would only require the suppression of the usual

bissextile once in every 128 years, and there would be no necessity for any

further correction, as the error is so insignificant that it would not

amount to a day in 100,000 years.

_Of the Lunar Year and Luni-solar Periods._--The lunar year, consisting of

twelve lunar months, contains only 354 days; its commencement consequently

anticipates that of the solar year by eleven days, and passes through the

whole circle of the seasons in about thirty-four lunar years. It is

therefore so obviously ill-adapted to the computation of time, that,

excepting the modern Jews and Mahommedans, almost all nations who have

regulated their months by the moon have employed some method of

intercalation by means of which the beginning of the year is retained at

nearly the same fixed place in the seasons.

In the early ages of Greece the year was regulated entirely by the moon.

Solon divided the year into twelve months, consisting alternately of

twenty-nine and thirty days, the former of which were called _deficient_

months, and the latter _full_ months. The lunar year, therefore, contained

354 days, falling short of the exact time of twelve lunations by about 8.8

hours. The first expedient adopted to reconcile the lunar and solar years

seems to have been the addition of a month of thirty days to every second

year. Two lunar years would thus contain 25 months, or 738 days, while two

solar years, of 365¼ days each, contain 730½ days. The difference of 7½

days was still too great to escape observation; it was accordingly proposed

by Cleostratus of Tenedos, who flourished shortly after the time of Thales,

to omit the biennary intercalation every eighth year. In fact, the 7½ days

by which two lunar years exceeded two solar years, amounted to thirty days,

or a full month, in eight years. By inserting, therefore, three additional

months instead of four in every period of eight years, the coincidence

between the solar and lunar year would have been exactly restored if the

latter had contained only 354 days, inasmuch as the period contains 354 × 8

+ 3 × 30 = 2922 days, corresponding with eight solar years of 365¼ days

each. But the true time of 99 lunations is 2923.528 days, which exceeds the

above period by 1.528 days, or thirty-six hours and a few minutes. At the

end of two periods, or sixteen years, the excess is three days, and at the

end of 160 years, thirty days. It was therefore proposed to employ a period

of 160 years, in which one of the intercalary months should be omitted; but

as this period was too long to be of any practical use, it was never

generally adopted. The common practice was to make occasional corrections

as they became necessary, in order to preserve the relation between the

octennial period and the state of the heavens; but these corrections being

left to the care of incompetent persons, the calendar soon fell into great

disorder, and no certain rule was followed till a new division of the year

was proposed by Meton and Euctemon, which was immediately adopted in all

the states and dependencies of Greece.

The mean motion of the moon in longitude, from the mean equinox, during a

Julian year of 365.25 days (according to Hansen's _Tables de la Lune_,

London, 1857, pages 15, 16) is, at the present date, 13 × 360° +

477644".409; that of the sun being 360° + 27".685. Thus the corresponding

relative mean geocentric motion of the moon from the sun is 12 × 360° +

477616".724; and the duration of the mean synodic revolution of the moon,

or lunar month, is therefore 360° / (12 × 360° + 477616".724) × 365.25 =

29.530588 days, or 29 days, 12 hours, 44 min. 2.8 sec.

The _Metonic Cycle_, which may be regarded as the _chef-d'oeuvre_ of

ancient astronomy, is a period of nineteen solar years, after which the new

moons again happen on the same days of the year. In nineteen solar years

there are 235 lunations, a number which, on being divided by nineteen,

gives twelve lunations for each year, with seven of a remainder, to be

distributed among the years of the period. The period of Meton, therefore,

consisted of twelve years containing twelve months each, and seven years

containing thirteen months each; and these last formed the third, fifth,

eighth, eleventh, thirteenth, sixteenth, and nineteenth years of the cycle.

As it had now been discovered that the exact length of the lunation is a

little more than twenty-nine and a half days, it became necessary to

abandon the alternate succession of full and deficient months; and, in

order to preserve a more accurate correspondence between the civil month

and the lunation, Meton divided the cycle into 125 full months of thirty

days, and 110 deficient months of twenty-nine days each. The number of days

in the period was therefore 6940. In order to distribute the deficient

months through the period in the most equable manner, the whole period may

be regarded as consisting of 235 full months of thirty days, or of 7050

days, from which 110 days are to be deducted. This gives one day to be

suppressed in sixty-four; so that if we suppose the months to contain each

thirty days, and then omit every sixty-fourth day in reckoning from the

beginning of the period, those months in which the omission takes place

will, of course, be the deficient months.

The number of days in the period being known, it is easy to ascertain its

accuracy both in respect of the solar and lunar motions. The exact length

of nineteen solar years is 19 × 365.2422 = 6939.6018 days, or 6939 days 14

hours 26.592 minutes; hence the period, which is exactly 6940 days, exceeds

nineteen revolutions of the sun by nine and a half hours nearly. On the

other hand, the exact time of a synodic revolution of the moon is 29.530588

days; 235 lunations, therefore, contain 235 × 29.530588 = 6939.68818 days,

or 6939 days 16 hours 31 minutes, so that the period exceeds 235 lunations

by only seven and a half hours.

After the Metonic cycle had been in use about a century, a correction was

proposed by Calippus. At the end of four cycles, or seventy-six years, the

accumulation of the seven and a half hours of difference between the cycle

and 235 lunations amounts to thirty hours, or one whole day and six hours.

Calippus, therefore, proposed to quadruple the period of Meton, and deduct

one day at the end of that time by changing one of the full months into a

deficient month. The period of Calippus, therefore, consisted of three

Metonic cycles of 6940 days each, and a period of 6939 days; and its error

in respect of the moon, consequently, amounted only to six hours, or to one

day in 304 years. This period exceeds seventy-six true solar years by

fourteen hours and a quarter nearly, but coincides exactly with seventy-six

Julian years; and in the time of Calippus the length of the solar year was

almost universally supposed to be exactly 365¼ days. The Calippic period is

frequently referred to as a date by Ptolemy.

_Ecclesiastical Calendar._--The ecclesiastical calendar, which is adopted

in all the Catholic, and most of the Protestant countries of Europe, is

luni-solar, being regulated partly by the solar, and partly by the lunar

year,--a circumstance which gives rise to the [v.04 p.0992] distinction

between the movable and immovable feasts. So early as the 2nd century of

our era, great disputes had arisen among the Christians respecting the

proper time of celebrating Easter, which governs all the other movable

feasts. The Jews celebrated their passover on the 14th day of _the first

month_, that is to say, the lunar month of which the fourteenth day either

falls on, or next follows, the day of the vernal equinox. Most Christian

sects agreed that Easter should be celebrated on a Sunday. Others followed

the example of the Jews, and adhered to the 14th of the moon; but these, as

usually happened to the minority, were accounted heretics, and received the

appellation of Quartodecimans. In order to terminate dissensions, which

produced both scandal and schism in the church, the council of Nicaea,

which was held in the year 325, ordained that the celebration of Easter

should thenceforth always take place on the Sunday which immediately

follows the full moon that happens upon, or next after, the day of the

vernal equinox. Should the 14th of the moon, which is regarded as the day

of full moon, happen on a Sunday, the celebration Of Easter was deferred to

the Sunday following, in order to avoid concurrence with the Jews and the

above-mentioned heretics. The observance of this rule renders it necessary

to reconcile three periods which have no common measure, namely, the week,

the lunar month, and the solar year; and as this can only be done

approximately, and within certain limits, the determination of Easter is an

affair of considerable nicety and complication. It is to be regretted that

the reverend fathers who formed the council of Nicaea did not abandon the

moon altogether, and appoint the first or second Sunday of April for the

celebration of the Easter festival. The ecclesiastical calendar would in

that case have possessed all the simplicity and uniformity of the civil

calendar, which only requires the adjustment of the civil to the solar

year; but they were probably not sufficiently versed in astronomy to be

aware of the practical difficulties which their regulation had to

encounter.

_Dominical Letter._--The first problem which the construction of the

calendar presents is to connect the week with the year, or to find the day

of the week corresponding to a given day of any year of the era. As the

number of days in the week and the number in the year are prime to one

another, two successive years cannot begin with the same day; for if a

common year begins, for example, with Sunday, the following year will begin

with Monday, and if a leap year begins with Sunday, the year following will

begin with Tuesday. For the sake of greater generality, the days of the

week are denoted by the first seven letters of the alphabet, A, B, C, D, E,

F, G, which are placed in the calendar beside the days of the year, so that

A stands opposite the first day of January, B opposite the second, and so

on to G, which stands opposite the seventh; after which A returns to the

eighth, and so on through the 365 days of the year. Now if one of the days

of the week, Sunday for example, is represented by E, Monday will be

represented by F, Tuesday by G, Wednesday by A, and so on; and every Sunday

through the year will have the same character E, every Monday F, and so

with regard to the rest. The letter which denotes Sunday is called the

_Dominical Letter_, or the _Sunday Letter_; and when the dominical letter

of the year is known, the letters which respectively correspond to the

other days of the week become known at the same time.

_Solar Cycle._--In the Julian calendar the dominical letters are readily

found by means of a short cycle, in which they recut in the same order

without interruption. The number of years in the intercalary period being

four, and the days of the week being seven, their product is 4 × 7 = 28;

twenty-eight years is therefore a period which includes all the possible

combinations of the days of the week with the commencement of the year.

This period is called the _Solar Cycle_, or the _Cycle of the Sun_, and

restores the first day of the year to the same day of the week. At the end

of the cycle the dominical letters return again in the same order on the

same days of the month; hence a table of dominical letters, constructed for

twenty-eight years, will serve to show the dominical letter of any given

year from the commencement of the era to the Reformation. The cycle, though

probably not invented before the time of the council of Nicaea, is regarded

as having commenced nine years before the era, so that the year _one_ was

the tenth of the solar cycle. To find the year of the cycle, we have

therefore the following rule:--_Add nine to the date, divide the sum by

twenty-eight; the quotient is the number of cycles elapsed, and the

remainder is the year of the cycle._ Should there be no remainder, the

proposed year is the twenty-eighth or last of the cycle. This rule is

conveniently expressed by the formula ((x + 9) / 28)_r, in which x denotes

the date, and the symbol r denotes that the remainder, which arises from

the division of x + 9 by 28, is the number required. Thus, for 1840, we

have (1840 + 9) / 28 = 66-1/28; therefore ((1840 + 9) / 28)_r = 1, and the

year 1840 is the first of the solar cycle. In order to make use of the

solar cycle in finding the dominical letter, it is necessary to know that

the first year of the Christian era began with Saturday. The dominical

letter of that year, which was the tenth of the cycle, was consequently B.

The following year, or the 11th of the cycle, the letter was A; then G. The

fourth year was bissextile, and the dominical letters were F, E; the

following year D, and so on. In this manner it is easy to find the

dominical letter belonging to each of the twenty-eight years of the cycle.

But at the end of a century the order is interrupted in the Gregorian

calendar by the secular suppression of the leap year; hence the cycle can

only be employed during a century. In the reformed calendar the intercalary

period is four hundred years, which number being multiplied by seven, gives

two thousand eight hundred years as the interval in which the coincidence

is restored between the days of the year and the days of the week. This

long period, however, may be reduced to four hundred years; for since the

dominical letter goes back five places every four years, its variation in

four hundred years, in the Julian calendar, was five hundred places, which

is equivalent to only three places (for five hundred divided by seven

leaves three); but the Gregorian calendar suppresses exactly three

intercalations in four hundred years, so that after four hundred years the

dominical letters must again return in the same order. Hence the following

table of dominical letters for four hundred years will serve to show the

dominical letter of any year in the Gregorian calendar for ever. It

contains four columns of letters, each column serving for a century. In

order to find the column from which the letter in any given case is to be

taken, strike off the last two figures of the date, divide the preceding

figures by four, and the remainder will indicate the column. The symbol X,

employed in the formula at the top of the column, denotes the number of

centuries, that is, the figures remaining after the last two have been

struck off. For example, required the dominical letter of the year 1839? In

this case X = 18, therefore (X/4)_r = 2; and in the second column of

letters, opposite 39, in the table we find F, which is the letter of the

proposed year.

It deserves to be remarked, that as the dominical letter of the first year

of the era was B, the first column of the following table will give the

dominical letter of every year from the commencement of the era to the

Reformation. For this purpose divide the date by 28, and the letter

opposite the remainder, in the first column of figures, is the dominical

letter of the year. For example, supposing the date to be 1148. On dividing

by 28, the remainder is 0, or 28; and opposite 28, in the first column of

letters, we find D, C, the dominical letters of the year 1148.

_Lunar Cycle and Golden Number._--In connecting the lunar month with the

solar year, the framers of the ecclesiastical calendar adopted the period

of Meton, or lunar cycle, which they supposed to be exact. A different

arrangement has, however, been followed with respect to the distribution of

the months. The lunations are supposed to consist of twenty-nine and thirty

days alternately, or the lunar year of 354 days; and in order to make up

nineteen solar years, six embolismic or intercalary months, of thirty days

each, are introduced in the course of the cycle, and one of twenty-nine

days is added at the [v.04 p.0993] end. This gives 19 × 354 + 6 × 30 + 29 =

6935 days, to be distributed among 235 lunar months. But every leap year

one day must be added to the lunar month in which the 29th of February is

included. Now if leap year happens on the first, second or third year of

the period, there will be five leap years in the period, but only four when

the first leap year falls on the fourth. In the former case the number of

days in the period becomes 6940 and in the latter 6939. The mean length of

the cycle is therefore 6939¾ days, agreeing exactly with nineteen Julian

years.