who, after a reign of a few months, was compelled to fly. Sevajee Madhoo, the posthumous son of Narrain Row, was appointed Paishwa, and Ballajee Pundit, better known as Nana Furnavese, was elected dewan, or minister. The British, on the condition of his ceding to them certain territories, came to the assistance of Ragoba, which occasioned a war between them and the Mahrattas. This war, twice interrupted by treaties which were not completed, continued till 1782, when the treaty of Salbhye was concluded, by which Madhajee Sindia was confirmed in all his possessions, the places taken from him by the British were restored, and he was recognised by them as an independent prince.

Madhajee Sindia had now time and opportunity to prosecute his plans of aggrandisement. In 1785 he again appeared at Delhi, and by the murder of two of the imperial ministers once more got the emperor into his power; he also conquered Agra and Alyghur, and obtained possession of nearly the whole of the Doab About this time he engaged in his service a Frenchman, De Boigne, who became of the most essential service to him; for by his assistance he formed an army consisting of troops regularly disciplined, he fought pitched battles, besieged fortresses previously deemed impregnable, gradually subjected raja after raja to contribution, and added district after district to his possessions, till he became master of nearly all the territory southwest from the banks of the Ganges to the Nerbudda. The battle of Meerta, gained by De Boigne in 1790 over the collected forces of Joudpoor, had made Sindia master of that principality, as well as of the weaker state of Odeypoor, to these conquests was added soon after that of Jypoor, which was followed in 1792 by the defeat of the troops of Junka

RANOJEE SINDIA, who was originally a potail, or head man of a village. The Paishwa Bajerow, who succeeded his father Biswanath Row in 1720, appointed Ranojee to the humble office of bearer of his slippers. A circumstance which seemed to show his fidelity and attachment to his master is said to have led to his promotion. Bajerow one day found him asleep on his back, with the slippers firmly clasped to his breast, and was so much pleased as to appoint him immediately to a station in his body-guard. Ranojee Sindia was active and enterprising, and he was rapidly promoted. In 1743 he had risen to the highest rank of Mahratta chiefs; for when Bajerow came into Malwa in that year, Ranojee signed a bond which was required by the emperor of Delhi, Mahomed Shah, as a surety for the good conduct of his master the Paishwa. Before Ranojee died he had obtained the hereditary government of one-half of the extensive province of Malwa. By his wife, who belonged to his own tribe, he had three sons, Jeypah, Duttagee, and Juttabah; and by a Rajpoot woman he had two sons, Tu-jee Holkar, when four corps of regular infantry belonging kajee and Madhajee, of whom

MADHAJEE SINDIA became the head of the family. The date of his birth is uncertain; it was probably about 1743; he was present at the battle of Paniput in 1761, when the Mahrattas were defeated by Ahmed Shah Abdallah and his Afghans, in union with the Rajpoot and Mohammedan princes of northern Hindustan. In this disastrous battle one-half of the Mahratta army, which amounted to 200,000 men, are said to have been slain. Madhajee Sindia was pursued by an Afghan horseman for many miles, who at length overtook him, and left him for dead in a ditch, after having wounded him with his battle-axe in the knee in such a manner as to render him lame for life. The Sindia family, as well as the other Mahratta chiefs, were for a time deprived of all their possessions in Malwa and Hindustan proper; but this was not of long continuance. The Paishwa Bajerow died in 1761, and was succeeded by his son Madhoo Row, under whom, on the death of Mulhar Row Holkar in 1764, Madhajee Síndia became the most powerful of the Mahratta chiefs. Besides being the principal leader of the household-horse of the Paishwa, he had a large army of his own; and the return of Ahmed Shah to Cabul, and the contests among the Mohammedan princes under the weak emperor Shah Alim II., in a few years afforded opportunity to him and his brother Tukajee Sindia to recover their former hereditary government and possessions in Malwa and northern Hindustan.

In 1770, on the invitation of Nujeeb ud Dowlah, who was the minister of Shah Alim, Madhajee Sindia, Bassajee Row, and Tukajee Holkar entered Hindustan proper with their armies, for the purpose of expelling the Sikhs, who had invaded the emperor's territories. This was soon accomplished; and on the death of Nujeeb ud Dowlah in 1771, Mad hajee Sindia obtained possession of Delhi, whither he invited Shah Alim to return from Allahabad, where he had been living under the protection of the British since 1755. In December the same year the emperor was crowned with great pomp in his capital. He was not however the less in subjection. Madhajee compelled him to sign a commission by which he appointed the Paishwa vicegerent of the empire; and the Paishwa, by a like commission, appointed Madhajee his deputy.

In 1772, and again in 1773, with his two colleagues Bassajee and Holkar, Sindia invaded and ravaged Rohilcund, and was preparing to cross the Ganges, when the murder of the young Paishwa Narrain Row, the usurpation of the office by his uncle Ragoba, and the appearance of the British and the nabob of Oude, who had been invited to assist the Rohillas, caused him to return to Poona. A confederation of Mahratta chiefs was got up against Ragoba,

to Holkar's army, which were commanded by a French officer, were almost utterly destroyed Sindia himself had returned to Poona in 1791, where he died in 1794.

Madhajee Sindia's life was one of incessant activity; he was engaged in a series of contests in which he displayed great talent and untiring energy, and by which his power and possessions were gradually extended, consolidated, and confirmed. His habits throughout the whole of his career were those of a plain soldier; he was never seduced by luxury, and he despised the trappings of state. Though occasionally guilty of violence and oppression, his life was for the most part unstained by cruelty; his disposition was mild, and he was desirous of improving the countries which he conquered. Towards the British and those states which were unconnected with the Mahratta government he conducted himself as an independent prince, but in matters relating to the Paishwa he paid the most scrupulous attention to all the forms of humility, of which he made a curious display when Sevajee Madhoo Row, at the termination of his minority in 1791, entered upon the duties of his office, and Sindia came to Poona to pay his respects to him. Sir John Malcolm thus relates it: The actual sovereign of Hindustan from the Sutleje to Agra, the conqueror of the princes of Rajpootana, the commander of an army composed of sixteen battalions of regular infantry, 500 pieces of cannon, and 100,000 horse, the possessor of two thirds of Malwa, and some of the finest provinces in the Deckan, when he went to pay his respects to a youth who then held the office of Paishwa, dismounted from his elephant at the gates of Poona; placed himself in the great hall of audience below all the mankarries, or hereditary nobles of the state, and when the Paishwa came into the room, and desired him to be seated with others, he objected on the ground of being unworthy of the honour, and, untying a bundle that he carried under his arm, produced a pair of slippers, which he placed before Madhoo Row, saying, "This is my occupation; it was that of my father.' Madhajee, at the moment he said this, took the old slippers the Paishwa had in use, which he wrapped up carefully, and continued to hold them under his arm; after which, though with apparent reluctance, he allowed himself to be prevailed upon to sit down. It has been supposed that by this affected humility he aimed at obtaining the situation of dewan to the Paishwa; if such however was his object, he was frustrated in it, for Nana Furnavese still retained it.

Madhajee Sindia had no sons. His brother Tukajee had three, of whom the youngest, Anund Row, became the favourite of his uncle, who adopted Dowlut Row Sindia, the son of Anund Row, as his heir..

DOWLUT ROW SINDIA, at the death of his grand-uncle,

all which theorems are in fact contained in any one of them, as soon as that one is shown to be universally true. It frequently happens however that the student is allowed to assume the universal truth of these theorems upon too slight a foundation of previous proof: drawing a figure for instance in which both angles are less than a right angle. We givé, as an instance, the proof of the first formula when both angles are greater than two right angles. Let XOP =a, POQ=b, both angles being measured in the direction of revolution indicated by the arrow. The sum is four right angles +XOQ, which has the same sine and cosine as

we take ordinary algebra only [as in NEGATIVE, &c. `QUÂN-
TITIES, p. 134, col. 2], in which the impossible quantity is
unexplained, we have the most common mode of proceed-
ing. The explanations afterwards given would make this
theory the most simple imaginable, to a student who had
learned algebra from the beginning in the manner pointed
out. To take the middle course, let us assume the rules of
algebra [OPERATION] independently of the meanings of the
symbols. Let sin and cos x be defined as such func-
tions of that sin (x+y) gives sin x. cos y+cos x. sin y, and
cos (x+y)=cos x. cos y — sin x. sin y.' Observe that we do
not in thus defining say there are such functions; we only
say, if there be such, let them have these names.
Then, as
in NEGATIVE, &c. cited above, we see that if x=
cos +1.sin x, the relation p(x+y)=pxxpy fol-
lows; whence [BINOMIAL THEOREM] de can be nothing
but K, where K is independent of x. Let x=1, whence
(1) K, or we have
Cosx+1.sin

(cos 1+/- 1. sin 1) ... (1)

QN

QO'

e

-8

e

e +

27-1 27-}

-x

e+e e-e

+

27-1

To determine what algebraical formula e must he, take tne universal formula

and substitution immediately gives the first formula. We
shall not here dwell on the minor consequences of these
formulæ, but shall refer to the collection in TRIGONOMETRY.
The connection of the sine and angle depends in great part
upon the following theorem:-if may be made as small
as we please, sin :x may be made as near to unity as we
please. Observe that this theorem, supposes the angle x to
be measured by the theoretical unit [ANGLE], or the angle
I to be the angle of which the arc and radius are equal.
The proof depends upon the assumption that in the adjoining
obvious figure the arc AB is less than its containing contour
AC+CB. If the radius OB be r, we see that a must be
arc AB: r, or AB=rx. Also BM r sin x, BC sin x=
=
AM=r-rcos x, by definition. Now the arc AB is greater

/sin x

1+cos 2

Now e, as far as our definitions have yet extended, is wholly undetermined, every value of e being applicable. Let us add to our conditions that sin x:x shall approach to unity as a is diminished without limit: but sin x:x approaches to log e: -1; therefore log e-1, or

The preceding is purely symbolical; we merely ask how are previous symbols, used under certain laws, to be put together so as to represent certain new symbols which are to have certain properties. Let us now take the real geometrical meaning of sin x and cos x, and the complete system of algebra, in which -1 is explained [NEGATIVE, &c. QUANTITIES]. In that system, if a line equal to the unit-line be inclined to it at an angle, it is obviously represented by cos +-1. sin x, and any power of it, whole or fractional, can be obtained by changing into me,

so that

cos mx+√−1 . sin mx=(cos x+√−1. sin x) in which the second and third factors have unity for their is an immediate consequence of definition; and making x=1, the equation limit. Hence then, when is very small, and 1-x2 are very near representatives of the sine and cosine; and the goodness of the representation may be increased to any extent by diminishing .

The complete theory of the sine and cosine, from and after the two theorems just established, depends upon the introduction of the square root of the negative quantity. If

cos m+-1.sin m (cos-1.sin: follows at once. To prove that and cos 1+√-1 sin 1 are identical, in the most logical manner, requires a previous definition of an exponential quantity, in a sense so general, that exponents of the form a+b-1 shall be

where [ANGLE, p. 23] a is 01745,32925...., 00029,08882,...., 00000,48481,.... according as a means a number of degrees, of minutes, or of seconds.

The preceding is enough on the fundamental meanings of these terms, and on their connection with algebra. Some applications will be seen in TRIGONOMETRY.

SINE and COSINE, CURVES OF. By the curve of sines is meant that which has the equation y sin a, aud by the curve of cosines, that which has the equation y cos : it being understood that x stands for as many angular units as there are linear units in the abscissa. The undulatory forms of these curves are easily established and if the ordinate of a curve consist of several of them, as in y=a sin x+b cos x+c sin 2x, the several parts of the compound ordinate may be put together in the same manner as that in which the simple undulations are compounded in ACOUSTICS, p. 92. Except as expressing the most simple form of undulating curves, these equations are of no particular use in geometry.

SINE-CURE. Sine-cures are ecclesiastical benefices without cure of souls, and are of three sorts:-1. Where the benefice is a donative [BENEFICE, p. 220], and is committed to the incumbent by the patron expressly without cure of souls, the cure either not existing or being entrusted to a vicar; this is the strictest sine-cure. 2. Certain cathedral offices, viz. the canonries and prebends, and, according to some authorities, the deanery. 3. Where a parish is destitute, by some accident, of parishioners; this last kind has been called depopulations, rather than sine-cures.

known. The last-mentioned strait extends along the south. ern coast of the island of Singapore, and the most navigable part lies within the British possessions. It is the high road between the eastern and western portions of maritime Asia.

The surface of the island is gently undulating, here and there rising into low rounded hills of inconsiderable elevation. The higher ground rises in general not more than a hundred feet above the sea; the highest hill, called Bukit Tima, which is north-west of the town, but nearer the northern than the southern shores of the island, does not attain 200 feet. The shores of the island are mostly low, and surrounded by mangrove-trees. In a few isolated places low rocks approach the sea, chiefly along the Salat Tabrao. In several places however the coast is indented by salt creeks, which sometimes penetrate into the land three and even five or six miles. When the island was first occupied by the British it was entirely, and is still for the greater part, covered with a forest composed of different kinds of trees, five or six of which are well adapted for every object of housebuilding. The soil of the interior is composed of sand and of clay iron-stone, mixed up with a large portion of vegetable matter, which gives it a very black appearance. There is a general tendency to the formation of swamps. Rivulets are Their numerous, but they are of inconsiderable size. waters are almost always of a black colour, disagreeable taste, and peculiar odour, properties which they appear to derive from the peculiar nature of the superficial soil over which they pass, which in many parts resembles peat-moss. The water however drawn from wells which are sunk lower than the sandy base is less sensibly marked by these disagreeable qualities.

The climate of Singapore is hot, but equable, the seasons varying very little. The atmosphere throughout the year is serene. The smooth expanse of the sea is scarcely ruffled by a wind. The destructive typhons of the China Sea, and the scarely less furious tempests which occur on the coasts of Hindustan, are not known. The tempests of the China Sea however sometimes occasion a considerable swell in the sea, and a similar but less remarkable effect is produced by a tempest in the Bay of Bengal. It is only in this way, and as it were by propagation, that the sea is affected by remote tempests, and their effects are particularly remarkable in the irregularity of the tides, which at times run in one direction for several days successively, and with great rapidity. In the numerous narrow channels which divide the smaller islands, their rapidity is sometimes so great that it resembles water issuing through a sluice. The regular and periodical influence of the monsoons is slightly felt, the winds partaking more of the nature of land and sea breezes. To these circumstances must be attributed the great uni

Rectors of a parish in which vicars were likewise established with cure of souls have often by degrees exempted themselves from their ecclesiastical functions, and so have obtained sine-cures; but this is rather by abuse than legiti-formity of the temperature, the absence of a proper conmately.

Sine-cures are exempt from the statute of pluralities. (Burn's Ecclesiastical Law.)

SINEW. [TENDON.]

SINGAPORE is a British settlement in the East Indies, situated at the most southern extremity of the Malay Peninsula. It consists of the island of Singapore, and about fifty islets dispersed in the sea south and east of the principal island, or in what is called the Straits of Singapore. The territories of this settlement embrace a circumference of about a hundred miles, including the seas and straits within ten miles of the coast of the island of Singapore, and they lie between 1° 8′ and 1° 32′ N. lat., and between 103° 30' and 104° 10′ E. long.

The island of Singapore occupies about half the space between the two capes with which the Malay Peninsula terminates on the south, Capes Buru and Ramúnia (commonly called Romania). It has an elliptical form, and is about 25 miles in its greatest length from east to west, and 15 in its greatest width. It contains an estimated area of about 275 square miles, and is about one-third larger than the Isle of Wight. It is divided from the continent of Asia by a long and narrow strait called Salat Tabrao, or the old strait of Singapore. This strait is nearly forty miles long, and varies in width between two miles and a quarter of a mile. At its western extremity, near the island of Marambong, it has only a depth of 2 fathoms, but farther east it is nowhere less than five fathoms deep. This strait was formerly navigated by vessels bound for the China Seas; but the advantages which the Straits of Singapore offer for a speedy and safe navigation are so great, that the Salat Tabrao has not been used since the Straits of Singapore have become

tinual and periodical rainy season, and the more frequent fall of showers. Few days elapse without the occurrence of rain. According to an average of four years, the number of rainy days was 185, and that of dry only 180. The greatest quantity of rain falls in December and January, and the smallest in April and May. These frequent rains keep the island in a state of perpetual verdure.

The thermometer ranges during the year between 72° and 88°. The mean annual temperature is 80.7° of Fahrenheit. In the four months succeeding February it rises to 82.50°, and in the four months succeeding October it sinks to 79°. The daily range of the thermometer never exceeds ten degrees. Crawfurd states that the climate of Singapore is remarkably healthy, which he attributes to the free ventilation that prevails, and to the almost entire absence of chilling land-winds, but Newbold thinks that it is not so healthy as Malacca, and he ascribes this to the less regular alternations of the land and sea breezes.

Singapore is not rich in agricultural productions. No part of it was cultivated when the British took possession of the place, and at first the soil was considered ill adapted for agricultural purposes. But it now appears that considerable tracts near the town have been cleared by the Chinese, and that this industrious people have succeeded in cultivating different kinds of fruits and vegetables, rice, coffee, sugar, cotton, and especially pepper and the betelvine (Piper siriboa). Only the summits of the higher grounds are barren, but on their slopes and in the depressions between them the soil frequently has a considerable degree of fertility. Tropical fruits succeed very well, such as the mangusteen, pine-apple, cocoa-nut, orange, and mango. The mango is found wild in the forests. The tro

Nations constituting the
Population.
Natives of Hindustan
Javanese

pical vegetables, as the egg-plant, different kinds of pulse,
the yam, the batata, different varieties of cucumber, and
some others, grow very well, but the climate is too hot for
most European vegetables. The produce of the paddy- Bugis and Balinese
fields, as well as of the orchards, is far from being sufficient
for home consumption, and accordingly large quantities of
rice are imported from Sumatra and Java, and fruits from
Malacca.

The animals of Europe have been introduced, but most of them are few in number, as pasture-grounds are scarce. The Chinese however keep a great number of hogs. None of the large quadrupeds of the continent of Asia, such as elephants, rhinoceroses, tigers, and leopards, are met with on the island, but there are several kinds of monkeys, bats, and squirrels; also the Ictides, the porcupine, the sloth (Bradypus didactylus), the pangolin, the wild hog, and two species of deer, the Moschus pygmaeus, which is smaller than an English hare, and the Indian roe (Cervus munjac). Sometimes the dugong (Halicora dugong) is taken in the straits. It is ten or twelve feet long, and the flesh is considered for flavour and delicacy not inferior to beef: the skin is as strong as that of the hippopotamus. Birds are numerous, especially different kinds of passeres, climbers, and waders, particularly the first, which are remarkable for their novelty and beauty. Tortoises are common. The coral reefs and shoals in the vicinity of Singapore furnish that delicate fern-like sea-weed called aggar-aggar (Fucus Saccharinus) in abundance, and it forms an article of considerable export to China, where it is used in thin glues and varnishes. It is made into a very fine jelly by Europeans and the native Portuguese. The average annual produce is 6000 peculs, or 7980 cwt., and it is sold at three dollars the pecul.

In 1819, when the British took possession of the islands, the population amounted to about 150 individuals, mostly fishermen and pirates, who lived in a few miserable huts; about thirty of these were Chinese, the remainder Malays. The first census was taken in 1824, and then the population amounted to 10,683 individuals. Since that period it has constantly been increasing, and at the census of 1836 it was found to amount to 29,984 individuals. More than half of the population were settled in the town of Singapore, which contained 16,148 individuals, of whom there were 12,748 males and 3400 females. West of the town only a few settlements occur along the southern shores of the island, and on some of the small islands near the coast. These settlements constitute the district of Singapore town, and contained in 1836 only 4184 individuals, viz. 2338 Chinese, of whom forty-one only were females, and 1755 Malays, of whom 759 were females; and the remainder, with a trifling exception, Klings and Bugis. The country east of the town, which is named the District of Kampong Glam, contains a greater number of settlements, and they extend to the shores of the Salat Tabrao, and the islands of Tekong and Pulo Ubin, which lie within the strait. In this district there were 9652 individuals, viz. 4288 Malays, of whom 2050 were females; 3178 Chinese, of whom 72 only were females; 1515 Bugis, of whom 672 were females; and the remainder 671 were made up of Javanese, Balinese, and a few Bengalees and Klings. The islands of Tekong and Ubin contained 1901 inhabitants.

The population. is composed of nearly all the nations of Southern Asia and the Indian Archipelago, among whom a small number of individuals of European origin have settled, as appears from the following table, which also shows the increase of the population in two years, and the disproportion between males and females:

·

Population of the Island of Singapore in 1834 and 1836.
Males. Females, Males. Females.

Nations constituting the
Population.

Europeans, nearly all
Britons

1834.

1836.

Caffres
Siamese
Parsees

These censuses do not include the military, their followers, nor the convicts, as Singapore is a place of banishment from Calcutta and other parts of Hindustan. The number of these classes of inhabitants may be estimated at about 1200. The Europeans and Chinese constitute the wealthier classes. The Europeans are for the most part merchants, shopkeepers, and agents for mercantile houses in Europe. Most of the artisans, labourers, agriculturists, and shopkeepers are Chinese. The Malays are chiefly occupied in fishing, collecting sea-weed, and cutting timber, and many of them are employed as boatmen and sailors. The Bugis are almost invariably engaged in commerce, and the natives of India as petty shopkeepers, boatmen, and servants. The Chuliahs and Klings are daily labourers, artisans, and petty traders. The Caffres are the descendants of slaves, who have been brought by the Arabs from the Arabian and Abyssinian coasts. The most useful are the Chinese settlers. A common Chinese labourer gets from four to six Spanish dollars a month, a Kling from three to four and a half, and a Malay from two and a half to four and a half. A Chinese carpenter will earn about fifteen dollars a month, a Kling eight, and a Malay only five. The immigration of the Chinese is much favoured by circumstances. Among the dense population of China there are many paupers, who are a burden to the state, and the government connives at the poorer classes quitting the country, though it is contrary to their antient laws. The poor Chinese leaves his country without a penny, and agrees with the captain of the junk to pay from eight to twelve dollars for the passage. On landing he enters into one of the secret societies, which are always formed by the Chinese, and the society pays the passage-money and engages his services. In three months he has generally paid his debt, and then he begins to make his fortune. The Chinese emigrants at Singapore and Penang are mostly from Canton, Macao, or Fokien. Many of those of Fokien become merchants, and show a strong propensity to speculate largely The Canton emigrants are the best miners and artisans.

It is very probable that the population of the settlement now (1841) amounts to more than 36,000 individuals, which gives more than 130 individuals to a square mile, which is a considerable population even in a country that has been settled for centuries, and is certainly a very surprising population in a country which twenty years ago was a desert.

The town of Singapore stands on the southern shores of the island, in 1° 17′ 22′′ N. lat. and 103° 51′ 45′′ E. long., on a level and low plain of inconsiderable width, fronting the harbour. It extends about two miles along the shore, but only a thousand yards inland, where it is enclosed by hills from 100 to 150 feet high. The commercial portion of the town occupies the most western extremity, and is separated from the other parts by a salt creek, called the Singapore river, which is navigable for small craft. A good wooden bridge connects it with the eastern part, which contains the dwellings of the Europeans, the public offices, and the military cantonments. Contiguous to this portion of the town is the government-house, which is built on a hill. The most eastern part is occupied by the sultan of Johore, the Malays, and Bugis. The whole of the warehouses, and all the dwelling-houses in the principal streets in their vicinity, are built of brick and lime, and roofed with red tiles. The more distant dwelling-houses are built of wood, but roofed with tiles. It is only on the distant outskirts of the 8 town that there are huts with thatched roofs. The Malays and Bugis live in huts. The population (16,148 individuals) consisted, in 1836, of 8233 Chinese, 3617 Malays, 2157 Chuliahs and Klings, and the remainder was made up by Javanese, Bengalees, Bugis, native Christians, and Europeans. Ships lie in the roads of Singapore at the distance of from one to two miles from the town, according to their draught. With the assistance of lighters, cargoes are discharged and 102 taken in with scarcely any interruption throughout the year. VOL. XXII.-G

36
52

Native Christians,

mostly Portuguese.

201

4,510
879

Natives of the Coast

Armenians

Jews

Arabs

of Coromandel, Chu

and Klings

P.C., No. 1364.

liahs,

(Telingas)

8