western parts are far distant from market, | rapid. The rate hereafter will not be so and the eastern parts are so much poorer great, as the staple productions are not so land than Alabama, Mississippi, Tennessee, valuable; and slaves are not allowed to be Missouri, &c. whose products are the same, brought in from other states for sale. But that they can increase but little. The in- as the soil is very good, and cotton can be crease in this State has been very uniform. raised at half the expense it costs in Carolina, the increase will continue very great.

Population.

1790,

82,548

1800, 162,686 1810, 252,433

GEORGIA.

Settled 1733.

Inc.

per cent.

10 years 10 y. | 1 y.

29,519 64,3 13,2 10 years 10 y. 1833, 182,000 61,358 81,3 6,1 1834, 200,000

1840, 355,000 | 218,194 159,4 10,0 1835, 220,000

land from the Indians, and its vicinity to the The recent acquisition of the productive Mississippi river, will insure a large increase of population. Still the estimate must be doubtful, for it is uncertain how rapidly these lands may be vacated by the Indians and brought into the market.

LOUISIANA.

Settled 1699.

Govt. 1804.

Population.

Inc.

per cent.

State 1812.
Increase 7,500

1831, 223,000

1832, 230,500

1833, 238,000

Population in. 3,1 per cent. 80,138 97,1 7,0 1831, 533,000 89,747 55,1 4,5 1832, 549,000 88,556 35,1 3,1 1833, 566,000 10 years 10 y. | ly. 1830, 516,567 175,578 51,1 4,2 1834, 584,000 1810, 76,556 1840, 701,000 184,433 35,7 3,1 1835, 602,000 1820, 153,407 76,851 100,4 7,2 1830, 215,575 62,168 40,5 3,5 1834, 245,500 1840, 291,000 75,425 34,8 3, 1835, 253,000

1820, 340,989

The new lands of Georgia acquired from the Indians, have been so quickly taken up, that the population has increased very rapidly. Henceforth the increase cannot be as great. The policy of the State government in distributing the new lands by lottery, must have an injurious effect on the permanent prosperity and increase of population in the State. Care is not taken to preserve the land in a productive condition. By the method of cultivation, the soil is soon exhausted, and the planter, by lottery, draws another plantation, or purchases one at a low price, and leaves his own exposed to the washings of heavy rains which soon ruins much of the uplands. The new lands of Alabama and Mississippi, are more productive and less liable to injury; hence new settlers will prefer these States. The acquisition of new lands will secure a large increase for the present.

TABLE

OF SOME OF THE LEADING OBSERVATIONS AND DISCOVERIES IN MATHEMATICS AND NATURAL PHILOSOPHY.

THE following article, which we copy from the 'Companion to the British Almanac,' is intended to compress as much information as possible into a small compass. All doubtful matter is described as such, or is rejected. The discoveries which are doubtful, as to their time or author, are marked thus (?).

[Dates marked A. C. are before Christ, the others, the common era.]

ACOUSTICS. The doctrine of the different sounds of vibrating strings of different lengths, and the communication of sounds to the ear by the vibration of the atmosphere, probably first explained by Pythagoras, about A.C. The same mentioned by Aristotle, about A.C.

Date.

500

300

The conjecture of Aristotle first explained, or rather, perhaps, the theory of
sound rediscovered by Galileo

1600

Velocity of sound, first investigated by Newton, before

1700

[Theory perfected by Euler and La Grange, theory and practice reconciled
by La Place and Biot.]

Galileo's theorem of the harmonic curve, demonstrated by Dr. Brooke Taylor 1714
[The same further perfected by D'Alembert, Euler, Bernouilli, and La
Grange, at various periods of the 18th century.]

Speaking trumpet, said to have been used by Alexander
Constructed from Kircher's description, by Saland

Philosophically explained and brought into notice by Moreland

Constructed by Montgolfier

Filled with Hydrogen by Roberts and Charles, who made the first voyage
Parachute invented by Le Normand

A.C. 335

1654

1671

1755

. 1767

1782

1783

1783

ALGEBRA. Where first used, and by whom, unknown.
Earliest writing on, by Diophantus, probably about
Brought into Spain by the Saracens, probably about

Partial solution of cubic equations, by Scipio Ferreus, of Bologna
Further solution by Tartalea of Brescia (communicated to Cardan)
Solution of biquadratics, by Louis Ferrari

The introduction of general symbols for quantities whether known or un-
known, by Vieta, (the greatest step in the science)
Positive and Integral Indices, by Harriot and Descartes
Composition of the higher equations, by Harriot

Application of algebra to the expression of curves and use of indeterminate
quantities, Descartes

The binomial theorem of Newton, the basis of the doctrine of Fluxions, and
of the new analysis

[The subsequent improvements are very numerous, but they are individ-
ually small.]

ARITHMETIC.

1668

Where invented, unknown.

Said to be brought from Egypt to Greece by Thales, about
Oldest treatise on, known, by Euclid (7th, 8th, and 9th Books of his Ele-
ments,) about

ARITHMETIC, continued.

Greek arithmetical notation indefinitely extended by the octades of Archim-
edes

Sexagesimal arithmetic of Ptolemy, about

Simplified and brought very near to the principle of modern arithmetical
notation, by Apollonius, about
Notation by nine digits, and zero, known at least as early as the 6th century
in Hindoostan .

Date.

A.C. 220

130

220

600

900

1000

1050

.

1136 1202

1252

Introduced by Mohammed ben Musa from Hindoostan into Arabia, about
Generally used by Arabian writers in arithmetic and astronomy in the 10th
and 11th centuries

Probably introduced by them into Spain, about

The first known European work in which they appear, is a translation of
Ptolemy, (in Spain) in the year

Brought by Leonard of Pisa, from Bugia in Barbary, to Pisa, in
Probably circulated by the Alphonsine tables, in

This arithmetic generally cultivated by the Tuscans, in the 13th and 14th
centuries

Treatises on this notation (de Algorismo) published in many calendars in the
14th century: it was generally known and used in this country from the
beginning of the 15th.

Calendar in Corpus Christi Library, Cambridge, for 1380, contains an account
of them. Calendar for 1386, in English, contains them throughout. (This
almanac is very splendid, and is full of the astrological, astronomical, and
medical knowledge and prejudices of the period.)

The first monumental date in Arabic numerals, is on a brass plate in the
church at Ware, (on Ellen Wood)

Date in Caxton's "Mirrour of the World" (Arabic characters)
Date of the almanac of St. Mary's Abbey, Cupar, Angus

First printed book on algebra and arithmetic, by Lucas de Bargo, in
Introduction into the university registers in England, not before
First work printed in England on arithmetic, (de Arte Supputandi) by Ton-
stall, Bishop of Durham, in

Decimal fractions considered for the first time in La Disme of Stevinus,
published in

This work translated into English

Their theory and notation perfected by Lord Napier in his Rabdologia.
Continued fractions, by Lord Brounker, P.R.S.

[Since this, any alterations have been merely
ions have been merely formal.]

ARITHMETIC OF SINES. By Euler, about

[The theory had been hinted at by Christian Mayer in 1727.]

ASTRONOMY. Probably the first science studied; but when, or by whom, not
known. Cycle of the moon estimated at a very early period.

Observations at Babylon, transmitted to Aristotle by Callisthenes (according
to Porphyry,) about

La Place speaks confidently of Chinese observations
Eclipses of the moon observed at Babylon, with accuracy,
Globular form of the earth, the five zones, some of the principal circles of
the sphere, the opacity of the moon, and the true cause of lunar eclipses
taught, and an eclipse predicted by Thales of Miletus, about
That the planets are unconnected with the earth; that they are the habita-
tions of animated beings; that the fixed stars are the centres of other
systems; and that the earth moves round the centre of the system of the
world, maintained by Anaximander (the earliest philosophic astronomer
on record), who is also said to have been the inventor of maps and charts.
He was born about
A.C. 610
That the earth is a plane, and that the heavens are a firmament (oregaos),
or solid substance, like the earth, maintained by Anaximenes, who is said
to be the inventor of sun-dials (though probably only the introducer of
them into Greece.) He was born about
That the etherial, or upper regions of the atmosphere, were fire; that the
fire drew up from the earth, and ignited, masses of stone, which thus
became stars; that the comets were wandering stars; that the light of
small stars occasioned the white color of the milky way, and that the
moon is irregular in its surface, and habitable like the earth, maintained
by Anaxagoras-a meteoric stone that fell in Thrace, probably misled him
as to the etherial regions and the stars. His conjectures with regard to

VOL. VI.

3

A.C. 554