of heat and drought. The same observation has been made at various part of the coast, so that a person circumnavigating New Holland would be witness in different places to the singular phænomenon of a hot, dry, and parching wind blowing from every point of the compass; a circumstance that appears to us altogether inexplicable, except upon the hypothesis we have ventured to suggest.

The supposition also acquires great additional probability from a contemplation of the nature of the different rivers, that disembogue themselves into the sea on the various coasts of New Holland. So long as it was possible, that a great river or straight might be found to divide it into two parts, from the gulf of Carpentaria to that which lies behind the islands of St. Peter and St. Francis, nothing could be predicated with certainty as to the deficiency of rivers in the interior; because it was possible that they might have drawn their sources from hills or mountains, situated beyond the actual researches of Europeans, and have emptied themselves into the supposed straight. But now, that Captain Flinders has ascertained that the island is (if we may use the expression) one continued and compact continent, and that all the rivers throughout its extensive coast are mere torrents, flowing in a contracted channel, with waters shallow in dry weather, but subject to sudden rises from the accession of land floods after heavy rains; that they exhibit, in short, every symptom peculiar to streams whose sources are at no great distance from their mouths; we cannot avoid the conclusion, that the interior of the country is altogether destitute of water.

"Nor springs nor rivers fertilize the land,

Which stretches far and wide-a wilderness of sand."

Lastly, if any doubt still lurked in our minds, we think it would be removed by the circumstance recorded in almost every page of the history of M. Péron's circumnavigation, viz. that the greater part of the coast is absolutely destitute of fresh water. Now, if this be so of the coast, à fortiori, it must be still more emphatically so of the interior; for we do not believe that the experience of any navigator will prove, that, where fresh water is not to be found in a country within a mile or two of the coast, a search further inland has ever been successful in procuring it. We have communicated our idea with respect to the interior of New Holland to an eminent geographer, who is of opinion, that the data on which it is founded afford fair ground for concluding that the fact is as we suspect.

So far as a judgment can be formed upon a review of the volume before us, we are compelled to express an opinion, that as

the History of a Voyage of Discovery, M. Péron's work is perfectly ridiculous. Not one accurate geographical description, scarcely a point marked down with precision as to its latitude and longitude, not a chart or map of any kind (except a plan of Port Jackson), not a well-founded pretension to more than a slight and cursory inspection of the shores, along which they coasted! In short, however well qualified the combination of talent might have been for the purposes of the expedition, when it left the port of Havre, so much havoc had been made by disease, so many of the most valuable sçavans had quitted the expedition in disgust at M. Baudin's brutality, that very scanty means of scientific observation remained, when the vessels arrived at the south and south-west coasts of Australia.

Charts indeed, and scientific observations, and accurate descriptions, are largely promised in a subsequent volume, of which even the table of contents is given at the end of this. But the first has now been published three years, and all we have heard of the second is as follows. A gentleman connected with the Imperial Institute, who was in London a short time ago, stated, that it was just printed, and the charts engraved; but that the government had laid their prohibitory finger upon the work, and suppressed its publication. Two reasons only could have induced Bonaparte to act thus: either he perceived some favourable expressions concerning our character and settlements in the East which displeased him, or he thought it more convenient to wait till the French author had had the benefit of perusing the work, and consulting the charts, with which Captain Flinders is about to favour the literary world. If M. Péron wrote the second volume, the amiable character which we understand he possessed makes the former supposition not improbable. But we are ourselves more disposed to attach credit to the latter. We think it more consonant with the modern French character and practice, in the departments of real science. Their characteristic qualities too often appear to be, great pretensions followed by very scanty execution, and attempts to raise up trophies to national vanity at the expence of the credit, and manufactured of the materials belonging to others.

This is emphatically the character of the volume now before us, and of the circumstances attending its publication, considered as a history of scientific and original discovery. As a desultory and entertaining ramble among a race of mankind little known, and rarely visited, a more favourable judgment may be given. With the exception of a few specimens of filth and indelicacy, which, we fear, are thought necessary to recommend the work to the debauched taste of Parisian readers, the descriptions

of savage life and manners are spirited and entertaining, and accompanied by engraved illustrations curious and well executed. Yet it cannot be denied, that the falsehoods and misrepresentations to be detected in the scientific departments throw a shade of doubt over the authenticity of the facts related in the lighter parts of the narrative, and go far to degrade it from the rank of a book of instruction to one of mere amusement. We are really sorry that a sense of impartiality compels us to rate so very low a work held out by the learned Imperial Institute of France, as surpassing in utility and importance the labours of all preceding navigators. We hope that the disappointment experienced on its perusal, will, ere long, be compensated by the real information and accurate knowledge, which Captain Flinders's work will impart to the world.

We trust that his work, when published, will be translated into French, and means taken to circulate it on the Continent, and if the charts are not already engraved, that French translations of the names will be inserted. We should be glad that foreigners should judge for themselves on the subject.

We have no fear that any impartial person, who, on perusing this voyage, will place beside him on his desk the works of Cook, Vancouver, Broughton, Captain Flinders, or any navigator of established reputation, or will hesitate to acquiesce entirely in the justice of our opinion concerning it's merits. We are persuaded that they will think that M. Péron's book is advanced fully up to its proper level, when placed in an English dress by the side of Sir John Carr's Tours, and other entertaining peregrinations, in an octavo collection of Voyages and Travels.

ART. V. Six Lectures on the Elements of Plane Trigonometry; with the method of constructing Tables of Natural and Logarithmic Lines, Cosines, Tangents, &c. By the Rev. B. Bridge, A.M. Fellow of St. Peter's College, Cambridge, and Professor of Mathematics in the East India College. 8vo. pp. 83. London. Cadell and Davies, 1810.

THE science of Trigonometry was invented for the solution of plane triangles; and though by the accession of new theorems it continued gradually to enlarge its bounds, yet for many ages no idea could be formed of the rank which it would one day hold in mathematical pursuits. It was reserved for modern times to exhibit all its resources; and the progress of knowledge has at length assigned to it a very high degree of dignity and importance.

By the introduction of algebraical reasoning, many formulæ have been deduced, which are of essential service in the higher departments of analytics, in the various branches of mixed mathematics, and in the solution of problems in physical astronomy.

Plane Trigonometry may be divided into two parts; of which the one treats of the solution of triangles, and the other deduces formulæ and illustrates their use. Though the solution of triangles must ever be considered as forming a distinct and material part of the subject, yet a treatise, which should now be confined to that object, would be justly esteemed defective. Many of the most useful formulæ can easily be obtained; and the illustration of their use in the construction of the trigonometrical canon and of the tables, if judiciously executed, will neither add much to the length nor to the difficulty of the work. In the present state of science, every treatise upon trigonometry should comprise some portion of trigonometrical analysis. The extent to which it may be carried in every instance must be left to the judgment of the writer, who will best understand the nature of his own work, and the object for which it is composed.

It is by no means necessary that every student should apply himself to those parts of the subject which are useful only in the higher branches of the mathematics. The physical astronomer and the proficient in analytics will be anxious to derive from trigonometry all the aids which the science can afford; it is therefore of importance that they should possess many formula, which to an inferior class of students are of very little service. They will also be anxious to arrive at their conclusions by the shortest method; and, since the geometrical process must be somewhere abandoned, they will seek to get rid of it as soon as possible. Where the principles are familiar, no conclusions can be more satisfactory than those which are derived from analysis. But a very slight experience will soon convince us, that works of this nature are but indifferently suited to the class of ordinary students. Their very form is repulsive; the reasoning may in itself be clear, yet to the beginner it will long appear to be involved in obscurity; and, though the conclusions be just, yet will they frequently be admitted rather from authority than conviction.

According to the system which prevails in our universities, and from which no material deviation can be made, when a young man is furnished with the first six books of Euclid, and a slight knowledge of equations, he is ushered into trigonometry. His mathematical ideas are yet in their infancy; and the application even of the sixth book of Euclid, connected with the new terms which he is required to adopt, will in general require as much attention as he is able to bestow. He has not yet learned to generalize; and the analytical method, if applied in all cases where it

can be applied, would present difficulties, which he is yet hardly qualified to surmount, and which are adapted rather to discourage than to promote exertion. A single instance will illustrate this remark.

The well known problem, which requires to express the sines of the sum and difference of two arcs in terms of the sines and cosines of the arcs, admits both of a geometrical and algebraical demonstration. In the geometrical, the values are determined by means of similar triangles; the memory is burthened with nothing extraneous, and the application of a few plain principles in the sixth book of Euclid will serve the purpose.

The investigation of the same result by analysis depends upon the recollection of expressions deduced from two former propo sitions; the first of which gives the value of the cosines, and the second of the sines of the angles, in terms of the sides. The proof for the sine of the sum of the arcs (to which we here confine ourselves, for the sake of brevity), runs thus:

Let A, B, C be the three angles of a triangle, a, b, c the opposite sides. Then by former propositions,

e+b+c

2

and Sin. B, where N2 = 4 ×

N ac

~a) (a+b+c_b) (a + b + c - c).

2

이

2

From

these expressions we have Sin. A. Cos. B + Cos. A. Sin. B =

and Sin.c
of an angle

Sin. A+B

2 a b c2

=

2 N c2 2abc2

Sin. (180°) A + B) = Sin. A + B, since the sine is equal to the sine of its supplement. Hence Sin. A. Cos. B + Cos. A. Sin. B. Q. E. D.

All this is perfectly legitimate; but how is it to be understood by a youth, qualified as we have already stated? It is not difficult to believe, that many a tyro might enable himself to write down the demonstration, who would find it a hard task after all, if a circle were drawn for him, to point out the arcs and the sines and cosines, respecting which he had reasoned.

The tendency of these observations is to shew, that one sort of book may be calculated for proficients, and another for beginners; that a rejection of geometrical proof in every case, where it can be rejected, is attended with inconveniences more serious than mere prolixity; and that the most useful work which can be presented to a student, who possesses neither extraordinary talents nor much knowledge of the subject, is one which consults perspicuity