peror may declare the property hereditary; a parent may give the income of any part of his disposable property to any of his children for his life, with a limitation of the property itself to their children; and a person dying without issue may, in like manner, give a life interest to any of his brothers or sisters, and may direct the substance of the property to vest, at their deaths, in their children.

These are the principal regulations in the present Code respecting inheritance and successions. It is observable that it confines representation within the twelfth degree. Whether consanguinity should, in respect to succession and inheritance, be universally extended, was a great question both among the antient and among the modern civilians; the former contended for limiting it within the 10th degree, and the latter for its universal protraction ;-the early canonists generally confined it to the 7th degree. In England, unlimited consanguinity is allowed in respect to the right of succession: but, in some other legal rights, it is confined to the fourth degree. Thus, in writs brought to recover landed property by persons claiming in the character of cousin, no one can maintain this writ if his common ancestor be removed higher than the father of the great-grandfather; that is, unless the common ancestor be within four degrees of the claimant. A good reason against unlimited consanguinity does not present itself to us; and we are at a loss to discover any ground for confining it to the twelfth degree. Henry IV. stood in the twenty-fourth degree of consanguinity to Henry the Third, his immediate predecessor.

One of the most interesting discussions in the Code before us arises on the nullity of Sales for inadequacy of price; or, to use the language here adopted from the Roman law," the rescision of a sale on account of Lesion.” The Roman law considered the sale to be void, if the property was sold for less than one half of its worth: but the equity of this law was a subject of much dispute among the civilians. One of the greatest objections to it is, that the seller and the purchaser stand in the same predicament to each other, and are equally intitled to the justice and the favour of the law; and therefore, if inadequacy of price should authorize the seller to annull the contract, excess of price should equally authorize the purchaser to set it aside. The Chief Consul contends for the rescision of

the contract. H's strongest argument is, that the seller should be more favoured by the law than the purchaser, because the seller is forced to the sale by his wants, and his family is injured by it: but the purchaser is perfectly free, and has the whole profit of the contract. The advice of the Chief Consul prevails;

prevails; and the Code orders that, if the property be not sold for five-twelfths of its value, the seller shall be intitled to an action for the rescision of the sale, though he has expressly renounced his right to this action in the contract of sale: but the action must be brought within two years after the contract; and the law extends only to the sale of real property, and to no sale by public auction.

In civil concerns, Imprisonment is confined to some cases of gross fraud, and of gross breach of trust, which are particu larly enumerated. In all cases of debt, the person of the debtor becomes free by his making over all his property to his creditors but this does not extinguish the debt; so that the future acquisitions of the debtor are still liable to the demands of his creditors. We think that this legislative provision deserves the serious consideration of every country in which imprisonment for debt is allowed. It is obvious that this imprisonment inflicts wretchedness on the sufferers, deprives the public of their industry, and makes them a heavy and destructive weight on the state: while the Code Napoleon restores them to comfort, gives the public the benefit of their toil, and frees the state from the burthen. Surely, then, the addition of physical and mental strength, which a state acquires by the abolition of imprisonment for debt, must be very great; and this advantage should not, for want of reflection, be presented by us to Bonaparte.

Towards the close of the second volume, we have an inte resting discussion on the registration of Mortgages. By the Roman law, no publicity of a mortgage was necessary for its validity; and it should seem that the law of France, which required this publicity, was of a recent date. The Code before us prescribes a particular form of publicity, as necessary for the legal validity of a mortgage.

In our opinion, the Code Napoleon does honour to the persons by whom it was compiled. The general arrangement of the work appears to be very good: the divisions and subdivisions seem to be produced by the subject; and the attention of the reader easily follows them. The style is unaffected, nervous, and clear, and is perfectly free from the metaphysical subtlety and pomp of phrase with which the Institutes of Justinian are truly reproached. It evidently was the object of the compilers to effect a simple system of legislation; and, so far as we are able to judge, they have attained their object. The Discussions are also creditable to the parties, and the First Consul appears no where in a disadvantageous light. We certainly discover no thing assumed or overbearing in his manner; his expressions are sometimes quaint, and his language and turn of thought

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have

have occasionally something of that peculiarity which marks his state papers: but generally his conceptions are just and his language is clear, and he always appears inclined to take the liberal side of the question. If the literary intercourse between the countries could be renewed, we shall endeavour to furnish ourselves with such works as will enable us to lay before our readers a complete view of the Napoleon legislation.

ART. II Mémoire sur la Relation, &c. ; i.e. A Memoir on the Relation subsisting between the respective Distances of any five Points whatever, taken in space; to which is added an Essay on the Theory of Transversals. By L. N. M. CARNOT, of the French National Institute, &c. 4to. pp. 111. Paris. 1806. Imported by De Boffe, London. Price 8s. sewed.

EVE

'VERY plane figure is divisible into triangles, and therefore geometry of two dimensions may be made to depend on plane trigonometry alone: but science is extended by the theorems which express the relation between four points taken in the same plane. Moreover, in geometry of three dimensions, since every solid may be decomposed into triangųlar pyramids, and since a triangular pyramid has four solid angles, the relation between four points taken in space is sufficient in such geometry: but, passing beyond what is merely sufficient, we shall enrich geometry by determining the relation that exists between any five points taken in space; and it is this relation which M. CARNOT endeavours in this tract to establish, or, to speak more exactly, to represent by simple and regular formula.

The number of combination of five things combined two and two is = 10; and nine being given, the tenth may be determined. Previously to the solution of this general problem in geometry of three dimensions, M. CARNOT solves several preliminary and subsidiary problems; which, however, as he observes, are by themselves interesting; such are, to express in values of the sides alone of a triangular pyramid, all the parts that enter into the construction of that pyramid, that is, the angles which the sides form with each other, or with the faces, the radius of the inscribed and of the circumscribed sphere, &c.-To prevent references to other works, the author prefixes certain triogonometrical formulæ, such as b2 + c2 — a2 (A, B, C, angles; a, b, c, opposite sides)

Cos. A

2bc

√(2 a2 b2 + 2 a2c2 + 2b2 62—a'—b1—6°) &c.

but

but he gives these formula without demonstration, and therefore, to a reader who in his progress wishes to make every step sur, reference to other works, or the enterprize of investigation, will become necessary. As M. CARNOT gave the above forms, we are rather surprized that he did not express their formation by means of factors: thus, in the preceding expression for sin. A, the quantity under the vinculum

= (a + b + c) (a+b−c) (a + c—b) (b + c—a) ;

so that, by the aid of factors, the area of the triangle, the radii of the inscribed and circumscribed circles might have been expressed. We mean only that these latter expressions should have been added, not that they supersede the use of those which the author has inserted; for, in many instances, his expressions, considering the end in view, are under the most convenient form.

In the pages preceding the 48th, several questions relating to pyramids &c., which some may esteem curious, are discussed; and at the latter page we arrive at the formula which expresses the relation between ten lines that join, two and two, any five points taken in space, so that nine being given the tenth may be found. This formula is so far from being concise, that it contains 130 terms: but many of the terms are formed after the same law, and are symmetrical; thus if s and are opposite edges, then of quantities such as st s we have fifteen. Again, of quantities such as " there are 30, and so on: so that putting F. G, &c. to represent such collections, M. CARNOT arrives at this formula:

F-2 G+ 4H-2 K+ 2 L = 0.

This extremely remarkable formula (says the author), and which is the particular object of this memoir, gives the solution of a multitude of difficult questions. For instance, this; four points being given in space, to find a fifth point from which the distances. from the first four are in a given ratio, or which have among them any other given relation. Again: four spheres being given in space, to find a fifth which shall be tangent to the four others, or which shall cut off from them given arcs.'

The second tract in this thin quarto is an essay on the theory of transversals; and a transversal, according to the author's own definition, is a straight line or curve that traverses, after any manner whatever, a system of other lines, either straight or curved, or even a system of planes or of curve surfaces. This theory of transversals, he says, is in itself curious, and often furnishes very elegant demonstrations. A person who has paid much attention to any subject, and add

ed

ed to either its variety or its extent, naturally becomes enamoured of it, and speaks of it in terms which to a less interested reader seem rather ex ravagant. In this predicament, we should say, M. CARNOT himself stonds. He speaks much of the importance and curiosity of the subjects of his disquisition; yet, after no very negligent perusal, we cannot discover the precise nature or magnitude of the benefits conferred on science by the relation between five points,' and the theory of transversals. Is physical astronomy, or is any part of physics mathematically treated, benefited? Or can the registered formulæ be drawn forth on some future occasion, for the use and improvement of the arts? We rather think, but we do not mean hence to depreciate them, that these investigations, with regard to their importance, are to be placed in the same rank with the multiplied properties of the conic sections with which some treatises abound. With regard to the curiosity of the investigations as a source of amusement, we must confess, whatever cause may be assigned for the fact, that to us the entertainment afforded by these pages has been rather dull; and indeed, on the score both of profit and amusement, we place the author's little tract on the Metaphysics of the infinitesimal Calculus before the present, as well as before the formidable quarto on the Geometry of Position which we noticed in our last Appendix.

ART. III. Exposition des Opérations, &c.; i. e. An Exposition of the Operations performed in Lapland, for the Determination of an Arc of the Meridian, in 1801, 1802, 1803. By Mess. Ofverbom, Svanberg, Holmquist, and Palander; the whole drawn up by Jons SVANBERG, Member of the Royal Academy of Sciences at Stockbolm, &c. and published by the Academy of Sciences. 8vo. Stockholm.

THE

HIS volume describes the operations, together with their result, which were conducted for measuring an arc of the meridian, before measured in 1736 by Clairaut, Celsius, Maupertuis, &c. In those preceding operations, the la

titudes of the two extremities of the arc were determined by means of a zenith sector of Graham, and of observations made on and a Draconis. Yet, notwithstanding the fame of the artist and the tried skill and science of the observers, the Swedish and other astronomers have suspected the accuracy of the measurements; because, if we assume such measurements, the ratio of the diameters of the spheroid will come out different from the ratio afforded by operations conducted with the greatest nicety in France and elsewhere.