:

advanced then, which have not been maintained both in theory and practice, ever since the time of Xenophon. The conduct of the English ministry can be defended on the rule laid down by Grotius, and supported by Zouch and Buddoeus liceat locum occupare, qui situs sit loco pacato, si non imaginarium sed certum sit periculum ne hostis cum locum invadat et inde irreparabilia damna det.* Zeiglerust thinks the right exists, but that caution should be used in the exercise of it. The majority of writers on the law of war, so far as we have examined them, are of the same opinion, and Heineccius‡ in particular, declares that the right cannot be denied. Hic sane nos jure nostro uti nemo negabit.

Bynkershoek's Quaestiones Juris Publici were never before fairly translated into English. Lee's Essay on Captures, professing to be" an enlarged translation" of this work, is a treatise of equivocal value, which has no merit as a translation because extraneous matter is frequently thrust into the text without acknowledgement, and little as a law book, because he seldom ciies his authorities, and in both capacities is completely superceded by the labours of Mr. Du Ponceau. His translation, though sometimes stiff, and almost always diffuse, is faithful and impartial. It is introduced by an able preface, and accompanied by a body of notes, which we wish had extended through the whole, instead of being confined to the last fourteen chapters. The tables and indices are copious and accurate. Mr. Du Ponceau has occasionally omitted long passages, and once an entire chapter, because their value was merely local. The reason is sufficient; but the right should seldom be exercised. We do not mean to complain, but we should not have been displeased had he translated the whole. We must, however, confess our dissatisfaction at his frequent interpolations. In the following passages, the words which are italicized, have no counterpart in the original.

"Whenever men are formed into a social body, war cannot exist between individuals, the use of force between them is not war; but a trespass cognizable by the municipal law." Chap. I.

"But when the Roman consuls wrote to king Phyrrus: We do not wish to contend with you by means of bribery or fraud, and at the same time gave him notice of the offer that had been made to poison him, they certainly did an act of the greatest generosity." Chap. I.

* De Jur. Bel. et Pac. 1. 8. c. 3. § 11.

† Page 332.

+ Page 260.

After Bynkershoek has been speaking of the lex talionis of princes, Mr. Du Ponceau inserts a reflection which is very proper in itself; but has no right to its present station.

"It is thus that princes, though bound by no positive law, enforce upon one another the law of reciprocity." Chap. III.

Owing probably to an error in his text book, he has translated in mores Gentium, cap. 2. "customs handed down by the Germans."

We forbear all verbal criticisms, although it would be very easy to select many exceptionable passages from a work of this size, and in the trifling defects we have noticed, we have endeavoured to avoid all acrimony. We do not wish, however, to disguise the pleasure we feel at receiving a work of Bynkershoek's in a respectable English dress, and we sincerely hope that this is not the last time we shall meet Mr. Du Ponceau in the character of a jurist.

DEFENCE OF THE REVIEW OF MR. LAMBERT'S MEMORIAL.

OUR review of Mr. Lambert's Memorial, in October last, has produced an answer from that gentleman, published in the Chronicle, and also in a pamphlet which has been forwarded to us. In this answer he is very liberal in his charges of "twistical cunning-ingenious quibbling-sophistical evasions-subtle prevarications-local and political prejudices-zeal for the honour of the British nation, and the convenience of British mariners-and has the assurance to insinuate that in our review we were endeavouring to promote the dignity and influence of a foreign nation, to the prejudice of our own," &c.

Charges like these are beneath our notice, and the manner in which Mr. Lambert has chosen to treat the subject, might justify us in passing over his answer with silent contempt: but as the object is of considerable national importance, and as Mr. Lambert has among his illiberal reflections undertaken to contradict some of our statements, and roundly asserted that the remarks we made on some of his rules, are wholly destitute of truth, we have thought it our duty to exhibit such proofs and authorities as will fully substantiate our observations in the minds of all scientifick men.

In page 261 of our review, we stated that the angle formed at the star by the vertical circle, and circle of declination, was

called the angle of position by Mr. Lambert, contrary to the definitions of the greatest astronomers. This assertion Mr.

Lambert (6 says seems to be either gross ignorance in you, or a wilful perversion of the truth. I call the angle opposite to the latitude of the place, (or rather its complement to 90°) the angle of position, not contrary, but in conformity to the appellation given it by the greatest astronomers.”

On this point we shall bring proofs of Mr. Lambert's incorrectness, from two of the most celebrated works on astronomy extant. To facilitate the understanding of this question, we shall suppose, on a celestial globe, the point corresponding to the zenith of the spectator to be marked with the letter Z, the pole of the equator by P, the pole of the ecliptick by E, and the place of the sun, moon, or star, whose angle of position is to be found, with the letter S. Great circles being drawn through these points, the angle of position according to Mr. Lambert is the spherical angle PSZ,* whereas by the usual definition it is the spherical angle PSE, formed at the star S, by the circle of latitude ES, and the circle of declination PS. For Vince, in his System of Astronomy, Vol. I. page 7. Def. 53, edition of 1797, 4to. says, "The angle of position is the angle at an heavenly body, formed by two great circles, one passing through the pole of the equator, and the other through the pole of the ecliptick," or in other words, it is the angle PSE, as we have defined it. The same author has once in his work, (Vol. I. page 535.) employed the term angle of position differently, (and as Mr. Lambert has used it,) but at the same time he apprizes the reader that he there

To prevent any dispute about this, we shall quote Mr. Lambert's rule for calculating that angle, in page 12.

Arith. comp. cosine true alt. +log. sine horary angle+log. cos. lat. place=log. sine ang. position. Or sine ZS: Sine SPZ:: Sine PZ: Sine Angle of Position. Now the usual rules of sphericks applied to the triangle SPZ, give Sine ZS : Sine SPZ:: Sine PZ: Sine PSZ. Hence PSZ is the angle of position as defined by Mr. Lambert.

+ In page 41 of the same volume, Vince gives this rule for calculating the angle of position; Sine PS: Sine PES :: Sine PE: "Sine angle of position," which angle is therefore equal to PSE agreeable to his definition.

uses it in a peculiar sense, and expressly states (in page,536) that the angle "ZSP which is here called the angle of position, is not the angle generally understood under this appellation." In the second volume of the same work, he has given three tables for calculating more easily the angle of position, agreeably to the common acceptation of the term, and to his 53d definition. If farther proof of the correctness of our assertion were wanted, we might quote the words of La Lande, an authority equal to any in a point of this kind, since all (or nearly all) the terms of astronomy are the same in the French as in our language. In Vol. I. page 380 of the third edition of his astronomy. 4to. 1792, he says "In calculating eclipses we make use of the angle formed at the centre of the planet by the circles of latitude and declination, which is called the angle of position, because it is a fixed angle, depending only on the position of the planet with respect to the ecliptic and equator," &c.* which is directly contrary to Mr. Lambert's assertion.

Having shewn by these authorities that Mr. Lambert was wholly mistaken in his objections to this part of our review, we shall proceed to examine another. We observed in page 262 of our review, that the formula for calculating the moon's parallax, page 13, contained a term depending on the cosine of the moon's latitude, which it ought not to do. On this Mr. Lambert, with his usual modesty, triumphantly remarks

Where did you obtain this information, gentlemen reviewers? You had better consult your books again, and see whether the moon's true latitude is not a necessary element in and for the computation. I contend that it is, your positive assertion and high authority to the contrary notwithstanding. You seem to be determined to impose on others, or on yourselves, by some of your critical remarks."

*The original is thus "On se sent, dans le calcul des eclipses, de l'angle formé au centre d'un astre par le cercle de latitude et le cercle de declinaison : qu'on appelle angle de position, parceque c'est un angle fixé qui ne depend que de la position de l'astre, par rapport à l'ecliptique et à l'equateur et qui designe lui-meme la position des principaux cercles qui se coupent au centre d'une etoile." In the same page La Lande gives a rule for finding this angle, which is in substance as follows. Cos. lat Cos. Right Ascension:: Sine 23° 28': Sine Angle Position agreeably to his definition.

We shall make no other reply to these observations, than that of proving Mr. Lambert to be wrong by applying his own rule* to a simple example where the moon is supposed to be in the same longitude as the nonagesimal, or in the great circle passing through EZ. For it is well known that when the object is in that situation, (whatever be its latitude) the parallax in latitude is equal to the parallax in altitude, consequently the sines of these angles must also be equal, and this is agreeable to what Mr. Lambert himself says in page 9. Now when the object is thus situated, the angle between the parallel to the ecliptick and vertical circle is evidently equal to 90°, and its log. sine is equal to radius. Substituting these in Mr. Lambert's equation (quoted in the note below) and reducing it by neglecting the terms that destroy each other, we have Arith. comp. log. cos. 's lat.log. radius.

Whence it would follow that the moon's latitude is at all times equal to nothing, because the moon is at every moment in the

*This rule, as given in page 13, is as follows.

"Log. sine parallax in altitude+log. sine angle between vertical circle and parallel to the ecliptic+arith. comp. log. cosine 's true latitude=log. sine parallax in latitude nearly approximated..

"If the moon's true latitude be north, subtract the approximated parallax in latitude therefrom, for the moon's apparent latitude approximated; then

"Log. sine parallax in altitude+log. sine angle between vertical circle and parallel to the ecliptic+arith. comp. log. cosine moon's apparent latitude approximated=log. sine parallax in altitude farther approximated and very near the truth.

"Repeat the process, using the moon's apparent latitude last found, and the correct parallax in latitude will be obtained."

Now we assert that this repetition of the process is wholly wrong, and that the correct rule upon the principles assumed by Mr. Lambert, is simply this.

Log. sine par. in alt.+log. sine angle of vertical and parallel to the ecliptic log. sine par. in alt. as may be proved from what is said by La Lande in Vol. II. page 295 of his Astronomy, by Vince, in pages 65, 66, Vol. I. of his System of Astronomy, or by President Willard, in Vol. I. pages 13, 14, of the Memoirs of the American Academy of Arts and Sciences.