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The Author gives us the medium result of fourteen separate determinations of the sun's parallax 8" 57, the extremes being 811 41 and 811 75. He also presents the reader with two tables, in one of which he exhibits the principal circumstances of all the transits of Vexus, from the year 902 to the year 2984, and all the transits of Mercury from 1605 to 1894. From these tables we shall extract all which relates to future transits, beginning with that which is to occur in the present year, but which, from some singular omission, is neither mentioned in the Nautical Almanac, nor the connaissance des Tems. These results cannot but be interesting to men of science; and possess tlris peculiar advantage, that being computed from modern tables of the sun and planets, they are much more correct than the results of Dr. Halley, which havc usually been presented in our Encyclopædias and other general repositories of scientific information.

The reader will observe that the times of conjunction, and of the middle of the transits, are given in the following tables for Paris. They will be reduced to the corresponding times for the meridian of London, by deducting 9 minutes, and 43 seconds, from each.

TRANSITS OF MERCURY.

Years.

Conjunc- Mean Geocentric Middle
tion. time. Longitude: True Time.

Semi-du. Shortest ratiou. listance.

hm

S 0 1815 11 Nov. 14 44 19 7 18 52 42 1822 of Nov. 14 2 34 7 12 6 53 1832 5 May 0 0 43 1 14 56 45 1835 7 Nov. 7 57 15 7 14 43 8 1845 8 May 8 3 39 1 18 1 49 1848 9 Nov. 8 1 47 7 17 19 19 1861 11 Nov. 19 29 54 719 54 44 1868 4 Nov. 18 53 6 13 9 42 1878 6 May 6 47 51 1 16 3 50 1881 Nov. 12 46 59 7 15 46 57 1891 9 May 14 54 18 1 19 9 1 1894 10 Nov. 6 36 26 17 18 22 9

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h m 1874 8 Dec. 16 17 44 1882 6 Dec. 4 25 44 2004 7 June 21 0 44 2012 5 June 13 27 0 2117 10 Dec. 15 6 37 2125 8 Dec. 3 18 40 2247 (1) June ( 30 23 2255 8 June 16 53 56 2360 12 Dec. 13 59 9 2368 10 Dec, % 10 2 2490 12 June 3 58 35 2498 9 June 20 21 2 2603 15 Dec. 12 54 16 2611 13 Dec. 1 11 12 2733 15 June 23 56 2741 12 June 23 43 59 2846 16 Dec. 11 53 15 2864 14 Dec. 0 13 29 2984 14 June 3 2 22

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13 51 N. 10 29 S. 11 19 S.

8 20 N. 13 ON. 11 28 S. 13 17 S.

6 23 N. 11. 49 N. 12 37 S. 15 14 S.

4 29 N. 1050 N. 13 20 S. 17 9 N. 2 35 N. 9 56 N. 14 12 S.

45 N.

3 53 23
3 7 24
1 54 10
3 56

9

The third volume, te which we must now proceed, comprehends eleven chapters, and treats of the following subjects : viz. stations and retrogradations of the planets; rotations of the planets ; aberration and annual parallax of the stars ; nutation ; displacing of the ecliptic, and different motions of the stars ; comets; satellites ; magnitude and figure of the earth; nautical astronomy; projections of the sphere; the calendar.

This volume, like the preceding two, abounds with elegant investigation, comprehensive deductions, and useful tables. "We can, however, select only a few particulars. The subject of aberration is important, hy reason of the striking confirmation of the Copernican hypothesis which it furnishes, and of the way in which correct formulæ for this species of réduction tend to give accuracy to astronomical observations. M. Delambre ex. hibits many theorems for aberration which are both simple and new; at least new to us, and to astronomers generally, although he assures us he has employed them for thirty years. We regret much that they are not of such a kind as can easily be presented in this analysis.

To the subject of comets the Chevalier devotes 275 pages. Besides the methods of Lambert, Olbers, Lagrange, Laplace, and Legendre, which he exhibits with considerable perspicuity, be gives an entirely new method of his own. He gives the expression for the anomaly and the radius vector, on the elliptic hypothesis, and all the theorems for cometary orbits, under a form of which the first term is the only one to be retained when the orbit is regarded as parabolic. Thus the student may always see what may be safely neglected, and if the parabola is insufficient, he may attempt several ellipses.

• Cette méthode,' he remarks,“ n'emploie que des opérations les plus usuelles de l'astronomie ; elle n'offre aucun calcul difficile ni Iong, les erreurs y sont presque impossibles, et quand on a trouvé une parabole approximative, on en peut corriger à la fois tous les élémens sur la totalité des observations, par le moyen des équations de condition, comme on fait pour les planètes. Ce moyen de recti- , fication me paraît plus simple, plus direct, et plus satisfaisant qu'aucun de ceux qu'on a proposés jusqu'ici, et qui sont tous fondés sur les méthodes de fausse position.'

The Author next presents a few speculations upon the nature of comets, and their tails; upon which, however, as if conscious he could throw no new light on that obscure subject, he does not dwell. He gives, what is much more valuable, some excellent tables for the orbits of comets, occupying 40 pages, and serving greatly to simplify both the direct and inverse problem concerning these bodies, which has so long perplexed astronomers. Here he acknowledges his obligations to the preceding labours of Barker and Zach, and seems by a comparison of their tables to have detected some errors in those of the latter astronomer.

The thirty-fifth chapter, on the figure and magnitude of the earth, may be regarded as a very comprehensive and valuable abridgement of the principal theorems and deductions in the celebrated · Base du Systeme metrique.' M. Delambre gives first a succinct history of attempts at ineasuring the earth ; then traces the plan of operation, and the best methods of computation, in reference to the triangles, azimuths, latitudes, compression of the terrestrial spheroid, terrestrial refraction, re. duction to the level of the sea, &c. He also points out the means of confirming or correcting the measurements of meri. dians by experiments on the lengths of pendulums, in different latitudes. We regard this as, altogether, one of the most interesting portions of Delambre's work.

The two last chapters contain an elegant treatise on projections of the sphere, and a dissertation on the calendar, in which some curious theorems are investigated by means of the indeterminate analysis. Among other irgenious rules and formulæ, we noticed those which have been proposed by M. Gauss, for the determination of Easter. They differ from all other rules we have seen, in this respect, that they are independent. We shall

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give them here, not merely as a matter of curiosity, but as of some utility.

'1. Divide the number of the year proposed by 19, and call the remainder a.

• 2. Divide the same number by 4, and call the remainder b. 6. 3. Divide it also by 7, and call the remainder c.

4. Divide (19a+M) by 30, and call the remainder d. . 5. Divide (25+4c+6d+N) by 7, and call the remainder e.

' 6. For the Julian Calendar, make M = 15, and N=6, conştantly.

M N * For the Gregorian Calendar, from 1582 to 1699 22....3

1700....1799 23

.3 1800....1899 23....4 1900....1999. 24. 5 2000. • 2099 24....5 2100....2199. 24....6 2200 2299.

25....0 2300. 2399. 26....1

2400....2499....25....1 6 7. You will have for Easter-day, either (22+dte) of March.

(d+(-9) of April. This rule is general for the Julian Calend ar ; in the Gregorian, there are only two exceptions.

. 1. If the computation give April 26th, substitute the 19th. • If it give

-April 25th, substitute the 18th.'. Suppose, to exemplify this rule, we find Easter-day for 1816. 1816 19.95 +11

11

209 19 19

23 1816 4.454+0

6 0 19 a+M 232 4

4 1816 7.259 +3

3 7

7 19 a + M 232 30.7 + 22

d 22 30 30

30 2 6+40+6d+N 0+12+132+4 148 7.21+1

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7 7 22+dte=22+22 +1= 45 March = 14. April. or dte-9= 22+ 1. 9 = 14 April, as before,'

Hitherto we have been speaking of M. Delambre's complete treatise in three quarto volumes. Of his 8vo. Abridgement we need not say much. It is conducted upon the same plan as the larger work, but with fewer details, fewer developments, fewer tables, fewer examples to illustrate the theoretical processes, and a less variety of methods. In the complete treatise, it was the object of the Author to give all which might be useful to the professed astronomer, except what relates to physical theory : in the Abridgement, he has restricted bimself to the exhibition of such theorems and processes, as may serve for one who wishes to obtain a correct idea of the science, without attaining expertness as an observer, and without tracing all the minuter points which would be examined with care by the profound investigator. In the publication of the two works, the Author followed a different course from what has been usually pursued, and permitted the Abridgement to appear about two years before the larger treatise from which it was extracted.

We shall conclude with two remarks. First, Although these volumes are by no means such as English readers in general will be inclined to regard as elementary, they are certainly not of difficult perusal. Let any one who is moderately conversant with geometry, analytical trigonometry, and the first principles of the Differential Calculus, set himself 'in good earnest to go through the Chevalier's longest investigations; and, how startling and formidable soever they may at first appear, he will find them comparatively simple. This arises from the Author's admirable perspicuity, and his true regard to logical order..

Secondly, We know of no work in which writers of all couptries are quoted, and their methods described, adopted, criticized, or amended, with so perfect a freedom from national partiality. M. Delambre seems to regard science as of no country, or we should rather say, of all countries. The English, Germans, Swedes, Italians, Spanish, Sicilians, men of all countries, and of all ages, are made to contribute to this great work : all are treated fairly; their talents are duly appreciated; the merits of their respective improvements and discoveries unhesitatingly admitted ; and every one who has in any measure promoted the science, if his labours are known to our Author, receives ample justice. This is truly an enviable example of candour!

On the whole, we regard the Chevalier Delambre's as by far the most comprehensive, methodical, and erudite treatise on astronomy which has yet appeared. Unfortunately, it abounds With press errors : but we have no doubt that the Author will soon be enabled to lay before the world a new edition in which these will be removed : we shall then regard his performance as one of the finest models of human genius and industry which have been produced in the nineteenth century,

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