Notwithstanding the striking points of dif ference referred to in the foregoing remark, the effects produced by the combination of the two constituent inequalities are identical in both cases as respects the law of variation, and are also nearly so in respect of absolute magnitude. This may be easily shewn in the following manner. Let AC represent the line of sizygees, B D the line of quadratures, E F the line of apsides, м the place of the moon in her orbit.

Let A TE, ATM = ( Hence A ETM = 0.

0=4.

B

M

$.

2 (40) A = 2 0 — (0 — 4) = 0 + Þ. Therefore ♪ = 6° 18′ sin a + 1° 20′ sin (2 (« — ©) — ▲),

=

6° 18′ sin (0) + 1° 20′ sin (0 + P),

D

4° 58' sin (0-4)+ 1° 20' sin (8-4)+1° 20′ sin (+), = 4° 58′ sin à + 2°‍40′ cos & sin 0.

=

The first of these terms is manifestly the equation of the centre as deduced by Ptolemy from observations of the moon in sizygees. The second term also represents the evection as it exhibited itself to that astronomer. Thus let us suppose the moon to be in either of the sizygees. In such a case 0=0, or 180°, and consequently the second term vanishes.

Hence 4° 58′ sin A.

Again, if the moon be in quadratures, we have = 90°, and therefore d4° 58' sin A+ 2° 40' cos

=

= 4° 58′ cos + 2° 40′ cos 4,

= = 7° 38′ cos .

In this case, then, the two inequalities conspire together. The effect is obviously a maximum, when = 0, or 180°. We have then

dy = 7° 38'.

These conclusions agree with Ptolemy's description, subject to a slight difference in the numerical values. Indeed the precision with which that astronomer determined the combined effects of the two inequalities in sizygees and quadratures, is one of the most astonishing circumstances connected with the ancient astronomy.

Since the evection as represented by Ptolemy has always the same sign in the quadratures as the equation of the centre, it is manifestly positive when the moon is revolving from conjunction to opposition, and negative throughout the remaining half of the orbit, or vice versa; according as the perigee is situate in the first and fourth, or in the second and third quadrants of the lunar orbit, counting from the point of conjunction in the direction of the moon's motion.

In order to determine the zero points of the evection as represented by modern astronomers, we have

sin (0 + 4) = 0;

0 =

- p, or 180° - P.

Hence it is manifest that by drawing G H, making with a c the same angle which E F makes with it, the extremities G, H, will indicate the zero points of the inequality.

It has been stated (p. 424) that Horrocks first explained the evection upon the Keplerian principles of astronomy, by supposing the eccentricity

of the lunar orbit to be variable, and attributing a libratory motion to the line of apsides. Allusion has also been made to the difficulty experi enced for some time in computing, by the theory of gravitation, the motion of the lunar apogee, upon which the inequality to a great extent depends. It is worthy of remark that in the original edition of the "Principia," published in 1687, Newton states that he computed the motion of the lunar apogee in sizygees and quadratures, and also the mean motion. He asserts that he found the daily progression in sizygees to be 23', the daily regression in quadratures to be 16, and the mean annual motion to be 40°. He remarks that these results do not accord exactly with the tables, a circumstance which he thinks may be attributable to the errors of the observations. The calculations being very intricate and embarrassed with approximations, and the results not possessing all the accuracy that was desirable, he refrained from publishing the details of his researches on the subject. (Computationes autem, ut nimis perplexas et approximationibus impeditas, neque satis accuratas, apponere non lubet.)

The results which Newton obtained on this occasion cannot by any means be considered very inaccurate, when the intricacy of the subject and the imperfect state of analysis in his time are taken into account. They give 11° 21' for the monthly progression of the apogee in sizygees, and 8° 1' for the monthly regression in quadratures. The modern tables of the moon assign, in round numbers, 11° and 9° as the corresponding values of the motion of the apogee. Newton found the mean annual progression of the apogee to be 40°; the modern tables of the moon make it 40° 40′ 32′′.

Newton appears to have been so dissatisfied with his researches on this subject, in all probability from the circumstance of the results not presenting a more complete accordance with those deducible from observation, that he suppressed all allusion to them in the second edition of the "Principia," published in 1713, under the superintendence of Cotes. Whatever may have been the method of investigation employed by him on this occasion, it was manifestly one which was capable of grappling with the main difficulties of the question. It is not improbable that a careful inspection of those manuscripts of Newton, which are still in existence, might serve to throw some light on this interesting point.

V.

NOTE RESPECTING HORROCKS.

At page 421 I have hazarded the conjecture that it was duties of a religious nature which called away Horrocks so peremptorily, while engaged in looking out for the transit of Venus on the 24th of November, 1639. This is confirmed by a note which the late Prof. Rigaud discovered in one of Hearne's Memorandum Books preserved in the Bodleian Library, Oxford, from which it appears that Horrocks was a hard-working curate at Hoole, subsisting upon a wretched pittance (Rigaud's Correspondence of Eminent Men of the Seventeenth Century, vol. ii. p. 112). It appears also, from one of Flamsteed's letters to Collins, contained in the same work, that Crabtree's death occurred in the year 1652, and not shortly after that of Horrocks, as Wallis erroneously stated in the dedicatory epistle to Lord Brouncker, inserted at the commencement of the "Opera Posthuma" of the latter.

VI.

ACCOUNT OF SOME RECENT RESULTS OF ASTRONOMICAL OBSERVATION.

Two instances of a total eclipse of the sun have recently furnished opportunities of observing the circumstances usually attending these phenomena. The first of these eclipses happened on the 8th of August, 1850. It was visible only in the Pacific Ocean. An account of the phenomenon as observed by M. Kutczycki at Honolulu, the chief town of the Sandwich Isles, appeared in the Comptes Rendus for the 21st of April, 1851. The second eclipse happened on the 28th of July, 1851. Being visible in the northern countries of Europe, it was observed by a great number of astronomers. Two important facts were satisfactorily estab lished by the observations of these eclipses. In the first place, the reddish protuberances usually visible on such occasions, appeared in some instances to be isolated from the moon's limb. Secondly, those protuberances that were visible towards the point of immersion, were seen gradually to diminish as if concealed by the passage of the moon over the solar disk; while, on the other hand, those towards the point of emersion appeared to enlarge as if gradually disclosed to view by the same cause. Both these facts tend to support the opinion that the protuberances are solar phenomena. A serious difficulty attending the explanation of their physical cause, consists in the material difference of aspect which they exhibit to spectators distant from each other by only a very short interval.

Five more planets revolving between the orbits of Mars and Jupiter, have been discovered in addition to those referred to in the body of this work (see p. 240). Three of these bodies were discovered in the year 1850. The first (Parthenope) was discovered by De Gasparis on the 11th of May; the second (Victoria), by Hind on the 13th of September; and the third (Egeria), by De Gasparis on the 2nd of November. The remaining two planets were discovered in the course of the year 1851. The first of these (Irene) was discovered by Hind on the 19th of May, 1851. By a singular coincidence, De Gasparis also independently discovered this planet on the 23rd of the same month. The second planet (Eunomia) was discovered by De Gasparis on the 29th of July. Parthenope revolves round the sun in 1401 days, Victoria in 1303 days, Egeria in 1496 days, Irene in 1510 days, and Eunomia in 1424 days. These numbers, of course, can only be regarded as provisional. The total number of asteroids now discovered amounts to fifteen. It is not improbable that hundreds of these minute bodies may be revolving in the same region.

On the 4th of December, 1850, intelligence reached this country that on the 15th of the previous month, Mr. Bond, Director of the Observatory of Cambridge, U. S., had discovered a new ring round Saturn, interior to the bright rings already known to exist. It soon turned out that the same phenomenon had been observed in England by Mr. Dawes on the 29th of November, before he received any intimation of Mr. Bond's discovery. The most surprising circumstance, however, connected with the phenomenon is, that it was actually observed as early as the year 1838, by Dr. Galle of Berlin; although no further notice seems to have been taken of it till the announcement of its rediscovery as above mentioned. The ring now forms an interesting object of observation to astronomers armed with powerful telescopes. In brightness it is very much inferior to the outer rings. Its breadth is equal to about two-fifths of the interval included between the bright rings and the body of the planet. It would

appear from most of the observations that it is not a distinct appendage of the planet, but simply a continuation of the inner bright ring.

On the 24th of October, 1851, Mr. Lassell discovered two new satellites revolving round Uranus. He has subsequently succeeded in seeing them with his powerful reflector, on every occasion on which he looked for them. He finds that the observations may be pretty well satisfied by supposing the period of the inner satellite to be 2.506 days, and that of the outer satellite to be 4.150 days. It appears, therefore, that they are interior to the two bright satellites discovered by Sir William Herschel in 1787. From the diagram of their positions inserted in the Monthly Proceedings of the Astronomical Society for November, 1851, they appear, like the other satellites, to revolve in orbits nearly perpendicular to the plane of the ecliptic.

It has been mentioned (p. 139) that a comet discovered by M. Faye, in the year 1843, was found to revolve in an elliptic orbit, and that its perturbations for the ensuing revolution were calculated by Le Verrier, who arrived at the conclusion that its passage through the perihelion would take place on the 2nd of April, 1851. It is a gratifying fact that the comet has actually returned at the appointed time. It was first seen by Prof. Challis, with the Northumberland refractor, on the 28th of November, 1850. The observations of its apparent position have been found to present a remarkable agreement with the corresponding results derivable from the calculations of M. Le Verrier.

Allusion has been made at page 243 to the discovery of a small ultrazodiacal planet (Metis) at the observatory of E. Cooper, Esq., of Markree, in the north of Ireland. An achievement of vastly greater importance has since emanated from that observatory in the shape of a catalogue of 14,888 stars near the ecliptic, the places of which, in general, are not to be found in any catalogues hitherto published. This catalogue was constructed from observations made in the years 1848, 1849, and 1850, and was published in 1851, the expense of printing' having been defrayed by the Government, upon the recommendation of the Royal Society. A second catalogue, destined to contain the places of about 12,000 additional stars, observed in the year 1851, is in the course of preparation at the same observatory. Mr. Cooper and his active assistant, Mr. Graham, are also engaged in executing a series of celestial maps upon a magnificent scale. Each map has a range of 8° both in right ascension and in declination. The scale is four times larger than that of the Berlin maps. It is contemplated to insert in these maps all the stars within their range which have either been observed at Markree, or have been already published in other catalogues. The epoch of reduction is 1850.0. The advantages which cannot fail to accrue to astronomical science from the construction of these maps is incalculable. It must be acknowledged that the labours at Markree Observatory exhibit a loftiness of aim as well as a unity of design, and a spirit of skilful perseverance, which not only serves effectually to remove that establishment from the category of mere amateur observatories, but entitles it to an honourable place in the highest class of those institutions that have been founded for the promotion of astronomical science.

In concluding this note it may be stated, that the Astronomer Royal has now (February, 1852) completed the arrangements at the Royal Observatory for recording transits of stars by means of an electro-magnetic apparatus. The accuracy of this method may be relied on to the twentieth

of a second of time. It is contemplated, in connexion with this improvement, to transmit Greenwich time, by means of the electric telegraph, to all the most important places in the kingdom. The realisation of this project will constitute a boon of inestimable value to the outports, by affording on all occasions a reliable standard for the regulation of chronometers. The successful construction of the submarine telegraph between Dover and Calais will also enable the Royal Observatory to record transits simultaneously with the Royal Observatory of Paris and other similar establishments on the Continent, by which means their respective longitudes relatively to each other may be more accurately ascertained. The immense importance of this object must be obvious to any person who possesses an ordinary acquaintance with astronomical

science.

VII.

COPY OF THE NOTE OF THE OBSERVATION OF y DRACONIS, made by Bradley, at Kew, with the zenith sector of Molyneux, on the 21st of December, 1725; the discordance of which with the results of previous observations, revealed to him the first glimpse of his immortal discovery of the Aberration of Light.

It has been mentioned at page 337 that the original note of the observation, of which the subjoined words are an exact copy, was found a few years since by Prof. Rigaud, among the manuscripts of Bradley, written upon a loose piece of paper.