It would be impossible for us, in a work of this nature, to exhibit the scientic processes by which these irregularities in the planetary motions are explained, and their general cause investigated, and by which the effects of universal gravitation are completely developed; we shall therefore select one instance as an example of the rest, as exemplified in the Sun's action upon the Moon. This indeed is much simpler than the action of the planets upon each other; but the general method of resolving the action of gravity into forces acting either in the direction of the radius vector, or at right angles to it, may be adopted in them all. The solution of the problem relative to the force by which the Sun disturbs the motion of the Moon round the Earth is given with so much elegant simplicity by Professor Playfair, in the article Physical Astronomy, in the Supplement to the Encyclopædia Britannica, that we shall not hesitate to adopt it.

'The motion of the Moon round the Earth is disturbed by the action of the Sun; the gravity of the Moon to the Earth is increased at the quadratures, and diminished at the syzygies; and the areas described by the radius vector, except near these four points, are never exactly proportional to the times.'

'Let ADBC (Fig. 5) be the orbit, nearly circular, in which the Moon revolves, in the direction CADB, round the Earth.

Let S be the Sun; and SE, the radius of the Earth's

orbit, be taken to represent the force with which the Earth gravitates to the Sun.

1 1

Then

SE3

::: SE:

SM2

the force by which the Sun draws the Moon in the direction MS. Take

and let the parallelogram KF be described, having MG for its diagonal, and having its sides parallel to EM and ES. The force MG may be resolved into the two MF and MK, of which MF, directed towards E, the centre of the Earth, increases the gravity of the Moon to the Earth, and does not hinder the areas described by the radius vector from being proportional to the times.'

The other force MK draws the Moon in the di rection of the line joining the centres of the Sun and the Earth. It is, however, only the excess of this force above the force represented by SE, or that which draws the Earth to the Sun, which disturbs the relative position of the Moon and the Earth. This is evident; for if KM were just equal to ES, no disturbance of the Moon relatively to the Sun could arise from it. If, then, ES be taken from MK, the difference HK is the whole force in the direction parallel to SE, by which the Sun disturbs the relative position of the Moon and the Earth. Now, if in MK, MN be taken equal to HK, and if NO be drawn perpendicular to the radius vector EM produced, the force MN may be resolved into the two, MO and ON; the first lessening the gravity of the Moon to the Earth, and the second, being parallel to the tangent of the Moon's orbit in M, accelerates the Moon's motion from C to A, retards it from A to D, and so alternately in the other two quadrants.'

'Thus, the whole solar force directed to the centre of the Earth is composed of the two parts MF and

MO, which are sometimes opposed to one another, but which never affect the uniform description of the areas about E. Near the quadratures, the force MN vanishes, and the force MF, which increases the gravity of the Moon to the Earth, coincides with CE or DE. As the Moon approaches the conjunction at A, the force MO prevails over ME, and lessens the gravity of the Moon to the Sun. In the opposite point of the orbit, when the Moon is in opposition at B, the force with which the Sun draws the Moon is less than that with which he draws the Earth, so that the effect of the solar force is to separate the Moon and the Earth, or to increase their distance; that is, it is the same as if, conceiving the Earth not to be acted on, the Sun's force drew the Moon in the direction from E to B. This force is negative, therefore, in respect of the force A, and the effect in both cases is to draw the Moon from the Sun in a direction perpendicular to the line of the quadratures.'

ERRATUM

In the Volume for 1818.

Page 195, line 12, for Scorpio read Virgo.

The Naturalist's Diary

For DECEMBER 1819.

Now bleak DECEMBER chills with icy hand
The drooping features of the lingering year,
And warns the wildered wanderer of home.

RAIN and wind are now extremely prevalent, and, as the frost seldom sets in till the latter end of December, this month may be reckoned the most unpleasant of the whole year. Its gloomy character and soul-chilling effects, often applicable to its precursor, November, are well pourtrayed in the following little poem, by MALLETT:

A WINTER'S DAY.

Written in a State of Melancholy.

Now, gloomy soul! look out-now comes thy turn;
With thee behold all ravaged nature mourn.
Hail the dim empire of thy darling night,

That spreads slow-shading o'er the vanquished light.
Look out with joy; the ruler of the day
Faint, as thy hopes, emits a glimm❜ring ray;
Already exiled to the utmost sky,

Hither, oblique, he turned his clouded eye.
Lo! from the limits of the wintry pole
Mountainous clouds in rude confusion roll;
In dismal pomp, now hov'ring on their way,
To a sick twilight they reduce the day.

And, hark! imprisoned winds, broke loose, arise,
And roar their haughty triumph through the skies,
While the driv'n clouds, o'ercharged with floods of rain,
And mingled lightning, burst upon the plain.
Now see sad earth-like thine her altered state,
Like thee she mourns her sad reverse of fate!
Her smile, her wanton looks-where are they now?
Faded her face, and wrapt in clouds her brow!
No more th' ungrateful verdure of the plain,
No more the wealth-crowned labours of the swain;
These scenes of bliss no more upbraid my fate,
Torture my pining thought, and rouse my hate;
The leaf-clad forest and the tufted grove,
Erewhile the safe retreats of happy love,
Stripped of their honours, naked now appear;
This is, my soul! the winter of their year:
The little noisy songsters of the wing,
All shiv'ring on the bough, forget to sing.
Hail, rev'rend silence! with thy awful brow,
Be music's voice for ever mute-as now;
Let no intrusive joy my dead repose
Disturb-no pleasure disconcert my woes.

In this moss-covered cavern hopeless lard,
On the cold cliff I'll lean my aching head,
And, pleased with Winter's waste, unpitying see
All nature in an agony with me.

Rough rugged rocks, wet marshes, ruined tow'rs,

Bare trees, brown brakes, bleak heaths, and rushy moors,

Dead floods, huge cataracts, to my pleased eyes

(Now I can smile)-in wild disorder rise;

And now, the various dreadfulness combined,

Black Melancholy comes to doze my mind.

See! night's wished shades rise spreading through the air, And the lone hollow gloom for me prepare!

Hail, solitary ruler of the grave!

Parent of terrors! from thy dreary cave!
Let thy dumb silence midnight all the ground,
And spread a welcome horror wide around.-
But, hark!—a sudden howl invades my ear!
The phantoms of the dreadful hour are near!
Shadows from each dark cavern now combine,
And stalk around, and mix their yells with mine.
Stop, flying Time! repose thy restless wing;
Fix here nor hasten to restore the spring:
Fixed my ill fate, so fixed let winter be-
Let never wanton season laugh at me.

But every medal has its reverse. Whatever inconvenience may be experienced from the cold and gloomy days and long nights of winter, all is compensated by the cheerful blaze of the evening fire with the social circle around it. MILTON, in an exquisite sonnet, addressed to his friend LAWRENCE, adds this pleasing testimony to the attractions of a fire-side:

LAWRENCE, of virtuous father virtuous son,

Now that the fields are dank, and ways are mire,
Where shall we sometimes meet, and by the fire
Help waste a sullen day,-what may be won
From the hard season gaining? Time will run
On smoother, till Favonius re-inspire

The frozen earth, and clothe in fresh attire
The lily and rose, that neither sowed nor spun.
What neat repast shall feast us, light and choice,

Of Attic taste, with wine, whence we may rise
To hear the lute well-touched, and artful voice
Warble immortal notes and Tuscan air?
He who of these delights can judge, and spare
To interpose them oft, is not unwise.

An evening fire-side by twilight is thus well described in the Reflector:- How observed with the smallest effort is every trick and aspect of the fire! A coal falling in,-a fluttering fume,-a miniature mockery of a flash of lightning,-nothing escapes the eye and the imagination. Sometimes a little flame