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stationary. After which, it will increase; and the ecliptic will recede from the equator, in the same manner as it approached it; these alternate states producing perpetual oscillations between fixed limits. These limits, however, have not yet been accurately determined; but, according to the constitution of the planetary system, their existence has been demonstrated, and they are confined within a narrow compass. Hence it may be safely affirmed, contrary to the opinion of the antients, that the ecliptic never did, nor ever will, coincide with the equator; and this furnishes one among the numerous instances in which the incomprehensible wisdom and goodness of Creative Power are displayed, in providing for the stability of his works.
What has hitherto been observed relates only to the slow and secular diminution of the obliquity of the ecliptic. But this obliquity experiences other small oscillations, which cause it to deviate from its mean value in contrary senses; or so as to be sometimes more than this value, and at others less than it. The most considerable of these oscillations is accomplished in a period of about eighteen years; that is, in that period, all that depends upon this inequality is compensated, and there remains only the general and constant effect of the progressive diminution. The law of these small oscillations has been derived from observation, and theory has explained the cause. These oscillations are produced by the action of the Moon, and constitute part of the phenomena called nutation. There is also a small effect of the same kind produced by the Sun; but its quantity is much less, and its period half a tropical year.
We may take this opportunity of observing, that all the elements of the system of the world experience variations like the obliquity of the ecliptic, which are of two kinds; the one, so slow in their progress, that they are only to be ascertained by comparing the tient observations with the modern. For this reason
they are called secular inequalities. The others are more rapid in their march, and return to the same state, after small intervals of time; and astronomers have already observed several of their revolutions. These are called periodic inequalities, in order to distinguish them from the preceding, which, though they are periodic, are comprised within limits incomparably more extensive'.
For the sake of such of our astronomical readers as may wish to see the method of calculating these two kinds of ine qualities, we shall here insert the following formulæ, reduced from the Mécanique Celeste, tom. iii, page 158. The year 1750 was rendered celebrated by the labours of Lacaille, and has, on that account, become the origin of almost all astronomical determinations. The mean obliquity of the ecliptic, or that corrected for all the small periodic oscillations, was then 23°-47308. Let V denote the value of this obliquity, at any number of Julian years from that epoch; it being negative before and positive after that time. Then the secular inequality will be expressed by this formulæ, viz.
V=23°.47308-0°.929736 sin t 32".11575-0°.661788 sin2 t 6".97323.
As to, at the commencement of the period, or at 1750, all the terms of this formula vanish except the first, which consequently gives the obliquity for that epoch. When t is negative, they all become positive, which shows that the obliquity increases as we ascend from that time; and when t is positive, all the terms except the first are negative, which evidently shows the diminution. Making t equal to unity at any time, and the expression for V will give the annual variation in the mean obliquity at that period.
In order to calculate the periodic inequalities, let V be the value of the obliquity at the commencement of any year, and D the actual diminution for that year; V and D being calculated by the preceding formula. Then, after any number of days n has elapsed, the apparent obliquity E will be
+0.43452 cos 2L+9".63199 cos N.
where L is the longitude of the Sun, and N. the longitude of the Moon's ascending node, or the point where her orbit cuts the ecliptic, as she ascends above this plane towards the north,
The Naturalist's Diary.
The green moss shines with icy glare;
When faint the sunbeams smile.
For Nature soon in Spring's best charms
And bid the flowret bloom.
IN February, the weather in England is usually variable, but most inclined to frost and snow. The thermometer is often down below the freezing point, but is generally found at noon between 36° and 46°; towards the end of the month it sometimes rises to 50°, or even 52° or 54°. The severe weather generally breaks up with a sudden thaw, accompanied by wind and rain; torrents of water pour from the hills, and the snow is completely dissolved. Rivers swell and inundate the surrounding country, often carrying away bridges, cattle, mills, gates, &c., and causing great injury to the farmer. But so variable is the weather in this month, that frequently frost again usurps the year.'
In the course of this month all nature begins, as it were, to prepare for its revivification. God, as the Psalmist expresses it, renews the face of the earth ;' and animate and inanimate nature seem to vie with each other in opening the way to spring. About the 4th or 5th, the woodlark (alauda arborea), one of our earliest and sweetest songsters, renews his note1; a
To the WOODLARK.
Is it the voice of Winter that I hear
Hoarse murmuring in the late umbrageous wood?
Are o'er my path in wild profusion strewed.
week after, rooks begin to pair, and geese (anas anser) to lay; the thrush sings; the yellow-hammer is also heard. The chaffinch sings; the green woodpecker (picus viridis) makes a loud noise; and the redbreast continues to warble.
A suppliant to your window comes,
Who trusts your faith, and fears no guile;
For cold and cheerless is the day,
That wears the scarlet stomacher.
Turkey-cocks strut and gobble. Partridges (tetrao perdix) begin to pair; the house pigeon has young; field crickets open their holes; missel thrushes couple; and wood owls hoot:-gnats play about, and insects swarm under sunny hedges; frogs (rana temporaria) croak, and the stone curlew (otis ædicnemus) clamours. By the latter end of this month, the raven (corvus corax) has generally laid its eggs, and begun to sit. Moles (talpa europaeus) commence their subterraneous operations.-(See T. T. for 1814, p. 49.)
Adieu, then, loveliest minstrel of the glade!
Which lately, till th' approach of evening's shade,
And silent as the Muse's golden strings,
Late waked to rapture by their darling boy',
The flowers of the crocus (crocus vernus) appear, before their leaves are grown to their full length; the barren strawberry (fragraria sterilis); the laurustinus (viburnum tinus); and the yew-tree (taxus baccata), are in flower. The elder-tree (sambucus nigra) begins to put forth its flower buds, and the catkins of the hazel are very conspicuous in the hedges. The gooseberry bush (ribes grossularia) and the red currant (ribes rubrum) show their young leaves about the end of the month.
Many plants appear above ground in February, but few flowers, except the snowdrop, are to be found. This icicle changed into a flower' is sometimes fully opened from the beginning of the month.
Now to the wonted church or abbey lone,
The few fine days towards the latter end of this month cannot be more agreeably employed than by cultivating our knowledge of Nature, even in her