« ZurückWeiter »
mersed in the Earth's shadow, which so much exceeds it. Hence, whenever the Moon traverses the middle of this shadow, or her centre either coincides, or nearly so, with its axis, there will be a total eclipse of the Moon.
The diameter above calculated is that of the shadow projected by the opaque body of the Earth. But the inferior beds of the atmosphere absorb so much of the light as to cause a sensible shadow ; for the apparent diameter of this shadow which is deduced from observation always exceeds that found by calculation. This difference is generally estimated at 09.0279, or about toth of the whole diameter ; but it must necessarily vary with the state of the terrestrial atmosphere. The time which the Moon requires to pass through this shadow depends upon the difference of her diameter and that of the shadow, as well as upon the proximity of her centre to its axis and her horary motion. Both these circumstances will be elucidated in a subsequent part of this article.
The apparent diameter of the lunar shadow at the distance of the Earth may be calculated in the same manner, by substituting the corresponding quantities as they would appear to an observer situated at the surface of the Moon. Thus, the semidiameter of the lunar shadow, with respect to that observer, would be equal to the sum of the parallaxes of the Sun and the Earth, diminished by the apparent semidiameter of the Sun, the value of each quantity being calculated for an observer situated at the Moon. The parallax of the Earth is only the apparent semidiameter of the Moon, seen from the Earth; all the necessary quantities are therefore given. The formula would be simplified by neglecting the parallax of the Sun, the influence of which upon the result is almost insensible, as it is always less than half a second. Then, the semidiameter of the lunar shadow is equal to the excess of the apparent semidiameter of the Moon above that of the Sun.
As this conclusion may not appear very evident to such of our readers as are not conversant with astronomical subjects, we shall illustrate it by means of the following figure. Let S (fig. 8) be the centre,
and SS' the apparent semidiameter of the Sun ; m the centre, and mn the apparent semidiameter of the Moon; EE' a part of the Earth's orbit; and let the line SnC be drawn meeting the axis of the shadow and the orbit of the Earth in C. Then, since the apparent magnitude of any object is the angle it subtends at the eye of the observer, the apparent semidiameters of the Sun and the Moon will be the same to an observer situated at C, as they both subtend the angle mCn; and hence the extremity of the shadow will just reach that point.
Now, let m'n' be the apparent semidiameter of the Moon when it is in a part of its orbit nearer to the Earth than before ; and draw S'n'C' and join Cn'; then the apparent semidiameter of the Moon in that position will be measured by the angle m'Cn', and, consequently, the excess of this semidiameter, above that of the Sun, is the angle nCn'. The apparent semidiameter of the lunar shadow, as seen from the Moon, is evidently the angle Cn'o.
As the greatest variation in the apparent semidiameter of the Moon is only about 2', the angle nCn' can never exceed that quantity; and the dist
ance of the Sun from the Earth being about 400 times that of the Moon, the angle CS'n' can never
2' 120" exceed 2 minutes divided by 400, or
400 400 Yths of a second of a degree; and, consequently, the lines S'C and S'O may be regarded as sensibly parallel to each other. The angle Cn'O is therefore equal to nСn'; or the apparent semidiameter of the lunar shadow is equal to the excess of the apparent semidiameter of the Moon above that of the Sun, as previously stated.
If we make the calculations indicated at the close of the preceding part of this article, under circumstances the most favourable to the length of the shadow, or those in which the Sun is in apogee, and the Moon in perigee, it will be found that the semidiameter of the lunar shadow, at the distance of the Earth, as seen from the Moon, is equal to 60".264; the apparent semidiameter of the Earth at that distance is equal to the horizontal parallax of the Moon at the same time; that is, to 10.024722. Hence, in the most favourable circumstances, the breadth of the lunar shadow is to that of the disc of the Earth as 1 to 61.2; and, therefore, this shadow will not cover a 60th part of the breadth of the terrestrial hemisphere, and consequently not zoboth part of its surface. Under circumstances less favourable, the breadth of the shadow would be still less; and when the apparent diameter of the Moon is just equal to that of the Sun, it becomes equal to nothing; and negative when the apparent diameter of the Sun exceeds that of the Moon. In the first case the vertex of the shadow will just reach an observer on the Earth, and, in the latter, it will fall short of him.
Notwithstanding the extremity of the Moon's shadow would not arrive at an observer situated on one part of the Earth, it might reach another differently situated; for the difference of situation alone causes a
considerable yariation in the distance of the Moon from the Earth. We have already remarked that this difference amounts to about oth of the distance between the Moon being in the horizon and in the zenith of the observer; and this has a sensible effect upon her apparent diameter ; but the great distance of the Sun renders this effect upon his apparent diameter insensible. Hence it follows, that to one of the observers so situated, the apparent diameter of the Moon would be less than that of the Sun, while to the other it would be greater. In the former case the shadow would not reach the observer ; in the latter it would arrive at him. The position of the observer at the moment of a solar eclipse is, therefore, very important; as according to this it either may or may not be visible to him. The least apparent diameter of the Sun is about 1891", and that of the Moon at her mean distance, being 1878", less than that of the Sun, there cannot be any total obscuration at this limit, and still less when the Moon is beyond her mean distance from the Earth. It is also evident, from what is observed above, that only a small portion of the terrestrial hemisphere can be covered with it at once, and that frequently the shadow does not reach the Earth at all; hence eclipses of the Sun ought to happen much seldomer than those of the Moon, which experience likewise proves to be the case.
(To be continued next month.]
The Naturalist's Diary.
Now sober Autumn, with lack lustre eye,
And hears the woodman's song
And early sportsnian's foot. SEPTEMBER, like the following month, often boasts many fine days, at least till the commencement of the autumnal equinox on the 22d, when a
change in the weather generally takes place. The mornings and evenings are cool, but possess a delightful freshness, while the middle of the day is pleasantly warm and open.
Still many a flower bedecks the garden walks,
Within the last few years, indeed, September has proved the finest and most settled month of the whole twelve; this was particularly the case in the autumns of 1815 and 1816. On the protracted delightfulness of the weather in the former year, we quote the following lines of an anonymous poet :
SEPTEMBER wanes, and still the Summer's smile Hangs lingering -- lovely-o'er Britannia's isle; SEPTEMBER wanes and yet the autumnal blast O'er nature's scenes no devastations cast; Still clings the foliage to the parent tree; Still bloom the flowers to feast th' insatiate bee. The swallow bent his emigrating way, Found climes that feel the sun's unfading ray; Yet on his journey, as he looked behind, Saw still the SUMMER's fairy charms combined; Turned on his wing again to that dear home, And saddning mourned that Winter e'er should come With her chili blast, her cold ungenial air, To make him seek a land more warmly fair. SEPTEMBER wanes, protracted Summer laughs, And all around her cup of gladness quaffs ". Each season of the revolving year produces a variety of picturesque appearances peculiar to itself. The emotions which affect the mind, while it contemplates
* These lines are by the author of the Cossack,' a poem, and appeared in the Morning Chronicle of November 16, 1815.