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and p 8".62; and consequently, by the substitution of these values,
1890.96 x 3665
for the breadth of the lunar penumbra. The semidiameter of this penumbra, in the same case, is also (D' + D) p'
2(p' — p)
(2011".392 + 1890′′.96) × 3665"
The apparent semidiameter of the Earth, as seen from the Moon, under the same circumstances, which is equal to the horizontal parallax of the Moon, is 3665"; and consequently, in the most favourable positions of these bodies, the lunar penumbra covers only a little more than half the breadth of the terrestrial disc, and therefore only about one-fourth of it's surface.
In the preceding inquiries, no regard has been paid to the refractions which the solar rays experience in their passage through the terrestrial atmosphere; but, as it is requisite to take these effects into the account, the following explanation will enable the reader to appreciate them.
When the effects of the atmosphere are not considered, the pure shadow is limited by two lines, which are tangential to the Sun and the Earth; but when the effects of the atmosphere are taken into the account, the limits are not the same. In this case, the luminous rays are bent out of their rectilineal course, both in passing through the atmosphere before they arrive at the Earth, and in traversing it after they have become tangents to that body, so as to cut the axis of the conical shadow much nearer the Earth than if they had preserved their rectilineal direction in all parts of their course, in the manner which we have supposed in the preceding researches. Thus, in fig. 7, the luminous ray AB, instead of
meeting EC, the axis of the conical shadow in C, would be refracted by the atmosphere, and caused to meet that line in O. The rays from the inferior parts of the Sun's surface would also meet this line in points situated between O and C; and therefore an observer situated beyond the point where a ray from the superior edge of the solar disc, forming a tangent to the upper surface of the Earth, would not be wholly in the shadow, but would perceive the disc of the Earth encompassed with a luminous ring, since he would see the circumference of the solar disc by refraction. The farther he is supposed to recede from the Earth in the line SEC, the broader the luminous ring would appear, until the whole disc of the Sun became visible.
The different limits of this shadow may easily be determined in the following manner. Let SB (fig. 9) be a ray proceeding from the solar disc at S, and touching the surface of the Earth at B. Then, if the Earth be considered as spherical, both parts of the curve described about this surface will be symmetrical; and if the direction be ST when it enters the atmosphere, and T'O when it leaves it, the angles BTZ and BT'Z, formed by these directions and the tangent TT', will be equal to each other. Now, the
angle BTZ, or DTS, is very nearly equal to DBS, or to the horizontal refraction, because the point Z is very little elevated above the point B ; and the lines SZ and SB, drawn from these two points to the Sun, are very nearly parallel to each other. Thus
This sensible parallelism is demonstrated by M. Biot, in Note 4 to Book I of his Astronomie Physique, 2d edit.
the angle BTZ is also very nearly equal to the horizontal refraction; and consequently the angle SZA, which expresses the inflexion of the ray, is equal to BTZ+BTZ, or to double this refraction.
The effect of the atmosphere upon the solar rays may, therefore, be regarded as increasing the apparent diameter of the Sun by a quantity equal to double the horizontal refraction; for, when the rays have once quitted the atmosphere, they proceed in rectilineal directions, in the same manner as if they had been originally projected in those directions. The ray SBO in the above figure, for example, emanating from the superior edge of the true Sun S, arrives at O, as if it came from the upper limb of a fictitious Sun, the diameter of which exceeded the true one by a quantity equal to the angle AZS. Hence it is obvious that, in order to find the distance of the vertex of the pure shadow from the centre of the Earth, as affected by the refractive power of the atmosphere, it will be sufficient to increase the semidiameter of the Sun by a quantity equal to double the horizontal refraction, and then the preceding formulæ may be used for this case also; and, consequently, instead of having sin (D-p) in the denominator, we shall have sin (D+2r~p.)
If now, instead of supposing the ray to proceed from the exterior part of the solar disc, it be considered as emanating from any other point at a given distance from the centre, by substituting that distance for the semidiameter in the preceding formula, it will give the distance of the Earth at which that point will begin to appear; and therefore the zones that will successively become visible at each distance may be thus found.
From these calculations, astronomers conclude that an observer, situated at the surface of the Moon, even in the most favourable circumstances, would see three-fourths of the solar disc by refracted light, which had traversed the Earth's atmosphere; and this
is the reason why the Moon appears of such a red colour during a lunar eclipse. The light of the Moon would, therefore, appear much more brilliant at those times, if it were not for the absorbent power of the terrestrial atmosphere through which it passes.
From what has been shown in the former part of this article relative to the comparative breadths of the lunar shadow and the terrestrial disc, it is evident that total eclipses of the Sun can only be local and of short duration; while eclipses of the Moon are general for all parts of the terrestrial hemisphere which has the Moon above the horizon at the time of the eclipse; and that these, on account of the extent of the Earth's shadow, may often have a much greater duration than eclipses of the Sun, in which the total darkness can never exceed five minutes.
[To be continued next Month.]
The Naturalist's Diary.
Late does the SUN begin his shortened race,
Languid, although no cloud obscures the view;
Where waved, erewhile, the cool refreshing dew.
And ev'ry field in firmer fetters binds;
Slow from the tree, the sport of eddy winds.
And intercepts the wing that flaps in vain.
To shun the rigid winter's coming storms,
And drifted snow the desert field deforms.
Domestic redbreast, on the window sits,
THE groves now lose their leafy honours; but, before they are entirely tarnished, an adventitious beauty, arising from that gradual decay which loosens the withering leaf, gilds the autumnal landscape with a temporary splendour superior to the verdure of spring or the luxuriance of summer. The infinitely various and ever-changing hues of the leaves at this season, melting into every soft gradation of tint and shade, will long continue to engage the imitation of the painter, and the contemplation of the poet and the philosopher.
What pomp, what vast variety of hues,
Nature having perfected her seeds, her next care is to disperse them: the seed cannot answer its purpose while it remains confined in the capsule. After the seeds, therefore, are ripened, the pericarpium opens to let them out; and the opening is not like an accidental bursting, but, for the most part, is according to a certain rule in each plant. Some seeds which are furnished with hooks or spines, attach themselves to the rough coats of animals, and thus promote their dispersion. Others are contained in berries, and, being swallowed by birds, are again committed, without injury, to the earth in various places.-See
More changeful than the falling leaf