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The parallax of the Sun is,
At his mean distance
And, therefore, the half of the former numbers, diminished by the latter, as above stated, gives for the divisors, when the Sun is
At his mean distance
At his mean distance
In apogee Consequently, by reducing these seconds into minutes, and dividing the radius of the Earth by the sine of each number respectively, we shall obtain the length of the shadow in terms of the terrestrial radius. The following are the results of these operations; viz. when the Sun is
The relation of these numbers shows that the length of the shadow increases as the distance of the Earth from the Sun augments. The greatest distance of the Moon from the Earth, as shown in the preceding article, is only 63.94145 terrestrial radii, and which is, therefore, much less than the least of the preceding numbers; and, consequently, if the Moon moved always in the plane of the ecliptic, she would pass through the Earth's shadow in each of her revolutions.
The length of the conical shadow, projected behind the Moon, may also be calculated in a similar manner, supposing her to be a spherical body, the apparent diameter of which is known. For this purpose the relative values of the Sun's apparent diameter and parallax, as they would appear at the surface of the Moon, must be employed; and these may be readily deduced from those quantities at the surface of the Earth, and which have been used in the preceding
calculations. As the Moon is supposed to be in conjunction at the time the length of her shadow is required, the apparent diameter of the Sun, as seen from her surface, will be equal to the diameter of the same body seen from the Earth increased in the inverse ratio of the distances of the Earth and the Moon from the Sun at that time. In the same manner, the parallax of the Sun for the Moon is equal to the parallax of the Sun for the Earth augmented in the same ratio, and diminished in the ratio of the lunar and terrestrial radii.
According to these principles, if the distance of the Earth from the Sun be denoted by D, that of the Moon from the same body by D'; the apparent diameter of the Sun as seen at the Earth by d, and the same as seen at the Moon by d', we shall have
D':D::d: d'= ;
and by substituting the respective values of these letters, as already given, in this formula, the following values of d' will be obtained.
Mean distance 1895 .6410
1895 .9552 Now, in order to find the reduced parallax, let p and p' denote the horizontal solar parallax at the surface of the Earth and the Moon respectively; and R the terrestrial and lunar radii; then we shall
Sun in perigee
Sun at mean
Sun in apogee
D': D:: P
which expresses the solar parallax augmented in proportion to the diminution of the distance: and again, for the effect of the difference of the radii of the Earth and the Moon,
Now, as the ratio between the terrestrial and lunar
radii is constant, and
: p' =
= 0.27293; if this be sub
in the above formula, we shall obtain
Then by substituting the respective values of the other letters, as found in this and the preceding articles, in this last formula, the parallaxes corresponding to the apparent diameters above found, under the same circumstances, will be easily obtained.
Having obtained these reduced values of the apparent diameter of the Sun and his parallax at the surface of the Moon, the same formula we have given for calculating the length of the Earth's shadow will serve equally for determining that projected by the Moon. The two following results have been thus calculated, and refer to the two extremes, in which the length of the conical shadow is the greatest and least, in comparison with the distance of the Earth.
When the Sun is in apogee, and the parallax the greatest, the length of the conical shadow projected by the Moon is 59.73 terrestrial radii; and her distance from the Earth 55.902 radii.
The Sun being in perigee, and the parallax the least, the length of the shadow is 57.76, and the distance of the Moon 63.862 radii.
In the first of these cases, the shadow of the Moon extends beyond the Earth, and, in the other, it evidently falls short of it. Hence, when the Moon is in the plane of the ecliptic at the time of
her conjunction, she will not always produce a total eclipse of the Sun: sometimes only a part of the Sun's surface is hid, and, at others, no eclipse at all can take place, in consequence of the shadow not reaching the Earth.
[To be continued next Month.]
The Naturalist's Diary.
Farewel the pleasant violet-scented shade,
The primrosed hill, and daisy-mantled mead;
Farewel the fragrant trefoil-purpled field;
THE powerful influence of the solar rays now contributes to ripen the various sorts of grain, which are benevolently given for the food of man and cattle. Fine weather is very desirable, that the principal source of the farmer's wealth may be safely housed; for sudden storms beat down the nearly ripe corn, and materially injure it. The time of commencing the harvest varies greatly in different districts. It is usually begun in the southern and midland parts of the kingdom towards the end of July, but principally at the beginning of this month; in the northern districts of Scotland, the harvest does not commence until the first or second week in September. And, it is but rarely that, in these parts of England, it is finished, even in the most favourable situations, before the end of October; and, not unfrequently, this time is protracted till the middle of November, till the corn has been ripened by the frost. At Inthe seat of the Duke of Argyle in Scotland,
the corn is so often spoiled by the rain, that the duke has built an immense barn, with a draft of air through it, and pins to hang his wheat on to dry it.
The manner of taking the harvest is not more various than the periods at which it begins. In some cases, it is the custom to reap or cut the corn with a sickle, and bind it up into sheaves of a moderate size; in others, the cutting of the grain is executed by the scythe in some particular method, and often left, without being bound up, or bound into a sort of bundles. A toothed sickle is employed by some farmers; while others use a sickle with a cutting edge. The grain, when reaped or mown, is, in some counties, set up into a sort of hattock, and capped or covered with sheaves of the same; but, in others, the practice is widely different. Some cut the grain high, so as to leave a rough stubble; while others cut it quite close to the land. In Surrey and Kent, women may be seen wielding the sickle. Rye and oats usually become ripe first; but this depends upon the time of sowing, though grain of every species may, sometimes, be seen at once fit for the sickle.
The utmost diligence is now exerted, and labourers from all parts are eagerly engaged to give their assistance in this delightful occupation: all is bustle and activity.
In diff'rent parts what diff'rent views delight,
Spreads o'er the steepy slope or wide champaign.
The smile of Morning gleams along the hills,
And wakeful Labour calls her sons abroad;
And bid the fields resign their ripened load.
In various tasks engage the rustic bands,
And here the scythe, and there the sickle wield;
Or range in heaps the swarths upon the field.