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independently of any astronomical calculations, by attending to the following observations. In the preceding figure, suppose the Moon to be at S and the Sun at s', at a much greater distance from the earth (and which is actually the case), then each of the observers, situated at O and O', would see both bodies at the same time, and perceive the distance which separates them ; but at the point E, in the line CS', which passes through their centres, this distance would not appear, and the Sun would be eclipsed. Thus, when a cloud passes between us and the Sun, we find ourselves enveloped in its shadow, while places at a little distance experience the full influence of the solar beams : the difference of these effects is owing to the parallax
In order to avoid the irregularities depending upon the different aspects under which the same body is seen from different points on the globe, or the difference of its apparent situations in the heavens, and render the observations susceptible of being compared with each other, astronomers suppose the earth to be either a sphere or a spheroid, and refer all their observations to its centre; regarding that as the true place of a heavenly body in which it would appear if seen from this point. The place in the celestial sphere, in which a body appears to be situated when seen from any point of the earth's surface not in the right line which joins the centre of the earth and that of the body, they denominate the apparent place of that body, in opposition to the true place. Now, in this case, one of the observers may be considered as situated at E, and then the subtending chord becomes OE, and the parallactic angle OSE ; and which being the same as OSC, the parallax is said to be the angle which the radius of the earth, drawn to the point of observation 0, subtends at the centre of the heavenly body. We shall endeavour to illustrate this on the supposition that the earth is spherical, and the distance between it and the heavenly, body constart; and which, even in calculation, is sufficiently accurate for most common purposes.
If the zenith distance of the Sun, Moon, or a star situated at S, be observed at the point O, it will be equal to the angle ZOS, Z being the zenith; but if it had been observed from the centre of the earth, it would have been equal to the angle ZCS, or to ZOS-OSC; because the angle ZOS is the exterior angle of the triangle COS. This angle CSO, found by the two visual rays drawn from the body S to O and C, is called the parallax of altitude. Hence, if this parallax be subtracted from the apparent or observed z enith distance, it will give the true distance of that body from the zenith of the observer. . .
From this it may also be observed that the two visual rays SO and SC, being both situated in the same vertical plane, the effect of parallax, like that of refraction, is wholly in a vertical direction; or, in general terms, always in the plane passing through the body, the centre of motion, and the eye of the observer. The parallax must be subtracted from the zenith distance, or added to the altitude ; but, on the contrary, refraction is to be subtracted from the altitude and added to the zenith distance, since their effects take place in opposite directions.-See our observations on refraction, after the Astronomical Occurrences of last month.
This depression occasioned by the parallax depends upon the magnitude of the angle CSO; it is not the same for aīl altitudes. The distance of the body from the earth being supposed constant, this angle will be the greatest at the horizon; as OSC (fig. 4, p. 102), which is denominated the horizontal parallax. If, from the point S, two tangents to the circle which represents the circumfererence of the earth be drawn to O and O', the horizontal parallax will be half the visual angle OS'O', under which the earth would appear to an observer placed at the body; or which is, in effect, the same with respect to an observer so
situated, it is equal to the angle subtended by half the apparent diameter of the earth. The horizontal parallax is therefore the greatest ; and the parallax of altitude, or the angle OSC, diminishes as the body is more elevated above the horizon, until it becomes nothing at the zenith, because the visual ray from the observer and that from the centre of the earth then coincide, as OZ and CZ in figure 4, or ES' and CS', fig. 3. The law of this diminution is easily calculated by the common rules of plane trigonometry, supposing the distance of the body from the earth's centre not to vary during a diurnal revolution. On these principles, we find that the parallax answering to any apparent altitude, is equal to the horizontal parallax multiplied by the sine of the apparent zenith distance'.
[To be concluded next Month.)
1 The apparent zenith distance (the angle SOZ=SOC) being known and denoted by %, in the triangle OSC (fig. 4), in which the sines of the angles are proportional to their opposite sides, we have SC : OC :: sin. SOC :sin, OSC. Then denoting the distance of the body S from the centre of the earth by D, the radius CO byr, and the parallax by P, we shall have from the preceding proportion sin. P= 0 . But when the body is in the horizon or the zenith distance equal 90°, the sine of x becomes=1; and the horizontal parallax being represented by h, we have sin. h=. Then, exterminating D, by means of its value in each of these equations, and we obtain sin. P=sin. h. sin. 2. Now, since the distances of the heavenly bodies are so great, compared with the radius of the earth, the parallactic angles will always be very small; even for the Moon, which is much the nearest to the earth, it is only about 1° at the horizon; and therefore the arcs may be substituted for their sines, with
1. out committing an error in the result, equal to g ath part of the whole arc. Hence P=h sin. % ; the result above stated.
From the above formula, sin. h=1, it is evident that the horizontal parallax is the greatest possible; and that it is insen
The Naturalists Diary.
Now the golden morn aloft
GRAY, If there has been a medium proportion of easterly winds in the previous part of the winter, the month of April may be expected to be mild, with gentle showers; thus affording to vegetables an abundant supply of water, which is so indispensably necessary to their existence. The many thousand tribes of vegetables are not only formed from a few simple substances, but enjoy the same sun, vegetate in the same medium, and are supplied with the same nutri-' ment. It is, indeed, wonderful that all orders of vegetables are produced from four or five natural substances, viz. caloric, light, water, air, and carbon. How admirable, then, must the formation of those organs be, which, by their peculiar actions, shall produce such various modifications of these sub
sible when the ratio s is very small, and nothing when the distance D of the body from the centre of motion is incomparably great with respect tor, the distance of the observer from the same point. This takes place with respect to the stars, the parallax of which cannot be ascertained by observation. In order, however, that the parallax may be absolutely nothing, it is necessary that D= infinity, or r=0, which is not possible; but if ñ=sin. 1"
=-06964-8, the parallax would at most be 1", which it is
ible to ascertain by observation.
stances, so as to form the different colours, tints, odours, tastes, &c. of the vegetable kingdom! How surprising must be the progress of vegetation! How rich the economy of nature !
It is now allowed, that there is both a vital circulation of the juices in vegetables, and a large perspiration from their pores; which latter is become a subject of great curiosity and importance, from the successful labours of those who have cultivated this part of natural philosophy. The circulation in plants is strong in the spring, and languid in the winter; in some it is so forcible and abundant, that, if their vessels are opened at an improper season, they will bleed to death, as when an artery is divided in the human body. If the finer spirit evaporates from a plant, and it has no fresh supply, it becomes instantly flaccid and fading, as an animal body dies with the departure of its breath.
The process of vegetation is forwarded in a wonderful manner by the vicissitude of day and night, and the changes of the weather. The heat of the sun raises a moist, elastic vapour, which fills and expands certain vessels in plants, and so gradually, enlarges their bulk; while the colder air of the night condenses and digests the matter which has been raised, and so confirms the work of the day. We coinplain of cold blasts and clouded skies, by the intervention of which vegetation rapidly advancing is suddenly stopped and seems stationary: but this may be wisely ordained by Providence; the growth of herbs, may be too hasty; they are weak in substance, if they are drawn forward too fast. A cold season prevents this too hasty growth.; as in the moral world some seasonable disappointment may give a salutary check to an aspiring mind, and establish it in wisdom and, patience. Even the roughest motions of the elements have their use. Winds and storms, which agitate the body of trees and herbs, loosen the earth about their roots, and make way for their fibres to multiply,