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either of the sun or moon, according to her situation. The whole of this is rendered clear by the lunarium, where the wire projecting from the earth, shews when the moon is above, below, or even with the earth, at the times of conjunction and opposition, and thus when there will be, or not, any eclipses.
The distance of the moon from the earth varies sensibly with respect to the sun ; it does not move in a circular, but in an elliptic orbit round us, the earth being at one of the foci of this curve.
The longer axis of the lunar orbit is not always directed to the same point of the heavens, but has a movement of its own, which is not to be confounded with that of the nodes; for the motion of the last is contrary to the order of signs, but that of the line of apsides is in the same direction, and returns to the same point in the heavens in about nine years. This motion is illustrated in the lunarium by means of the brass ellipses XY; which is carried round the earth in little less than nine years ; thus shewing the situation of the elliptical orbit of the moon, and the place of the apogee in the ecliptic.
Those who wish to extend the application of the instrument further, may have an apparatus applied to it for explaining the Jovian and Saturnian systems, illustrating the motion of her satellites, and of the ring of Saturn. But as this application would ex
* That point of her orbit wherein she is nearest the earth, is called her perigee; the opposite point, in which she is farthest off, is called her apogce. These two points are called her upsides, the apogee is the higher, the perigee the lower apsis.
tend the price of the instrument beyond the reach of most purchasers, I have thought it would be unnecessary to describe them ; the more so, as the phenomena they are intended to explain are accurately and clearly described in several introductory works of astronomy.
Having surveyed and endeavoured to illustrate the general phenomena of the heavens, let us turn the mental eye towards our Lord, who hath made all things in heaven and earth, and whose tender care is
$6 Innumerable worlds stood forth at thy command, and by thy word they are filled with gloria ous works
“ Who can comprehend the boundless universe ? or number the stars of heaven?
“ Amidst them thou hast provided a dwelling for man, that he might praise thy name.
“ The sun shineth, and is very glorious, and we rejoice in the light thereof.
“ We admire its brightness, and perceive its greatness; and our earth vanishes in comparison with it.
Many worlds are nourished by it, and its glory is great. By its influence the earth is clothed with plenty, and the habitation of man rendered exceeding beautiful.
“ Yet what is this amidst thy works? is it not as a point, and as nothing in the firmament of hea
“ What then is man, that thou art mindful of him, or the son of man, that thou visitest him:
Thy power is circumscribed by no bounds, both great and small are alike unto thee.
“ From the sun in the firmament of heaven, to the sand on the sea shore, all is the operation of thy hand.
“ From the cherubim and seraphim which stand before thee, to the worm in the bowels of the earth, all living creatures receive of thee what is good and expedient for them."*
Praise then the Lord, O my soul, praise his name for ever and ever.
* See “ Ilymus to the Supreme Being, in imitation of the Eastern Songs, London, 1780,
THERE is no part of mathematical science more truly calculated to interest and surprize mankind, than the measurement of the relative positions and distances of inaccessible objects.
To determine the distance of a ship seen on a remote spot of the unvaried face of the ocean, to ascertain the height of the clouds and meteors which float in the invisible fluid above our heads, or to shew with certainty the dimensions of the sun, and other bodies, in the heavens, are among the numerous problems which, to the vulgar, appear far beyond the reach of human art, but which are nevertheless truly resolved by the incontrovertible principles of the mathematics.
These principles, simple in themselves, and easy to be understood, are applied to the construction of a variety of instruments; and the following pages
contain an account of their use in the quadrant and the equatorial.
The position of any object, with regard to a spectator, can be considered in no more than two ways; namely, as to its distance, or the length of a line supposed to be drawn from the eye to the object; and as to its direction, or the situation of that line with respect to any other lines of direction; or, in other words, whether it lies to the right or left, above or below those lines. The first of these two modes bears relation to a line absolutely considered, and the second to an angle. It is evident, that the distance can be directly come at by no other means than by measuring it, or successively applying some known measure along the line in question ; and therefore, that in many cases the distance cannot be directly found; but the position of the line, or the angle it forms, with some other assumed line, may be readily ascertained, provided this last line do likewise terminate in the eye of the spectator. Now the whole artifice in measuring inaccessible distances consists in finding their lengths, from the consideration of angles, observed about some other line, whose length can be submitted to actual mensuration, How this is done I shall proceed to shew,
Every one knows the form of a common pair of compasses. If the legs of this instrument were mathematical lines, they would form an angle greater or less, in proportion to the space the points would have passed through in their opening. Suppose an arc of a circle to be placed in such a manner, as