This figure has a long axis, ab (fig. 512); and perpendicular to this a short axis, de, passing through the centre, c. The two points, S S′, are called the foci of the ellipse; also, as is evident from the construction of the figure, any two lines drawn from the two foci, to any point of the circumference, for instance, S and S′m, or Sm′ and S′m′, etc., which represent the thread when the pencil is at m or m′, are together equal to the larger axis of the ellipse. These lines, and we may imagine an infinite number of such, are called radii vectores. The distance of the foci, S or S′, from the centre, c, is called the eccentricity of the ellipse. It is evident that the smaller the eccentricity is, the nearer the figure approaches to that of the circle. The superficies of the ellipse is found by multiplying the two half axes, ac and dc, by each other, and this product by the number 3·14.
The Diagonal Scale is shown in the margin. It is used to make diagrams so as to bring the relative distances before the eye. The larger divisions represent, it may be, miles, or any given distance; the figures on the left side tenths, and the upper range hundredths of a mile. So a measurement from Z to Z´ will represent two miles, we may say, with so many tenths and hundredths.
Fig. 514.—Transit instrument.
The Transit instrument is due to Roemer, a Danish astronomer. It consists of a telescope so constructed as always to point to the meridian, and rotates upon a hollow axis, directed east and west. At one end is a graduated circle. The optical axis of the telescope must be at exactly right angles to the axis of the instrument; it will then move on the meridian. There is an eye-piece filled with two horizontal and five vertical wires, very fine, the latter at equal distances apart. The star appears, and the time it takes to cross is noted as it passes between each wire, and the mean of all the transits will be the transit on the meridian. For if we add the times of all the transits across the wires, and divide by five the number of them we shall get at a true result.
Fig. 515.—The eyepiece of transit instrument.
A good clock is also a necessary adjunct for astronomical observations, and the astronomical clocks and chronometers now in use record the time with almost perfect accuracy. The improvement in telescopes, the use of micrometers, etc., have greatly facilitated observations. In the transit clock we have a most useful timekeeper, for the ordinary clocks are not sufficiently accurate for very close observations. The sidereal time differs from solar time, and the twenty-four hours’ period is calculated from the moment a star passes the meridian until it passes it again. The sidereal day is nearly four minutes shorter than the solar day, and the sidereal clock marks twenty-four hours instead of twelve, like the old dial at Hampton Court Palace over the inner gate. The Chronograph has also been useful to astronomers, for by “pricking off” the seconds on a roller by itself, the observer can mark on the same cylinder the actual moment of transit across each wire of the instrument, and on inspection the exact moment of transit may be noted.
The Equitorial is another useful instrument, and by its means the whole progress of a star can be traced. The Equitorial consists of a telescope fixed so that when it has been pointed at a certain star a clock-work movement can be set in motion, which exactly corresponds with the motion of the star across the heavens, and so while the star moves from its rising to setting it is under observation. Thus continuous observations maybe made of that particular star or comet without any jerking or irregular movement.
We can thus see the uniform motion of the stars which go on in greater or lesser circles as they are nearer to or farther from the pole; and with the exception of the polar star, which, so far as we are concerned, may be considered stationary, every star moves round from east to west—that is, from the east of the polar star to the west of it, in an oblique direction. Therefore, as Professor Airy remarks, “Either the heavens are solid, and go all of a piece, or the heavens may be assumed to be fixed or immovable, and that we and the earth are turning instead of them.”