Stargazing: Past and Present

by Sir Norman Lockyer

The connection between the transit instrument and the transit clock is so intimate that either is useless without the other. In the one case we should note the passage of a star across the meridian without knowing at what time it took place; while, on the other hand, we should not learn whether the clock showed true time or not, unless we could check its indications in the manner rendered possible by transit observations. In what has been already said of time we referred to it as measured by our ordinary clocks, i.e. reckoning it from noon to midnight and midnight to noon, and regulated entirely by the length of the solar day. It would at first sight seem that it should be twelve o’clock by a clock so regulated when the sun passes the meridian; but the earth’s orbit is not circular, and the sun’s course is inclined to the equator, so that, as determined by such a clock, sometimes he would get to the meridian a little too late, and sometimes too early, so that we should be continually altering our clocks if we attempted to keep time with the sun.

One of the greatest boons conferred by astronomy upon our daily life is an imaginary sun that keeps exact time, called the Mean Sun, so that the mean sun is on the meridian at twelve o’clock each day by our clocks, regulated by the methods we have now to discuss. Such clocks regulated, as it is called, to mean time are sometimes a few minutes before, and at others a few minutes behind the true sun, by an amount called the Equation of Time, which is given in the almanacs. It would therefore be difficult to regulate our standard clock by the sun, so we do it through the medium of the stars, which go past our meridian with the greatest regularity, since their apparent motion depends almost wholly upon the equable rotation of the earth on its axis, while the apparent motion of the sun is complicated by the earth’s revolution round it.

This method at first sight is complex, and in fact we cannot obtain mean time directly by such transits of stars. It is accomplished indirectly by means of a clock set to star- or sidereal-time, and such a clock is the astronomer’s companion, to which he always refers his observations, and the indications of which alone are always in his mind. This he calls the Sidereal Clock.

Fig. 122.—Diagram illustrating the different lengths of solar and sidereal day.

We have, then, next to consider the difference between the clock used for the transit, or the sidereal clock, and an ordinary solar clock, or between a solar and a sidereal day. Let S, Fig. [122], represent the sun, and the arc a part of the orbit of the earth, the earth going in the direction of the arrow. Let 2 represent the position of the earth one day, and let 1 represent the position of the earth on the day before. A line drawn from the sun through the earth’s centre will give us the places a, b, on the earth at which it is midday on the side turned towards the sun, and midnight on the side turned from the sun. Now when a revolution of the earth with reference to the stars has been accomplished the earth comes to the second position, 2; and c is the point of midday; and there is a certain angle here between a and c, through which the earth must turn before it is noon at a, due to the change of position of the earth, or to the apparent motion of the sun among the stars, by which the sun comes to the meridian rather later than the stars each day. Now let us suppose that, while one observer in England is observing the sun at midday, another is observing the stars at the antipodes at midnight, the star is seen in the direction ⁎. We are aware that the stars are so far away, that from any point of the earth’s orbit they seem to be in absolutely the same place—they do not change their positions in the same way as the sun appears to do amongst them—an observer at b therefore sees on his meridian the star ⁎ while the observer at a sees the sun on his meridian; supposing b to represent the same observer, on the second day, he will see the star due south before the other observer at a sees the sun due south. The result of that is, that the sidereal day is shorter than the solar day, and the sun appears to lose on the stars. If we wish to have a clock to show 12 o’clock when the sun is southing, we shall want it to go slower by nearly four minutes a day than one which is regulated by the stars and is at 12 o’clock when our starting-point of right ascension—which is the intersection of those two fundamental planes, the equator and the ecliptic—passes over the meridian.

One of the uses of the clock showing sidereal time in connection with the convenient fiction of the “Mean Sun,” is to give to the outside world a constant flow of mean time regulated to the average southing of the sun in the middle of the period for which the sun is above the horizon each day in the year.

The stellar day, that is the time from one transit of a star to the next, is shorter than a solar day by 3m. 56s., so what is called sidereal time, regulated by the transits of well-known stars, in the manner we shall presently explain, by no means runs parallel with mean time so far as the clock indications go. Indeed when we look at a sidereal clock, we see something different to the clock we are generally accustomed to see. In the first place, we have twenty-four hours instead of twelve, and then generally there is one dial for hours, another for minutes, and another for seconds. That of course might happen in the case of the mean-time clock; but the mean-time clock is not often divided into twenty-four hours, although it formerly used to be, as the dials in Venice still testify.

We now see the importance of an absolutely correct determination of the right ascension of stars; for this right ascension, expressed in hours, minutes, and seconds, is nothing more nor less than the time indicated by the sidereal clock, by the side of the transit instrument, when a star passes over, or transits, the central wire of that instrument. Hence it is the sidereal clock which keeps time with the stars, and which we keep correct by means of the transit instrument.