Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/899

Rh Direction of Motion of a place on the Earth.

76. Of all the motions to which the earth is subject its orbital motion is the largest, and is the most important for aberrational effects; but two others must not be overlooked, since they may introduce secular variations into the amount of those effects, viz., the diurnal rotation and the motion of the system through space.

The speed of the motion of the system is only approximately known, but it is estimated at 10.9 miles a second, or 1.75 million C.G.S., and its direction is completely specified by stating a point among the fixed stars.

The speed of the diurnal rotation is $$\frac{\mathrm{equatorial\;circumference}}{1\;\mathrm{sidereal\;day}} \times \cos\;\mathrm{latitude}$$, or very small compared with that of light, and its direction is simply from west to east. It causes a variation in the observed total aberration, amounting to nearly 2 per cent. at the equator.

Both these motions are steady.

The orbital motion is not quite constant in speed, and goes through the whole plane cycle of directions, but its average value may be stated as $$\tfrac{1}{10,000}$$ that of light, and its direction is sufficiently expressed for practical purposes by saying that it is in the plane of the ecliptic, and at right angles to the Sun's direction. For instance, a half-moon is roughly in the line of the earth's orbital motion. We are moving as if going away from an increasing half-moon or towards a decreasing half-moon. Another way of putting the matter, is that at midnight the annual and diurnal motions approximately agree, in direction, at midday they are opposed. At the epoch of the solstices the agreement is good, i.e., the orbital motion at a solstice is from east to west at noon, from west to east at midnight; and at no time of the year is the error of this statement of very great practical import, for even at the equinoxes 91.7 per cent. of the motion is in the direction stated.

A clock might easily be made to point out the direction of orbital motion. By starlight it is never difficult to realize it, for there are usually planets enough to make the ecliptic manifest, and there is no difficulty in estimating whereabouts the Sun is. Hold a twenty-four hour watch in the plane of the ecliptic with its noon line pointing west, and its hour hand will constantly indicate the direction of the earth's orbital motion. The only difficulty is knowing where the plane of ecliptic is. Consider a terrestrial globe with its axis tilted $$23\tfrac{1}{2}$$° and rotating by internal mechanism once in twenty-four hours. The plane of ecliptic is horizontal, and the direction of motion will be given by a pointer revolving once a year in a horizontal plane, or, more simply, by the appropriate radius of a horizontal card with 365 days of the year written round its circumference. With that alone, however, it would be a little puzzling to compare this slowly changing direction with the position of any given locality on the rotating earth. The whole might be turned by hand till the required locality came to the top, with the axis in the meridian, and then the pointer would agree with the direction of Rh