ASTRONOMY
738 Year. b.c. b.c. b.c. a.d.
687 381 189 134 846 926 986 1625 1650 1675 1700 1725 1750 1775 1800 1825 1850 1875 1900
I. Ancient Eclipses. Deviation of longitude. + 41-0 + 12-1 + 11-6 + 5'2 + 0-9 + 3-1 + 0-4 II Modern Observations. 15 7 1-0 00 3-7 7-2 14-5 21-5 21-2 19-7 90 o-o 6-7
Time in advance. -76 -22 -21 - 9 - 2 - 6 + 1 s. -26 - 2 0 - 7 -13 -26 -39 -38 -36 -16 0 + 12
These numbers show that either the moon was moving more slowly, or the earth rotating more rapidly, through the whole 19th century, than during the period 1675 to 1775. To decide which was the case we must have recourse to transits of Mercury. The following table shows the excess of the observed times of the ingress and egress of Mercury in November transits over the sun’s disc from 1677 to 1894. May transits are omitted, because they were not observed at the earlier dates. The last column gives the weights of the observations. Seconds. Weight. 1666 I -47 . . 0-1 ,, E . +26 . . 0-1 1697 E . . -25 . . 0-2 1728 I - 8 . . 2-5 1736 I - 9 . . 0-6 „ E . . +1..0-6 1743 I 0 . . 1-5 „ E . - 3 . . 4-5 1769 I - 7 . . 2-5 „ E - 1 . . 0-5 1789 I . . +10 . . 3-5 „ E . +6..2-5 1802 I +4..6-0 1822 I . . +11 . . 0-4 ,, E . . - 7 . . 2-5 1848 I . . + 7 . . 6-0 ,, E . + 7 . . 0-5 1861 I +12 . . 2-0 „ E . . +11 . . 4-0 1868 I . . +2 . . 06 ,, E . - 5 . . 4-0 1881 I . . - 6 . 6-0 ,, E . . - 2 . . 60 1894 I - 6 . . 6-0 ,, E . +2..6-0 On the theory that the apparent variations in the motion of the moon really arise from changes' in the earth’s rotation, the numbers of this table should, in a general way, correspond to those in the last column of the table preceding. Evidently such is not the case, since, if we take the weighted means of the deviations during the three periods 1677-1743, 1769-1822, 1861-1894, the results are :— Sec. Mean date 1737 A + = -4-5 >> i> 1795 ,, +2 "4 ,, ,, 1880 ,, + 0'6 We are therefore led to the conclusion that either the motion of the moon is affected by some other cause than the gravitation of other bodies, or mathematicians have not yet succeeded in rigorously computing the effect of this gravitation.
Fundamental Astronomical Constants. The term constant is used in astronomy in a relative sense, most of the quantities thus designated being really subject to variation. The term is applied because the variations of these quantities are so slow that the quantities may be regarded as constant for the periods of time -over which computations usually extend. Some of these constants, especially those which relate to the motions of the earth and moon, are intimately related to the first principles of gravitational astronomy. We shall develop the fundamental principles of the subject, and show how, by means of them, the values of the constants may be derived. We begin by defining the units of those physical quantities which enter into astronomy. It will be remarked that in physics three units are regarded as fundamental or arbitrary, «/' while all others are measure. derived from them by definition. These fundamental units are those of length, mass, and time. In the system now most widely adopted for physical investigation —that known as the C.G.S. system—the centimetre is taken as the unit of length, the gramme as that of mass, and the second as that of time. The same fundamental units of length and time may be introduced in astronomy, but it will be more convenient to take the metre as the unit of length. The passage from the metre to the centimetre, and vice versd, is too simple to require discussion. The second may be taken as the unit of time for our present purpose; but it is more convenient to take the unit of mass as a derived one. The astronomical units will then be as follows :— The units of time and length are arbitrary, the second and the metre being chosen unless otherwise expressed. Unit velocity is that which carries a point over unit space in unit time. The unit of mass is that the gravitation of which acting on an equal mass at distance unity would generate a unit of velocity in a unit of time. The unit of force is that which would generate a unit of velocity by acting on unit mass during a unit of time. To distinguish the preceding unit of mass from that of physics it is called the gravitational unit. The physical unit of length, metre or centimetre, can be used in astronomy only to derive the values of certain astronomical constants, because, in practice, it is too short to use in expressing celestial distances. But by the use of logarithms we may extend our physical measures over the celestial spaces without the use of unmanageably large numbers. Yet, in any case, the relations between the terrestrial measure and the distance of the earth from the sun must always remain more or less doubtful. Hence it is necessary to adhere to the usual astronomical unit, namely, the mean distance of the sun, in expressing distances among all the heavenly bodies except the moon. The relation between the arbitrary physical unit of mass, the gramme for example, and the gravitational unit, is a fundamental problem of physics. To ascertain it we must measure the gravitation exercised by a known mass at a known distance. constant This will give us the attraction of a physical unit of mass at unit distance, a quantity known as the Newtonian constant of gravitation. Those older methods of determining this constant which rest upon the observed attraction of great masses of matter—mountains, for example—or upon the increase in the force of gravity found on descending into mines, are now entirely superseded, owing to the uncertainty as to the density and arrangement of the masses whose action is measured. Recent determinations depend entirely upon the attraction of portable masses, such as spheres or blocks of lead. It
