780 



TABLE 900.— THE EARTH'S ROTATION: ITS VARIATION 803 



From observations, Spencer Jones (Monthly Notices, Roy. Astron. Soc, vol. 99, p. 541, 

 19.39) deduces as the best value of the apparent solar acceleration 2.5"/ (century) 2 . Lunar 

 theory predicts 12.0"/(century) 2 leaving part attributable to tidal friction 10"/(century) 2 . 



Estimates of tidal friction losses (Jeffreys, Philos. Trans., A, vol. 221, p. 239, 1920) : 



Other contributions are small. Total for spring tides 22 X 10 18 erg/sec. 1.1 X 10 19 erg/sec 

 average, corresponding to about 7" secular acceleration per century per century. If fl 

 is earth's angular velocity of rotation, dSl/dt = — 2.5 X 10~ 22 /sec 2 . fi = 7.3 X 10~ B rad./sec. 

 12 changes by 10~ B of its amount in 3 X 10 l2 sec or 10 s years. The day should have 

 lengthened by 1 sec in 120,000 years. 



The fluctuations in the earth's rate of rotation indicated by astronomical evidence are 

 of a quite greater order of magnitude. Moreover the changes vary in sign whereas fric- 

 tional effects should not. The observations come from deviations of the sun and moon 

 from their gravitational orbits, the transits of Mercury, and eclipses of Jupiter's satellites. 

 Changes in the speed of rotation of the earth rotation seem the only explanation. This 

 may be due to shifts of matter within or on the earth. The following figure by Brown 

 indicates that in 1928 the earth was about 25 sec ahead of its average rotational motion 

 during the last three centuries. The greatest apparent change in the loss or gain of one 

 sec in a whole year. (1 part in 30,000,000.) 



Fig. 36. — Irregularities in the earth's rotation derived from the 

 moon's motions. 



Tidal friction should make the earth rotate more slowly and the moon recede from the 

 earth. The rate of dissipation of energy by friction is about 1.4 X 10 19 erg/sec. The earth's 

 rotation from this cause should have slowed by 4 hours during geologic time. The moon 

 should continue to recede until its period of revolution and that of the earth's rotation are 

 equal to 47 of our present days. The moon should then gradually approach the earth, 

 ultimately coming within Roche's limit (about twice the earth's radius) breaking up 

 possibly into a ring like Saturn's. 



301 Jeffreys, The earth, Macmillan, 1929; Innes, Changes in the length of the day, Scientia, vol. 42, 

 p. 69, 1927; Brown. Nature, vol. 119. p. 200, 1927; Jo -.rn. Roy. Astron. Soc. Canada, vol. 24, p. 177, 

 1930. Revised by G. M. Clemence, U. S. Naval Observatory. 



SMITHSONIAN PHYSICAL TABLES 



