RECENT ADVANCES IN SCIENCE 179 



probable values of the secular accelerations of the Sun and 

 Moon have been discussed by Dr. J. K. Fotheringham in a 

 recent paper {M.N., R.A.S., 80, 578, 1920). The various 

 lines of evidence have been brought under review, and the 

 previous work of Newcomb, Cowell, and Fotheringham has 

 been critically examined and supplemented by some fresh 

 material. Five sources of evidence are available for such a 

 discussion, (i) The times of ancient lunar eclipses give the 

 difference between the lunar and solar accelerations. The 

 difficulty in utilising the material is due to the inaccuracy or 

 indefiniteness of the recorded times and places at which the 

 eclipses were visible. For various reasons {M.N., 76, 395) 

 Fotheringham rejects the Babylonian eclipses. Several of the 

 Greek eclipses are also rejected owing to unsatisfactory material. 

 From the remaining eclipses a value of|+ 7''-9 i i^'S is found 

 for the difference between the secular accelerations of the 

 Moon and Sun. (2) The magnitudes of lunar eclipses give a 

 value for the secular acceleration of the Sun. The data have 

 been discussed by Fotheringham {M.N., 69, 666 ; 78, 422), and 

 give a mean solar acceleration of + i^-yS ± o''*45. (3) Re- 

 cords of ancient solar eclipses provide material for determining 

 the secular accelerations of both Sun and Moon. Fotheringham 

 finds that the eclipses of Hipparchus and Plutarch are critical 

 eclipses, and that the records of these cannot be satisfied if the 

 acceleration of the Sun is greater than about i ". With this 

 value for the Sun and a value of + io"-5 for the Moon, the 

 most reliable of the ancient solar eclipses are satisfied, and it 

 is concluded that these are the most probable values to be 

 deduced from the whole series. (4) From the records of 

 occupations of stars by the Moon, the lunar accelerations can 

 be found. Dr. Fotheringham and Miss Longbottom have 

 previously discussed these {M.N., 75, 393), and found a value 

 of -f io"-8 ± o"*7o. (5) A value for the solar! acceleration can 

 also be found from equinox observations if it is assumed that 

 Hipparchus used a fixed equator in his earlier series of equinox 

 observations, but that in his later series he used the same equator 

 as in his observations of the declinations of stars. In this way 

 a value of -f i"'93 dz o"*2 7 is found for the solar acceleration. 



Summarising, Fotheringham finds that the most probable 

 values furnished by the various lines of evidence are : 



Secular acceleration of 

 Moon. Sun. Difference. 



1. Lunar Eclipse Times + 7''"9 ± i"'3 



2. Lunar Eclipse Magni- 



tudes ... + I'jS ± o''-45 



3. Solar Eclipses . . + lo'-s + I'-o + g'-s 



4. Occultations . . + lo'S ± o^'-yo 



5. Equinoxes . . + i''93 ± o''"27 



