178 SCIENCE PROGRESS 



ber of tables must be reduced to the smallest possible, and the 

 interpolation between successive entries made to involve as 

 little labour as possible. With such skill and careful organisa- 

 tion have the new tables been prepared that, although they 

 include nearly five times as many terms as are contained in 

 Hansen's tables (from which the positions of the Moon given 

 in the Nautical Almanac are at present computed), the time 

 taken to obtain the annual ephemeris of the Moon will not be 

 greater than is at present involved in the use of Hansen's tables. 



There is one feature of the work which deserves mention : 

 there are certain constants involved in the theory, such as 

 the average time of revolution and the mean distance of the 

 Moon, which can only be determined from observation. The 

 basis of these determinations is the long series of observations 

 of the Moon made at Greenwich during the past 150 years, 

 and it is entirely due to this long-continued series of observa- 

 tions that these constants can be determined with such accuracy. 



Every possible gravitational term which can influence the 

 position of the Moon has been taken into account. It is 

 known, however, that the Newtonian theory of gravitation 

 will not fully explain the motion. (It is, perhaps, desirable 

 to add that neither will Einstein's theory.) It has been cus- 

 tomary, in the preparation of lunar tables, to introduce several 

 empirical terms, so chosen as to represent past observations 

 with sufficient accuracy. But such terms failed, after a few 

 years, to represent subsequent observations. Prof. Brown 

 decided to exclude all such empirical terms except Newcomb's 

 long period term. A comparison of observation with pure 

 gravitational theory therefore becomes very simple with the 

 aid of the tables. It follows, however, that the tables will 

 fail from the beginning accurately to represent the Moon's 

 motion : for purposes for which very accurate positions are 

 required, as in computations of eclipses of the Sun, a correc- 

 tion will need to be applied which must be based upon the 

 latest observations. In course of time, from the comparison 

 between Brown's theory and observation, it may be possible 

 to determine the empirical terms with greater accuracy than 

 has hitherto been possible. In order that the work may not 

 be invalidated by any subsequent change which may be 

 found necessary in any of the adopted constants, data are 

 given by means of which the resulting changes in the Moon's 

 place may be calculated. 



The new tables will be used in the computations for the 

 national ephemerides from 1923 onwards. Prof. Brown is to 

 be congratulated on the successful completion of his thirty 

 years' work on the Moon's motion. 



The Secular Accelerations of the Sun and Moon. — ^The most 



