A. MATHEMATICS AND ASTRONOMY. 27 



DEFECTS IX THE LUNAR TABLES. 



An important communication by the astronomer royal 

 of England to the Royal Astronomical Society explains the 

 existence of a serious defect in the present condition of the 

 lunar theory. In 1827 Sir George 13. Airy announced the 

 discovery of a term depending on the relative motion of the 

 earth and Venus, whose period was 239 years. The intro- 

 duction of this term into the lunar tables of Professor Hansen 

 was shown by Delaunay in 1863 to be unjustifiable, and De- 

 launay's results having been confirmed by the recent investi- 

 gations of Professor New T comb, Professor Airy, now admitting 

 the possibility of an error in his earlier investigation, and the 

 correctness of the results of Delaunay and Newcomb, has 

 sought to ascertain what will be the effect of withdrawing 

 from Hansen's tables of the moon the term in question. He 

 finds that, after applying the best known value of the mean 

 longitude and mean motion of the moon that can be obtained, 

 there remains a series of large and systematic discordances 

 quite beyond the limit of accidental errors. Furthermore, he 

 has examined into the effect of assuming that these system- 

 atic discordances arise from an error in the secular mean mo- 

 tion of the moon. If we diminish the secular acceleration 

 of the moon's mean motion so as to represent modern obser- 

 vations with sufficient accuracy, we diminish the tabular 

 longitude of the moon by 160 seconds of arc in every thou- 

 sand years, and the result of this would be to completely dis- 

 arrange the calculation of the exact dates of certain ancient 

 solar eclipses, which have been much relied upon in chrono- 

 logical investigations. Monthly Notices Hoy. Astro?i. Soc, 

 XXXIV, 1. 



THE APTARENT DIAMETER OF THE MOON. 



Xeison has investigated the value of the apparent diameter 

 of the moon, as given by occultations of stars. He finds 

 that, from thirty-five observations of the disappearance of 

 stars at the dark limb of the moon, the correction to the 

 adopted semidiameter is 1.7"; and, from tw T enty observa- 

 tions of the reappearance of stars at the dark limb of the 

 moon, the correction is 0.36". On the other hand, eleven 

 observations of the disappearance of stars at the bright limb 



