go CARNEGIE INSTITUTION OF WASHINGTON. 



second slit set on the Hj band. The measuring globe has been 

 readjusted for use with this series of photographs, and the prelim- 

 inary reductions of the plates already measured shows that the rota- 

 tipn period will probably be in good agreement with that obtained 

 from the Kenwood plates. On account of their larger scale, better 

 contrast, and sharper definition, the photographs taken with the 40- 

 incli telescope should yield results much more precise than those 

 hitherto obtained. 



Mr. Fox has also devoted some time to a photographic study of the 

 spectrum of lightning and to the measurement of photographs of 

 the spectrum of the spark, taken between iron poles in gases at high 

 pressures. 



Simon Newcomb, Washington, D. C. Grant No. 104. For deter- 

 rninmg the elements of the vioon'' s viotion and testi?ig law of gravity . 

 (First report is in Year Book No. 2, p. xxi.) $2,500. 



The circumstance which gives importance to the research is the 

 ascertained existence of inequalities of long period in the motion of 

 the moon for which no explanation has yet been found. These ine- 

 qualities are of such magnitude as to render impossible the prediction 

 of precise positions of the moon for many years in advance, and their 

 existence has been one of the two most perplexing problems of celes- 

 tial mechanics during the last half-century. 



To investigate the cause of these deviations, researches of two 

 distinct classes are necessary. These are : 



A. The computation from mathematical theory of the inequalities 

 of long period which may be produced by the action of the planets. 

 The problem involved in these computations is the most difficult and 

 complex in celestial mechanics. Although it has been attacked by 

 various authorities in recent times, it seems desirable, in view of the 

 importance of the subject, to reconstruct the whole work by methods 

 radically different from those hitherto adopted. 



B. The comparison of the positions of the moon as computed from 

 the tables, with astronomical observations of its position in the 

 heavens. The observations best adapted to the present purpose are 

 those of occultation of stars by the moon. In a work published by 

 the Naval Observatory in 1878 Dr. Newcomb discussed all the obser- 

 vations of this class, as well as those of eclipses, from the time of 

 the most ancient Babylonian records up to 1750. Much work was 

 subsequently done in the Nautical Almanac Office toward continuing 

 these computations to the present time. Dr. Newcomb' s retirement 

 from active service in the Navy having prevented the completion of 



