394 



SCIENCE 



[N. S. Vol. XL. No. 1029 



of observation. A considerable difference 

 appears about 1820, for which I have not 

 been able to account, but I have reasons for 

 thinking that the difference is mainly due to 

 errors in the occultations rather than in the 

 meridian values. In the last sixty years the 

 differences become comparatively small, 

 and the character of the deviation of the 

 moon from its theoretical orbit is vs^ell 

 marked. This deviation is obviously of a 

 periodic character, but attempts to analyze 

 it into one or two periodic terms have not 

 met with success ; the number of terms re- 

 quired for the purpose is too great to allow 

 one to feel that they have a real existence, 

 and that they would combine to represent 

 the motion in the future. The straight line 

 character of the deviations is a rather 

 marked peculiarity of the curves. 



The actual deviations on a smaller scale 

 are shown in the next slide ; the great em- 

 pirical term has here been restored and is 

 shown by a broken line. The continuous 

 line represents the Greenwich meridian ob- 

 servations ; the dots are Newcomb 's results 

 for the occultations before 1750, the date 

 at which the meridian observations begin. 

 "With a very slight amount of smoothing, 

 especially since 1850, this diagram may be 

 considered to show the actual deviations of 

 the moon from its theoretical orbit. 



The next slide shows the average values of 

 the eccentricity and of the position of the 

 perigee.^ The deviations are those from the 

 values which I have obtained. It is obvious 

 at once that there is little or nothing syste- 

 matic about them; they may be put down 

 almost entirely to errors of observation. 

 The diminishing magnitude of the devia- 

 tions as time goes on is good evidence for 

 this; the accuracy of the observations has 

 steadily increased. The coefficient of the 



s Tables II., III. of a paper on ' ' The Perigee 

 and Eeeentiicity of the Moon," Monthly Notices 

 B.A.S., March, 1914. 



term on which the eccentricity depends is 

 found with a probable error of 0".02, and 

 the portion from 1750 to 1850 gives a value 

 for it which agrees with that deduced from 

 the portion 1850 to 1901 within 0".01. 

 The eccentricity is the constant which is 

 now known with the highest degree of accu- 

 racy of any of those in the moon's motion. 

 For the perigee there was a difference from 

 the theoretical motion which would have 

 caused the horizontal average in the curve 

 to be tilted up one end over 2" above that 

 at the other end. I have taken this out, 

 ascribing it to a wrong value for the earth's 

 ellipticity ; the point will be again referred 

 to later. The actual value obtained from 

 the observations themselves has been used 

 in the diagram, so that the deviations shown 

 are deviations from the observed value. 



The next slide shows the deviations of 

 the mean inclination and the motion of the 

 node, as well as of the mean latitude from 

 the values deduced from the observations.* 

 In these cases the observations only run 

 from 1847 to 1901. It did not seem worth 

 while to extend them back to 1750 for it is 

 evident that the errors are mainly acci- 

 dental, and the mean results agreed so 

 closely with those obtained by Newcomb 

 from occultations that little would have been 

 gained by the use of the much less accurate 

 observations made before 1847. The theo- 

 retical motion of the node differs from its 

 observed value by a quantity which would 

 have tilted up one end of the zero line about 

 0".5 above the other; the hypothesis 

 adopted in the case of the perigee will ac- 

 count for the difference. 



The mean latitude curve is interesting. 

 It should represent the mean deviations of 

 the moon's center from the ecliptic; but 



■* "The Mean Latitudes of the Sun and Moon," 

 Monthly Notices B.A.S., January, 1914; "The De- 

 termination of the Constants of the Node, the In- 

 clination, the Earth 's Ellipticity, and the Obliquity 

 of the Ecliptic," ii., June, 1914. 



