398 



SCIENCE 



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



secular motion which is capable of being 

 determined from the modern observations 

 and is not affected by the discussion of 

 ancient eclipses — namely, the secular mo- 

 tion of the perigee — agrees with its theo- 

 retical value well within the probable error. 

 With this remark I pass to the empirical 

 terms. 



These unexplained differences between 

 theory and observation may be separated 

 into two parts. First, Neweomb's term of 

 period between 250 and 300 years and co- 

 efficient 13", and, second, the fluctuations 

 which appear to have an approximate 

 period of 60 to 70 years. The former ap- 

 pears to be more important than the latter, 

 but from the investigator's point of view 

 it is less so. The force depends on the 

 degree of inclination of the curve to the 

 zero line or on the curvature, according to 

 the hypothesis made. In either case the 

 shorter period term is much more striking, 

 and, as I have pointed out on several occa- 

 sions, it is much more likely to lead to the 

 sources of these terms than the longer 

 period. It is also, at least for the last sixty 

 years, much better determined from obser- 

 vation, and is not likely to be confounded 

 with unknown secular changes. 



Various hypotheses have been advanced 

 within the last few years to account for 

 these terms. Some of them postulate 

 matter not directly observed or matter with 

 unknown constants; others, deviations of 

 the Newtonian law from its exact expres- 

 sion; still others, non-gravitational forces. 

 M. St. Blancat^ examines a variety of cases 

 of intramercurial planets and arrives at the 

 conclusion that such matter, if it exists, 

 must have a mass comparable with that of 

 Mercury. Some time ago I examined the 

 same hypothesis and arrived at similar re- 

 sults. The smallest planet with density 



7 Annales de la FacultS des Sciences de Toulouse, 

 1907. 



four times that of water, which would pro- 

 duce the long inequality, must have a disc 

 of nearly 2" in its transit across the sun 

 and a still larger planet would be neces- 

 sary to produce the shorter period terms. 

 But observational attempts, particularly 

 those made by Perrine and Campbell, have 

 always failed to detect any such planet, and 

 Professor Campbell is of the opinion that a 

 body with so large a disc could hardly have 

 been overlooked. If we fall back on a 

 swarm instead of a single body, we replace 

 one difficulty by two. The light from such 

 a swarm would be greater than that from a 

 single body, and would therefore make 

 detection more likely. If the swarm were 

 more diffused we encounter the difficulty 

 that it would not be held together by its 

 own attraction, and would therefore soon 

 scatter into a ring ; such a ring can not give 

 periodic changes of the kind required. 



The shading of gravitation by inter- 

 posing matter, e. g., at the time of eclipses, 

 has been examined by Bottlinger.* For 

 one reason alone, I believe this is very 

 doubtful. It is difficult to see how new 

 periodicities can be produced; the periods 

 should be combinations of those already 

 present in the moon's motion. The sixty to 

 seventy years' fluctuation stands out in this 

 respect because its period is not anywhere 

 near any period present in the moon's mo- 

 tion or any probable combination of the 

 moon's periods. Indeed Dr. Bottlinger's 

 curve shows this: there is no trace of the 

 fluctuation. 



Some four years ago I examined^ a num- 

 ber of hypotheses. The motions of the 

 magnetic field of the earth and of postu- 

 lated fields on the moon had to be rejected, 

 mainly because they caused impossible in- 

 creases in the mean motion of the perigee. 

 An equatorial ellipticity of the sun's mass, 



8 Diss., Freiburg i. Br., 1912. 

 Amer. Jour. Sc, Vol. 29. 



