242 MEAN DISTANCES OF THE PLANETS. 



The deviation of Newcomb's elements from the mean 

 elements is marked, thus the perihelion of Neptune's actual orbit 

 is nearly 3° from its mean position, and the eccentricities of both 

 planets are considerably greater than the mean eccentricities. 



Newcomb's values for the semi-axes majores have been 

 deduced by him from the observed mean motions and then 

 corrected for the constants due to planetary action : — they are 



Log. a. 

 Uranus i .2830871 ] Including effects of the Great In- 

 Neptune i .4781432 ) equality. 



Gaillot gives 



Uranus i. 28371 13 

 Neptune i .4787045 



and states that these values have been deduced from the observed 

 mean sidereal motions after subtracting the parts proportional 

 to the time in the mean longitude due to the actions of Jupiter, 

 Saturn and Neptune. Gaillot's tables have therefore to in- 

 clude, in the pertubations of the radius vector, the constants 

 above referred to so that the semi-axis-major as defined in his 

 tables does not represent a true mean-semi-axis major. 

 From Monsieur Gaillot's own data, we derive 



Elliptic \"alue -|- :^ of Constant Terms = True semi-axis major. 



Uranus 1.2829239 + I (0.0007874) — i .2831207 

 Neptune i .4779160 -j- ^ (0.0007885) = i. 4781 131 



The calculation for Uranus is as follows : 



La/ I -|- ;// = 0.0000095 

 L k = 6. 1 125968 



6. 1 1 26063 

 L n = 4.1882205 



T .9243858 X # = 1 .2829239 

 The constant terms are i .2837113 — i .2829239 = 0.0007874. 



One cannot but remark that the uncorrected- elliptic values 

 are nearer the true mean distances than those given by Monsieur 

 Gaillot. If, therefore, it is not intended to apply the correction 

 to both the mean motions and the distances, it is better not to 

 apply any correction. 



The definition of mean distance given above does not depend 

 on the assumption that the planets travel in ellipses but is 

 derived from the differential equations of motion so that it 

 reads, '' The mean distance of a planet is that distance from 

 which it only deviates by strictly periodical quantities," when the 

 eccentric anomaly is the independent variable. 



But it is not likely that this journal would be referred to 

 by the student wdio wants to find the mean distances of the 

 planets,— he would naturally refer to one of the two authorities, 

 tne American Ephemeris for 191 3 or the Connaissance des 



