ASTRONOMY: A. 0. LEUSCHNER 
75 
diminished to GOS'^J, the last figure available. Thus in 1910 Hecuba had 
already encroached well within the previously known gap about 600'^ 
In von Zeipel's theory a transformation of the given osculating elements is 
made at the outset with the aid of the general tables for the group 1/2. The 
resultant elements which are retained as constants until the theory is com- 
pleted, are not exactly mean elements in the sense defined above, but they 
approximate the same. Since from 1877 to 1910, or in thirty-three years, 
the osculating mean motion has gradually diminished by approximately 
10", it might be supposed that our own approximate starting mean mean 
motion would lie somewhere within this range, or at least be less than the 
original maximum value of 617'^7 in 1877, but as a matter of fact our approx- 
imate mean mean motion is larger by l'^8. The numerical developments 
indicate that the mean motion may continue to diminish. Whether the 
mean motion of 598" will^ actually be passed, will form a significant problem 
of research in the theory of motion of minor planets. But the following 
facts stand out prominently even now: (1) The extent of the hitherto known 
gap about 600" has been greatly diminished; (2) stability has not been im- 
paired thereby as our representation of the 1914 observation shows, for which 
the perturbation in the mean anomaly has now diminished from the original 
24° in 1877 to a comparatively small quantity. (3) E. W. Brown's con- 
clusion stated in his vice-presidential address before the Section A of the 
A. A. A. S. that if instability exists at or near 598", it must be for mean mo- 
tion exceedingly close to that figure has been verified, and (4) if Andromache's 
mean motion should pass through 598" stability will probably not be im- 
paired, because our developments indicate no discontinuity for that condition. 
Another planet to which I desire to refer is the lost planet Aethra. From 
investigations by Dr. Dinsmore Alter the cause of the loss of Aethra is due to 
the fact that the elements on which extensive search has been based for sev- 
eral decades are wholly unreliable, although published to seven figures. In 
fact the observations can be represented by orbits ranging in mean motion 
from 800" to 900" and moje. All that can be said about this planet at the 
present time is that it may be anywhere at any time within a belt of the 
celestial sphere 2°20' wide and that its rediscovery and identification will be 
a matter of chance, unless it is located on the supposition that an unknown 
planet discovered in 1913 at the Lowell Observatory, but observed only once, 
was Aethra. An orbit representing all the original observations of Aethra 
from June 13 to July 5, 1873, as well as the position of the unknown object 
in 1913 would make the average mean motion in the interval of forty years 
equal to about 883". Details of the investigation and a search ephemeris 
extending to March 1 of this year, were pubhshed in a Lick Observatory 
Bulletin in November, 1915, but war conditions in Europe and unfavorable 
weather in California seem to have prevented adequate search. (An exhaus- 
tive, but unsuccessful, search has since been reported by Dr. Anna Estelle 
Clancy in Astronomical Journal, 31, No. 723, April, 1918.) 
