122 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Mr. Hau. spoke of the importance of the arithmetico-geometric 
mean in astronomy. . 
Mr. W. B. TAytor made a communication on 
A CASE OF DISCONTINUITY IN ELLIPTIC ORBITS * 
around an empty center of gravitative force. Diminution of the 
minor axis of the attracted body’s path (the major axis being con- 
stant) increases the ratio of distance at the two apses without limit, 
the “periapsis” continually approaching the attractive center, 
as long as the minor axis has a value, however small. But when 
this axis is made to vanish, and the motion is directly to the center 
of force, the body, instead of rebounding from it, as continuity 
would require, will pass through it, and describe an equal path on 
the opposite side, the orbit being at once doubled. 
This paper was discussed by Messrs. Bares, Caristir, Haun 
and others, and brought out a wide diversity of view as to the 
demeanor of a heavy point when coincident with an empty attract- 
ing center. 
15TH MEETING. . DECEMBER 38, 1884. 
The Chairman presided. 
Nineteen members and guests present. 
Mr. M. H. DooxrrrLe made a communication on 
THE VERIFICATION OF PREDICTIONS. 
[ Abstract. ] 
Mr. G. K. Gilbert has published (American Meteorological 
Journal, 8°, Detroit ; September, 1884, pp. 166-172) a method of 
estimating the ratio of skill in predictions of occurrences and non- 
occurrences of a simple event. Adopting his notation, we have 
s = the sum or total number of cases, 
o = the number of occurrences, 
p= the number of predictions of occurrences, 
i 
