394 



SCIENCE. 



[N. S. Vol. XIV. No. 350. 



the last six are of special interest to section 

 B, they were presented at a joint session of 

 sections A and B. 



' Supplementary Eeport on Non-Euclid- 

 ean Geometry ' : Professor G. B. Halstbd, 

 University of Texas. 



This is a supplement to the report read 

 at the Columbus meeting. It will be pub- 

 lished in Science. 



' Kepler's Problem for High Planetary 

 Eccentricities ' : Professor H. A. Howe, 

 University of Denver. 



The solution of the equation M= E 

 — e sin E is commonly called Kepler's 

 problem. The known quantities e and M 

 are respectively the eccentricity and the 

 mean anomaly. E is to be found. 



The purpose of this paper is to develop a 

 direct method of solving Kepler's problem 

 for planetary orbits of high eccentricity, 

 which shall be more expeditious than any 

 heretofore discovered, and shall be suffi- 

 ciently accurate to meet the most exacting 

 requirements of astronomers. This method 

 is an outgrowth of one published by the 

 author several years ago. 



Let E' be an approximate value of E 

 found by the well-known equation 



1 + e 



tan {E' — IM) 



'■ tan pf. 



(1) 



Let2?? = ^'— if— sin {E' — M), and 



2e = l{E^ — E) — si.n i{E^ — E). 



2v 



Then 



E' — E-- 



l — e(iOS,^{E^-\-E) 

 ■ ecos J(^^4--E) 



(2) 



4e. 



l — ecoB\{E^-\-E) 



But the unknowns, E and 4£, are in equa- 

 tion (2), and must be made to disappear. 

 In the most eccentric of the asteroid-orbits 

 the value of the last term of equation (2) 

 does not reach O."0006 ; this term is there- 

 fore rejected, and we write with sufficient 

 accuracy 



E'-E=— ^ ^. (3) 



1 — ecos \ E 



1 — e cos {E' — v) 



E' may be found from (1), and E' — E 

 from (3) ; then E' -(E' -E) = E, the 

 quantity desired. The paper was illustrated 

 by large charts and will be published in the 

 Astronomical Journal. 



' The Great Fireball of December 7, 1900 ': 

 Professor H. A. Howe and Miss L. L. 

 Stingley. 



On December 7, 1900, at about 3:20 p.m., 

 mountain time, there passed over the north- 

 western quarter of Colorado a magnifi- 

 cent fireball, which exploded with start- 

 ling detonations in the vicinity of the Bow 

 Bange near the north boundary-line of 

 the state. The director of the Chamberlin 

 Observatory prepared circulars of inquiry, 

 containing a number of questions, which 

 were lavishly distributed over the region 

 from which the meteor was visible. The 

 local press was also largely utilized for a 

 dissemination of the queries. About 150 

 letters came in reply. Miss Stingleyj of 

 the class of 1903 in the College of Liberal 

 Arts of the University of Denver, made a 

 digest of these letters, and determined the 

 meteor's path across the state. It passed 

 nearly through the zenith of La Salle, and 

 the main body came to earth in the vicinity 

 of the town of Pearl. Its distance from 

 the earth's surface, when near La Salle, 

 was about 25 miles, and about 12 miles at 

 the time of bursting. When the fireball 

 was near Pearl an observation made by 

 Mr. Thomas, of Manassa, a civil engineer, 

 who was 250 miles away, gave it a height 

 of 7 miles. Mr. Godshall, manager of a 

 copper mining company, who was in Wy- 

 oming, about 40 miles beyond Pearl, saw 

 the body come down in a curve somewhere 

 in the general direction of Pearl. 



Several observers thought that they saw 

 fragments fall before the meteor reached 

 Pearl, but on account of the wildness of 

 the country none of the pieces have yet 

 been found, though they have been searched 

 for. The orbit has been computed on the 



