332 



SCIENCE. 



[N. S. Vol. XVII. No. 426. 



where tlie D are simple functions of the 

 uncorrected observations, and 



c.= {X),-- 



.9m 



or otherwise 



Wi + 



9i 



fi9ni finffi 



(^)r 



UvniJ LmMiiJ 



and where c , c^ are given by similar ex- 

 pressions. If not previously available, a 

 first approximation to the triangular ratios 

 may be obtained by the 'Short Method, 

 etc.' Next p^, />„!, a;/, yj and z^' are ob- 

 tained by simple expressions. The accuracy 

 of the initial values of the ratios of the 

 triangles is now tested by recomputing 

 them from closed expressions or by the 

 series. Any disagreement between the 

 initial and final values is removed by means 

 of differential formulas. The elements are 

 computed by formulas VIII. of the 'Short 

 Method.' The use of rectangular coordi- 

 nates as outlined in the paper presents 

 many advantages and is applicable to long 

 ares. 



The Solution of an Orbit, Irrespective of 

 Parallax and Aberration: A. 0. 

 Leuschnee. 



In the 'Method of Computing Orbits in 

 Rectangular Coordinates' the effects of 

 parallax and aberration are fully elimi- 

 nated, except in the expressions for the 

 ratios of the triangles, in which the ^^'s 

 are affected by the difference of planetaiy 

 aberration (e. g., e^^= k{ i,,^ — ^i ) ) . In 

 certain rare cases, particularly for very 

 short intervals, the e^, c,. c^ become so 

 small that the solution will become indeter- 

 minate unless the accurate differences in 

 planetary aberration can be introduced at 

 the start. In a first orbit, therefore, re- 

 course is had to eliminating the first 

 powers of the differences in aberration, by 



segregating the first powers of the <?'s as 

 factors from c^, c^, c^ and then replacing 

 them by expressions involving the differ- 

 ences of aberration, e. g., 



e, = H/ — ka{p,,,-~p,). 



The fundamental equations then take the 

 form 



"Pi + bPo + epiii + d + kaep^iiPj^ + Wi'mPo 



■ + kagp^p^ = 0, 



where a is the aberration factor. 



The solution of these equations is re- 

 duced to the solution of two equations of 

 the form 



Po=/(Pm — ft) and p^^^ — p^ = ij,{p„) 



from which (^j„ — p^) and p^ are obtained. 



The Orbit of Comet 1902 a: A. 0. 



Leuschnee. 



The paper contains a preliminary re- 

 port on the investigation of the orbit of 

 comet 1902 a. A preliminary orbit based 

 on three observations, of which the third 

 represented a single micrometric measure 

 in a. and S was published shortly after the 

 appearance of the comet. The elements, 

 which were computed by the 'Short 

 Method,' indicated an unusually short 

 period. A comparison of the sum of the 

 squares of the residuals from the elliptic 

 with those from a parabolic orbit computed 

 at Kiel gave the following results for the 

 first nine observations; 



[w] parabolic orbit 2985 

 [w] elliptic orbit 711 



For further investigation the observations 

 were grouped into six places, three of 

 which represent single observations, one 

 was based on two, one on three, and 

 one on five observations. The best 

 three of these were selected for the 

 improvement of both the parabolic and 

 elliptic orbits. The final parabolic orbit 

 is completed and does not represent the 



