432 JSotices respecting New Books. 



The chief advantages claimed for Leuschner's method in its latest 

 form are : — 



The orbit can be computed with or without any assumption as to 

 the eccentricity. 



The influence of aberration and parallax can be completely 

 eliminated in the first approximation. 



Criteria are given by means of which the correctness of the 

 assumption of a parabolic or of a circular orbit can be decided as 

 the computation proceeds. 



It is easy to pass from a parabolic or a circular path to an orbit 

 of a general character in the course of the computation. 



By the introduction of expressions of a closed form the correc- 

 tion of the orbit can be extended to time intervals of any length. 



The limits of the possible periodic time may be easily determined 

 and thus the degree of certainty attaching to the computed orbit 

 may be estimated. 



For much disturbed bodies the perturbations may be considered 

 in the first approximation and so osculating elements obtained. 



The generality of the method permits its application without 

 change to comets, planets, or satellites. 



It may perhaps be of interest to state here that about the time 

 this book was passing through the press a striking illustration of 

 the capabilities of Leuschner's method was afforded in the case 

 of the minor planet MT 1911. This planet was discovered by 

 Palisa at Vienna on Oct. 3, 1911, and was observed again by him 

 on the 4th. It was also observed later on the same day by Pechiile 

 at Copenhagen. After an interval of bad weather all efforts to 

 recover it failed ; and as it seemed to be moving in an orbit of high 

 eccentricity, it was feared that the object was definitely lost. 



The problem of finding the orbit from three observations so close 

 together appeared well nigh hopeless ; but two of Prof. Leuschner's 

 assistants at the Berkeley Observatory, California, attacking the 

 problem by his powerful method, succeeded in finding an orbit 

 and computed an ephemeris by the aid of which a faint image 

 of the planet, previously overlooked, was detected on some of the 

 Greenwich photographic plates taken on Oct. 11. The planet was 

 subsequently picked up in the same way at Heidelberg and other 

 places. 



For the rest Prof. Buchholz's new volume is very similar to the 

 second edition, with the exception that the application of Gribbs' 

 method to the interesting case of Swift's comet of 1880, and 

 Lecture 94 on Mechanical Quadrature, have been omitted to make 

 room for Leuschner's method. But Prof. Buchholz has taken the 

 opportunity afforded by the appearance of a new edition to correct 

 many errors in the mathematical formulae and numerical compu- 

 tations which had escaped notice in the previous edition ; and 

 further he has published, in the form of a separate brochure supplied 

 with each copy of his work, a long list of errata found in 

 Bauschinger's textbook Die Bahnbestimmung der HimmelsTcorper, 

 and in Oppolzer's Lehrbuch zur Bahnbestimmung , which will be 

 much appreciated by computers of orbits who have occasion to 

 consult those important works. 



