A. MATHEMATICS AND ASTRONOMY. 33 



ter are those by Professor Bruuow, of Dublin, whose result, 

 0.09V", is of the highest apparent value. Previous to him, the 

 other determinations that had been made were as follows : 

 Otto Struve, 0.034 ; Wichmann, 0.114 ; Schluter, 0.166 or on 

 the average, 0.118 ; which latter value, as given by Auwers, 

 can not be suspected of a probable error greater than 0.02. 

 These four values of the parallax are, strictly speaking, only 

 relative parallaxes of the star in question, as compared with 

 four smaller neighboring stars. In a highly instructive mem- 

 oir by Auwers on the parallax of tliis star, he shows that, 

 although the heliometer used by Johnson at Oxford in 1852 

 and 1853 was one of the finest in existence, and ought there- 

 fore to have yielded a result of great value, yet the results 

 attained by him can not be considered worthy of comparison 

 with those made by the four observers before mentioned, on 

 account of defects in his method of observation. Johnson's 

 observations are subjected by Auwers to analysis in the 

 usual thorough manner of that able computer, an analysis 

 facilitated by the fact that he has himself made a series of 

 similar measurements with Bessel's heliometer at Konigs- 

 beror. The best result that Auwers is able to deduce from 

 Johnson's observations attributes to the star a parallax 

 whose probable error is larger than the parallax itself, and 

 that, too, without representing the original observations any 

 better than the simple assumption of no parallax at all. J/o- 

 natsbericht Acad, der Wissenschaften^ Berlin^ 1874, 569. 



MOVEMENT OF A PLANET IN A EESISTING MEDIUM. 



Among the many problems relating to the planetary mo- 

 tions, that of the movements of a point under the influence 

 of the force of gravitation and of a resisting medium oflers 

 always a high interest. This has been made the subject of 

 the inauofural dissertation of Dr. Hermann Hohnhorst, who 

 has considered the resistance of the medium to be propor- 

 tional to its density, and to the square of the velocity of the 

 moving body. The integration of the elementary differential 

 equations is sought to be accomplished by him by the appli- 

 cation of the theory of the variation of the arbitrary con- 

 stants. By this means he is led to four equations, giving re- 

 spectively the variations of the major axis, the eccentricity, 

 the inclination, and the longitude at the initial time. The 



B2 



