September 13, 1901.] 



SCIENCE. 



399 



Na. Such observations were secured on five 

 nights from February 26 to March 18, and 

 seven from July 19 to August 4. These 

 treated in the usual manner by the differ- 

 ences Na — Nb, corrected for scale value 

 furnish seven equations of condition of the 

 form : 



(O-C) (O-C) 



R B 



4-l.Oa; — 1.882/4-0.152 = — 0.003 or— 0.004, 



the equation derived from the observations 

 of February 26, where x = the correction 

 to the scale value, y = the parallax, and 

 z = the proper motion. 



A solution of the normals derived from 

 these equations gives : 



2/ = — 0.0003 ± 0.0013 = — 0."003 zfc o!bl7 Wt. 38.85 



or, 



•0.0002 ±0.0013 



-0.003 0.017 



But since the distance ah furnishes an 

 independent scale value, it was thought in 

 the beginning that with this independent 

 value we might solve the parallax from 

 each comparison star separately, and thus 

 see if there is any marked difference in the 

 parallaxes of the comparison stars them- 

 selves. A closer investigation later, how- 

 ever, showed that this method would in- 

 volve the parallaxes of the comparison 

 stars in precisely the same manner as be- 

 fore, and hence would furnish nothing 

 further than another value of the parallax 

 relative to that of the mean parallax of the 

 two comparison stars, differing from that 

 already found simply by the difierence in 

 the scale value used. 



The value found by this method was : 



7r = — 0.006 ±0'.022 



as compared with 



7r=— o'.bo3±o!bi7 



given above ; which agrees with the uncer- 

 tainty of the computations. 



The author was able to find only one of 

 the comparison stars in any other catalogues 

 than the A. G. Zone Catalogue for 1875, 



and this one shows no appreciable proper 

 motion. 



Of course the result here given must be 

 considered as only provisional, inasmuch as 

 nothing is known as to the proper motion 

 of the Nova and it is barely possible that 

 this may be such as to have just neutral- 

 ized the efi'ect of parallax. Should the 

 star remain sufficiently bright for another 

 six months, however, it will then be pos- 

 sible to determine the effect of proper mo- 

 tion and hence give a definitive result. 



' Hyperbolic Curves of the ?ith Order ' : 

 Mr. A. C. Smith, University of Colorado. 



In a plane are given n straight lines with 

 Cartesian equations. Any point in the 

 plane is taken as origin and through this a 

 line is drawn intersecting the n lines in n 

 points. In this manner n segments, meas- 

 ured from the origin, are obtained on the 

 line through the origin. The algebraic 

 sum of these segments taken on this same 

 line will determine a point, P, which will 

 describe a curve of the nih. order as the ray 

 through the origin rotates through 360°. 

 It was shown how the general equation of 

 the locus could be obtained and some linear 

 transformations were considered. 



' A Uniform Method of determining the 

 Elements of Orbits of all Eccentricities from 

 three Observations of Apparent Position ' : 

 Dr. F. E. MoiJLTON, University of Chicago. 



The methods of determining orbits which 

 are in most general use were devised by 

 Gauss one hundred years ago. They are 

 different for orbits in which the eccen- 

 tricities are less than, equal to, and greater 

 than, unity, although there is no singularity, 

 which is essential to the problem, for the 

 eccentricity equal to one. The method of 

 this paper is uniform for all orbits, it is 

 considerably more convenient than that of 

 Gauss, and the radius of convergence of the 

 series employed is examined in each case. 



The longitude of the node and the incli- 

 nation are computed by the usual methods, 



