420 



SCIENCE. 



[X. S. Vol. XXI. Xo. 



component is very well determined, being 

 close to 2.934 days. Belopolsky finds, how- 

 ever, certain irregularities in the observa- 

 tions of successive years which are best ex- 

 plained by the assumption that the line of 

 apsides rotates in about 1,400 days. 



Kecent spectrograms taken with the re- 

 mounted Mills spectrograph show that the 

 brighter component is also a spectroscopic 

 binary, and that the system of a Geminorum 

 is in reality a quadruple one. Since the 

 discovery of this interesting fact in Novem- 

 ber of this year a number of plates of both 

 stars have been secured. At present four- 

 teen plates are available for a rough pre- 

 lirainary determination of the period, which 

 seems to be about 27 days. Two early 

 plates of the bright component are rather 

 poor, so that their value in determining the 

 period is somewhat impaired and more 

 plates will be necessary before a more ac- 

 curate determination of the period can be 

 derived. 



Both stars are given in the Draper 

 Catalogue as of type A, and in the later 

 Harvard classification as type Villa. H 

 Gamma is rather broad and has not been 

 used in the measures. The line at A 4,481 

 due tf) magnesium is very good and there 

 are quite a number of other metallic lines, 

 rather broad and quite faint in the spec- 

 trum of the brighter component, and some- 

 what easier of measurement in the fainter. 

 Helium is apparently absent. There are a 

 number of lines due to titanium and iron, 

 most of the latter being enhanced lines; 

 two lines seem to be due to chromium. 

 With proper exposure (about sixteen min- 

 utes) from fifteen to twenty-five measur- 

 able lines are found. The total range in 

 the radial velocity is about twenty-one 

 kilometers, and the preliminary determina- 

 tion of the velocity of the center of mass 

 of the system is approximately -f- 5 km. 

 per second. The corresponding constant 

 for the fainter component is given by Belo- 



polsky in his latest paper as — 4.1 km. per 

 second. It is well known that w'here the 

 elements of the visual orbit of a binary and 

 the relative radial velocities of its com- 

 ponents are both known it is possible to 

 derive an accurate value of its parallax. 

 Assuming the relative radial velocity to be 

 nine kilometers and using the period of 

 347 years and the corresponding elements 

 which Doberck regards as the most prob- 

 able, we find a parallax of 0".03. Using 

 the other orbits given above, however, we 

 should get values differing widely from 

 this. It is evident that snch results are 

 meaningless till the elements of the visual 

 orbit are known more definitely. 



In the star a Geminorum we have a well- 

 established quadruple system, and it is 

 hoped that the more detailed investigation 

 which the writer has in progress will give 

 a definite determination of the relative 

 radial velocity of the two systems, so that 

 with the improvement of the visual orbit 

 we may in time have a relatively very ex- 

 act knowledge of the distance, mass and 

 orbital dimensions of this complex star. 



Use of the MetJiod of Least Squares to de- 

 cide hetiveen Conflicting Hypotheses: 

 Harold Jacoby. 



In 1901 the writer published* a theorem 

 concerning the application of least squares 

 when it is necessaiy to choose between two 

 different methods of reducing observations. 

 The theorem was doubtless well known, 

 but the writer was unable to find it in 

 print. Since then, Mr. Midzuhara, of the 

 Tokyo Astronomical Observatory, has writ- 

 ten three interesting articlesf in which, 

 among other things, he gives a different 

 proof of the writer's theorem, and also ob- 

 tains another analogous one. The ob.ject 

 of the present note is to point out a very 

 important divergence between Mr. Midzu- 



* .1 str. Jour., 514. 



t Astr. Jour., 521, 535, 568. 



