October 20, 1911] 



SCIENCE 



523 



system, and the complete work will soon appear 

 in the Astrophysical Journal. 



The VariaUlity of Polaris: Edwaed S. King. 



(Eead by Professor Stebbins.) 



The variability of Polaris haviag been an- 

 nounced by Professor E. Hertzsprung, I examined 

 the results obtained by photographing stars out of 

 focus, contained in Nos. 4, 5 and 6 of H. A. 59, to 

 discover what evidences of such changes might be 

 afforded. 



The corrections given for the individual plates 

 were used to show changes in Polaris for the dif- 

 ferent nights. The spectroscopic period, 3.9683 

 days, was accepted. A separate grouping accord- 

 ing to phase was made for each of the three in- 

 vestigations. The light curves derived from these 

 three independent series of observations are all of 

 practically the same form and amplitude as Hertz- 

 sprung 's, and confirm his discovery. The curve 

 derived from Nos. 5 and 6 of H. A. 59 suggested 

 a sine curve. And such a curve was found to 

 represent the ten points given by the grouping. 

 A sine curve having an amplitude of 0.108 mag. 

 is a very close approximation. The residuals, ex- 

 pressed in thousandths of a magnitude, for the 

 ten points are +' 6, -f- 2, — 9, + 6, -f 8, — 4, 

 — 6, +5, — 7 and -j- 3. The average deviation 

 is ± 0.0056. 



The effect of the variability of Polaris on the 

 magnitudes already determined by the out-of -focus 

 method was practically eliminated by the nature 

 of the reduction employed in the original work. 

 Corrections were made which included any varia- 

 tion in the light of Polaris, or any change in the 

 conditions occurring between photographing Po- 

 laris and the stars observed. The effect was the 

 same as if Polaris had been known to be variable. 



No special plates or measures have been made 

 to obtain the above results. All the material has 

 been derived from matter already in type. 



A Study of Visual Binary Stars: Henry Norris 



EUSSELL. 



1. The masses of visual binary systems computed 

 from their observed parallaxes vary through a 

 wide range, as Aitken has recently shown. But if 

 "hypothetical" parallaxes are computed on the 

 assumption that the mass of each of these systems 

 is 2.4 times that of the sun (the average for the 

 twelve best determined systems) only five out of 

 26 observed parallaxes differ from these hypothet- 

 ical values by quantities greater than might be 

 expected in view of the probable errors of the 

 former. The average difference between the ob- 



served and hypothetical parallaxes in the twelve 

 best determined cases, corresponds to a probable 

 error of only one fifth of the latter (including all 

 errors of observation). It is evident that the 

 binary stars are much alike in mass, and that the 

 assumption of equal masses gives very good ap- 

 proximations to the true distances, etc., of these 

 systems. 



2. It is well known that a relation between the 

 density P and the surface brightness J of a binary 

 star can be obtained independent of its parallax. 

 Let M and L be the actual mass and luminosity 

 (the sun being standard), r the radius, ir the par- 

 allax and I the apparent brightness (in suitable 

 units). Then (assuming a single mass) 



-Jr' 



PJ- 



M: 



: ML- 



The values of pJ'^f^ for the individual com- 

 ponents may be found when the ratios of their 

 masses and luminosities are known, and (as ex- 

 perience shows) estimated with suflScient accuracy 

 for the brighter component from the observed 

 difference in magnitude. 



Applying this to 83 binaries (the spectra of 29 

 of which, determined by Mrs. Fleming and Miss 

 Cannon, were very kindly furnished the writer by 

 Professor Pickering) it is found that the whiter 

 stars are very much brighter for equal masses than 

 the redder ones, while the stars of any one spectral 

 type are much more similar in brightness. 



The average masses of 73 of these binaries were 

 determined by means of their parallactic motions 

 on the assumptions (1) that the stars of a given 

 spectral type are of equal mass; (2) that they are 

 of equal luminosity. The two sets of values 

 agreed closely, showing both methods to be equally 

 legitimate. 



3. For most "physical pairs," shown to be so 

 by common proper motion, only the apparent dis- 

 tance and the rate and direction of the apparent 

 relative motion are at present known. The masses, 

 and related quantities, for the average of groups 

 of ten or more such stars, can be found by a 

 statistical process. Let r be the true distance, and 



V the true relative velocity in space; a the major 

 axis of the orbit; s the observed distance, and w 

 the observed relative velocity, as projected on the 

 celestial sphere; ii and i, the angles between r and 



V and the line of sight; M the mass and tt the 

 parallax of the system. 



