April 25, 1913] 



SCIENCE 



651 



degree of aeeuraoy; for example, the use of 72 

 unknowns would reproduce the observed values 

 exactly, in the case where the intervals are 5°. 

 Since, however, these observed values contain errors 

 of measurement, it is probable that a more exact 

 representation of the actual errors will be ob- 

 tained by omitting the terms with small coeffi- 

 cients; if this be granted, the number of terms 

 to be retained may in any particular case be 

 decided by a computation of the probable error 

 of a single observation. As several independent 

 measurements of the pivot errors are usually made 

 in a series, the probable error of a single ob- 

 servation may be computed directly from the 

 residuals; if now we have a formula which is 

 assumed to represent the actual pivot errors, the 

 differences between the observed values and those 

 computed from the formula may be used to form 

 another probable error; the relative magnitude of 

 these two probable errors will furnish a criterion 

 as to the number of terms required in the formula. 

 The freedom of the residuals from any systematic 

 tendency will of course furnish the final test as 

 to whether or not the formula is suitable. 



In the actual determination referred to, which 

 was made by the microscopic method, eight com- 

 plete measurements were made; the probable error 

 of a pair of microscope pointings (treated as a 

 single observation) was found to be 0.001.5 sec; 

 four terms of the Fourier expansion were found 

 to be sufficient to reduce the computed probable 

 error to the same value, and the resulting formula 

 was adopted as definitive. This formula, express- 

 ing the necessary corrections to the observed col- 

 limation, was 



AC = 0».0010cos (2« — 188° 29') 



+ 0^0117cos (39 — 3° 17') 

 + 0=.0021 cos {46 — .59° 45') 

 + 0^0008 cos (59—121° 58'), 



being the zenith distance. The residuals from 

 the formula were satisfactorily small (in no ease 

 exceeding 0.002 sec.) and appeared to be purely 

 accidental. 



Values of the formula were computed for dif- 

 ferent zenith distances, and from these a table 

 was prepared giving the zenith distances at which 

 the value of A" changed from one unit (in terms 

 of 0.001 sec.) to the next; it is this table which is 

 used in the reduction of transits. 



The Variable BV Capricorni: S. D. Townlet. 



The variability of EV Capricorni was discovered 

 by Sotz in 1905. From fourteen photographic 



observations scattered over an interval of five 

 years he deduced a light curve of the Algol type. 

 Seares and Haynes observed the star in 1906 and 

 found a light variation of the antalgol type, with 

 an approximate period of 10" 44"^. 6. The star is 

 classed as an antalgol by Hartwig, and Seares 's 

 epoch and period are used in computing the 

 ephemeris. 



Duriug the summer and fall just past BV Capri- 

 corni was one of a list of variables observed by 

 the writer with the 12-inch refractor and Eumford 

 photometer of the Lick Observatory, the use of 

 which was kindly granted by Director Campbell. 

 Three well-determined maxima were obtained and 

 these show that the Seares ephemeris now needs 

 a correction of about 3" 10'" — the observed maxima 

 coming that much before the computed. 



By comparing a well-determined maximum ob- 

 tained on October 11, 1912, with the first one 

 obtained by Seares, August 13, 1906, a period of 

 0''.447573 has been derived, while the period deter- 

 mined by Seares is 0''.4476, which is therefore 

 correct to the number of decimals given. 



The observations show conclusively that this star 

 is not of the Algol type, but there is perhaps 

 some question as to whether it belongs to the 

 antalgol or to the cluster type. Additional ob- 

 servations near minimum brightness, which I hope 

 to obtain next summer, will be necessary to decide 

 this point. 



Notes on the Real Brightness of Variable Stars: 



Henry Norris Eussell. 



The number of variables and of stars having 

 peculiar spectra contained in Boss's Preliminary 

 General Catalogue is large enough to enable an 

 approximate estimate of their mean distance and 

 real brightness to be made by the method of 

 parallactic motion. Assuming that the sun is 

 moving towards 18 h., + 30° at 19 km. per second, 

 the following values have been found, in the usual 

 way, from the data of Boss and Campbell, for the 

 parallactic motion M, the mean proper-motion t 

 at right angles to the parallactic motion, the mean 

 parallax tt, the mean peculiar velocity — r km. at 

 right angles to the line of sight and the solar 

 motion, and p in the line of sight, and finally the 

 absolute magnitudes corresponding to the mean 

 observed magnitude and mean parallax. Data for 

 three groups of stars selected at random from 

 Campbell's list of stars of Class B are added to 

 test the value of the method for small groups, and 

 some of the results of Campbell for large numbers 

 of stars are added for comparison. 



