272 PROCEEDINGS OP THE AMERICAN ACADEMY 



taking the products of these sums. The actual light would equal 

 (1 -|- m' sin (v' -{- a')) (I -\- 11' cos 2 t'') = 1 + m' sin {y' -}- a) 

 -|- «' cos 2 y' -}- m'n' sin {y' -\- a) cos 2 v'. The value of L' given 

 above is then subject to the systematic error of m'n' sin (v' -\- a) cos 2 v'. 

 The maximum value of this would equal ?n'n', and it would generally 

 be much less. The maximum value for ft Lyrce would be about 1 per 

 cent ; for rj Aquilce, 2 ; and for 8 Cephei, 2.6 per cent. If the star 

 underwent much greater change of light, it might be necessary to take 

 this term into account ; but in the present case it does not seem to 

 sensibly affect the average value of the residuals. 



Various attempts have been made to determine the light curve of 

 ./3 Lyice photometrically. The observations of Zollner and Wolff are 

 reduced according to the same method in the photometric work of the 

 latter, p. 110. The accuracy of the resuUs does not make this a 

 promising method of determining the light curve, unless the number 

 of observations is greatly increased. The maxima and minima were 

 also determined at the Harvard College Observatory.* Calling the 

 light at either maximum 100, that at the two minima would be 55.8 

 and 64.7, which agrees very closely with that given by computation, 

 if we neglect the term 3 sin 3 v. 



One great advantage of the study of the stars by physical instru- 

 ments, such as the spectroscope and photometer, is that some clew is 

 given to certain laws, for our knowledge of which we must otherwise 

 depend on theoretical considerations alone. While the conclusions to 

 be drawn from micrometric measurements are in general much more 

 precise, and the effect of the errors can be more certainly computed, 

 they fail entirely to aid us in studying such laws as those here con- 

 sidered. For example, the present investigation serves to study the 

 following important problem in cosmogony, to which micrometric 

 measures contribute nothing, and which can otherwise only be ex- 

 amined from the standpoint of theory. If we admit a common origin 

 to the stars of the Milky AVay, a general coincidence in their axes of 

 rotation seems not improbable, especially as such an approximate coin- 

 cidence occurs in the members of the solar system. If the coincidence 

 was exact, the direction must be that of the poles of the Sun, or, 

 approximately, that of the pole of the ecliptic. On the other liand, 

 since the stars of the Milky Way are supposed to be arranged in 

 the general form of a flattened disk, we should more naturally expect 

 that the axes of rotation would be symmetrically situated with regard 



• Annals, xi. 135. 



