( 469 ) 



Let e7„ represent the intensity at the maximum, G^ the corresponding 

 magnitude, J and G the same quantities at the time t, then, by the 

 formula of Pogson : 



G— G, = 2.512 {log J, — log J). 



Consequently : 



dJ 

 dG = — 2.512 m. — , (m = modulus of Brigg's log.) 

 u 



dJ 



dG= — 1.092 — . 



1 

 Now, if is the equivalent in magnitudes of a grade, then, g. 



V 



and o being the number of grades: 



o,—a — v[G—GJ=z 2.hl2v{logJ,-logJ) 



Therefore : 



dJ 

 da— 1.092v — 



%J 



Putting the value of Argelander's grade for the light-curve of 

 ^ Lyrae at 0.130 magnitudes, then : 



dJ 

 ^(7=8.413—. 

 J 



8. In the hypothesis which we adopted, the main phases (min.^, 

 max.i, min. 2, max. J take place for the values /?=0, -, .t, — of /?i. Let 



Li 2i 



y^, ^;2, v^, v^ represent the true anomalies for these values; M^, M^, 

 Mj, J/4 the corresponding mean anomalies. If, as is the case with 

 /? Lyrae, the intervals are nearly equal, e must be small and we 

 may put approximately: 



(a- := 2e cos (o; y =z 2e sin (o) 



or : 



Ji 



^4 — ^8 = y = {M, - M,) — cc — y 

 If the differences M^ — M^ • • • ') are known with equal and 



1) The time-equation for the reduction to the common centre of gravity, computed 

 from the spectroscopic orbit, is found to reach a value of somewhat over + 100 

 seconds and may consequently be neglected. 



32* 



