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PROCEEDINGS OF THE AMERICAN ACADEMY 



of 1.8, by subtracting the term 3 sin (3 v — 45°). 

 become 1.4 instead of 2.8, if we subtract 4 sin 3 v. 



Those of 8 Cephei 



TABLE XI. — Terms involving 3 v. 



jSTo natural explanation can be offered for such terms, and the 

 reduction might be thought accidental did it not occur in so many- 

 different curves. A careful distinction must be made between these 

 terms and those which might be assumed empiricalh^ since their form 

 is clearly pointed out by the residuals. If we tried to represent the 

 residuals by a function of 4 v, we should soon see that the effect was 

 wholly different, nor would any values of the arbitrary, constants in 

 this case materially reduce the residuals. 



Neglecting these last terms, as their reality may be questioned, we 

 may write the equations of the four stars under each other thus : — 



C Geminorum, L = 89.6 + 10.2 sin (v — 11.3°) 



^Lyr£E, Z=8l.l-i- 4.1sin(v — 90°)-l-20.0sin(2v— 90°) 



r] Aquilaj, L = 74.6 -[- 20.0 sin (v — 60°) -j- 6.0 sin (2 v — 120°) 

 8 Cephei, L = 72.1 -j- 20.0 sin {v — 4;)") -j- 7.0 sin (2 y — 120°) 



To compare them, it will be convenient to make the mean bright- 

 ness equal to unity in all cases, or to divide by n the equation L = a 

 -j- m sin (v -\- «) -\- n sin (2 v -\- (S). Instead of making « = 0, 

 when the light is a minimum, it will also be better to take as the start- 

 ing-point the position in which the shorter axis of the star is turned 

 towards the observer. If v' = v -[- y, we may write L' -=.1 -\- m' 

 sin iv' -j- «') -|- n' cos 2 v'. The various values of these constants 

 are given in Table XII., which contains in successive columns the name 

 of the star, the value of y, of «', of ??i', and of n'. Independently of 

 the form of the star, its light would vary, owing to the unequal bright- 



