16 ART. 19. — N. ICHINOHE : 



DENSITY OF ALGOLS. 



It is well known fact tliut the liniitiiiir value of the mean 

 density of an Algol-system will easily be found when w^e have 

 the duration of the eclipse as w^ell as the period determined. 

 In 1899, A. Roberts (A. P. J. X, 308} considered the densities 

 of the four southern Algols observed by himself. Denoting the 

 period of an Algol by P ; semi-major axis, by a ; the diameters 

 of the components (1) and (2) by ]:a and qa respectively and 

 the masses of the components by m^ and nu ; we have the for- 

 mulas for the densities of the both components. 



Densitv of (i)^ (O-OOg)Y ^^) 

 Density of (2)=i^0^f^^) 



where sidereal year is taken as the unit of time and that of 

 distance is the mean distance of the sun from the earth, namely, 

 the astronomical unit. Thus, if w^e know the ratios mi/m2 and 

 mzlttiu the density for each component will be separately known, 

 by the applications of the above formulas, as p and q are the 

 quantities to be determined from the examinations of the 

 elements of Algol-variation. Now, putting 



the latter flictors of the above formulas will be written as follows 



1 1 



1 + k' i + lJ' 



As T , , and , . ,. never exceeds unity, we can calculate the 

 absolute maximum value of the density for both components by 



