42 



ART. 19. — N. ICHINOHE : 



The graphical investigation of the above table indicates that 

 the ratio does not increase uniformly with the time, but there 

 is a certain limit to the ratio. In the work done in 1908, I 

 did not proceed further to find a mathematical expression of the 

 relation. 



Stein, in his paper on the density of Algols, derived a 

 formula which represents the relation between the period and 

 and the duration of the eclipse. Now modifying it so that we 

 can compare the above values obtained from the observed data 

 with the formula by him, we have 



1 



r = 



0.0797 + 



0.1875 



Then, the calculations of the ratios for the values of the 

 period in the first column will give a results which agree pretty 

 well with the second column of Table X. But, as the constants 

 are not very suitable for my case, the following formula is derived 

 from Table X, determining the constants by the application of 

 the method of least squares, 



1 



r = 



0.082 + 



0.151 



Now, the last column in the above table is computed with 

 this formula ; the agreement between the observed and computed 

 may be satisfactory, but we must remember that when we use 

 the formula, the ratio is limited to the extreme value 12.2, and 

 at the same time, the actual limit is 29 from observation. Whe- 



