26 



ABT. 10. — N. ICHINOHE 



referred to the same axes, then the cosine of the distance of the 

 star from the pole, P, becomes 



P=aX+l)Y + cZ. 



Then, squaring it, we have, 



P-=a-X2 + b-Y-+c'Z- + 2caZX4 2abZY + 2bcYZ. 

 Now putting 



B=2b^ 



C=2c^ 



D-Sab 

 E-Sac 



for the sums of all the Algols, we have 



2F=AX2+BY- + CZ- + DXY4-EZX + FYZ. 



Thus, actual computations on the 93 Algols give us 



A = 15.953 D= -4.397 



B = 40.896 E = + 13 248 



C=36.138 F= - 1.912. 



The condition, that SP" is a minimum, is d2P"=0, namely 



(AX + DY+EZ)dX+(DX+BY+FZ)dY + 

 (EX + FY + CZ)dZ=0. 



Besides this, the relation X^ + Y" + Z'^=l gives a condition 



XdX+YdY + ZdZ=0. 



Then, the Lagrangean process of an indeterminate multiplier 

 À is applied to determine the values of X, Y, Z. For this case, 

 /I will be determined by the solution of the cubic equation 



A-X D E 



D B-k F 



E F C-; 



= 



