STUDIES ON THE VARIABLES OF THE ALGOL-TYPE. 27 



Actual calculation of the above equation such that it is in 

 the usual form of the cubic equation, we have 



/^-93/= + 2508.4;.-15865.3 =0. 



Now solving this equation, we have three real roots, 



X, = dm, X,=S8.\5, 1=45.76 



Substituting the smallest root in the simultaneous equations, 



(A-/)X+ DY + EZ =0 

 DX +(B-yl) Y + FZ=0 

 EX +FY+(C-/)Z =0, 



the solution with respect to the three quantities X, Y, Z will 

 finally determine the position of the pole. But, in order to 

 derive the necessary co-ordinates of the pole, A and D in the 

 right ascension and declination, we have the following three 

 equations 



X = cos D cos A 

 Y=cos D cos A 

 Z=sin D. 



Thus, by the final reduction, we arrive to the result 



A=186°.2 

 D= 25°.6. 



Comparing this result with that from the galaxy including the 

 branch of it, we see that both the right ascension and the 

 declination do not exactly coincide, but the present result differs 

 very widely from the that obtained by Prof. Pickering from a 

 small number of Algols 



A=195° 

 D= 20°. 



