142 SHIX HIRAYAMA; 



point of intersection of this plane and the axis of z being the origin. 

 The axis of y is the intersection of the plane of reference and the 

 declination plane of the sun, positive towards the north pole. The 

 axis of x is perpendicular to the?/ axis in that plane of reference and 

 is positive towards the point whose right ascension is greater by 90° 

 than that of the sun. 



Referred to this system of co-ordinates, let us assume — 

 x, y, = : the co-ordinates of the moon ; 



c, r t , = the co-ordinates of the point of intersection of the line 

 joining the observer and the sun with the plane of re- 

 ference ; 

 I) = the distance of this point from the moon ; 

 a, d = the geocentric right ascension and the declination of the 



moon, respectively ; 

 a, d' = the geocentric right ascension and the declination of the 



sun, respectively ; 

 re, -' = the equatorial horizontal parallax of the moon and the 



sun, respectively ; 

 r, / = the geocentric semidiameter of the moon and the sun, 



respectively ; 

 z\ v = the geocentric zenith distance and the parallactic angle of 



the sun, respectively ; 

 <p, <p' = the geographical and the geocentric latitude, respectively ; 

 p — the radius of the terrestrial spheroid for the latitude <f ; 

 t = the hour angle of the sun ; 



e = the equation of time. 

 Then, we have the following formulas, the derivation of which, 

 being explained in the work of Sawitsch, is here omitted. 



The distance between the moon and the centre of the earth is 

 taken as the unit of distance. 



