On the Prediction of Solar Eclipses. 



By 

 Shin Hirayama, Ri'éakushi, 



Professor of Astronomy, Science College, Imperial University, Tokyo. 



1. Introduction. For the prediction of eclipses several methods 

 of computation have been proposed by different authors. Among 

 them the methods of Bessel, Hansen, and Woolhouse are used by 

 different nations for the construction of their ephemerides. Besides 

 these, there is another method given in Sawitsch's " Abriss der 

 praktischen Astronomie, 1879," which is said to have been invented 

 by Gauss. As described by Zech, it is similar to Hansen's method. 

 Hence, for the delineation of the curve the time is not always taken 

 as the argument, as in the case of rising and setting limits. In the 

 following pages I have treated this system of co-ordinates as Bt ssel 

 has treated his. The way of discussion is quite similar to that in 

 Chauvenet. In many cases it would be sufficient only to substitute 

 for x, y, etc., of Bessel the corresponding quantities in the other 

 system of co-ordinates. But I have thought it better to develop the 

 complete formulas for convenience of computation. I have also given 

 the approximate formulae for the computation of the northern and 

 southern limits of the umbra. 



2. Fundamental equations of Eclipses. The line joining the 

 centres of the sun and the earth is taken as the axis of z, positive 

 towards the sun. Let the plane passing through the centre of the 

 moon and perpendicular to the axis of z be the plane of reference, the 



