PREDICTION OP SOLAR ECLIPSES. 



155 



sin (p = m sin (M—N) 



r= — cos d> cos (M—N) 



11 T n 



T=T +r 



•(32) 



in which cos <p is to be taken with the negative sign for the beginning 

 and the positive sign for the end. 



The longitude and latitude of these extreme points may be found from 

 (29), by putting cos z'=Q or ^ = 90°. 



14. To find the duration of total or annular eclipse. 

 Let 



T= the time of central eclipse 



t = the duration of total or annular eclipse 



then T /= 7 ,= F-n- r is the time of beginning or end. 



Let x', ?/, £', ff be hourly ch.'inges of x, ?/, £, 7, respectively. 

 At the time 2", we have by (4) 



D sin a = x^f— x'v— ( <f T17 £'") ; 



D cos ^ = y + —y'T-(^ + —r/zJ . 



Hut we have x=£ ?/ = "tf ; hence 



B sin a= q:(x' — ç') -r- ; 



D cos <r ^-H:?/' -'«?') y ; 



where D = r—r' (l—p sin~ cos z') for the total eclipse 



D=r' {1—p sirnt cos z')—r „ „ annular „ 



,..(33) 



