and Transit of Mercury in 1832. 



31 



South America. Almost all Africa may see it ; but only the 

 west coast of Asia. 



For calculating the beginning and end of the eclipse for 

 places in Europe the following formulae may be made use of: 



Let the longitude of a place from Berlin = / (negative 

 if west), the corrected latitude = f, and let the following 

 values be calculated : 



u = 1-8816 cosi^ sin (45° + l) 



V = 1-7773 sin 4> — 0-6177 cos f cos (45° + I) 



u' = 0-4926 cos<f) cos (45° + /) 



v = 0-1617 coscf) sin (45° -f /) 



?K sin M = + 0-2404 — u 

 ?» cosM = + 0-1431 —V 

 w sin N = + 1-0862 — m' 

 n cos N = + 0'1554 — i/ 

 m sin (M — N) = cos \I/, 

 where vp must always be taken positive and less than 180". 

 The time of beginning and termination of the eclipse will 

 then respectively be 



3h + z_^cos(M-N)4:^^ 



apparent time of the place of observation expressed in hours 

 and parts of an hour ; the upper sign referring to the begin- 

 ning, the lower to the termination of the eclipse. The angles 

 which, at those two moments the respective radius of the sun's 

 disc at the point of contact forms with the horary circle of the 

 sun's centre, counted from north through east to 360°, will be 

 respectively ^Q = 90° + N + \I/, 



and the magnitude of the eclipse in inches will be 

 = 25 . sin \ rf'^ 



Elements of Solar Eclipses. 

 Apparent time of Berlin. 



February 1. 



July 27. 



Longitude of ([ and © 



Horary motion of (( in longitude 



o 



([ 's latitude 



Horary motion of ^ in latitude 



([ 's parallax 



O's parallax 



([ 's semidiameter 



O's semidiamet^ 



