MATHEMATICAL PAPERS. 31 



^'s true motion in geocentrick lat. in 4'' 53' 32". 4 12. 12 



252".. 126 

 Subtract the difference of parallaxes in latitude. 1. 094 



Visible motion in geocentrick latitude = ^ U. 251. 032 



Having found MU and S U, we easily find the length of 

 the visible transit line ^ M, as follows: M U, 1714". 103: 



U, 251". 032 : : Radius : Tangent < ^ M U, 8" 19' 54". 5 



Then Sine < ^ MU, 8° 19' 54". 5 : U ^ 251". 032 : : Rad- 

 ius : ^ M, 1732". 39; the half of which, viz. 8GG". 10o,= ^ 

 N, or M N. 



Having obtained ^ N and M N, we may proceed to find 

 ^ 's semidiamctcr by observation. 



At the time of the first contact, ^ 's horary motion on the 

 G's disc, reduced to the ecliptick, was 5' 49". 059 : therefore, 

 in 1' 48", the time from the first external to the first internal 

 contact, the motion was 10". 472. At the time of the last 

 contact, the horary motion, with respect to the ecliptick, was 

 5' 50". 955, which gives 10". 917 for 5's motion upon the 



disc, in 1 



d internal, and 



second external contact. The difference of the parallaxe; 

 between the first external, and first internal contact = 0". 01 

 being added to 10". 472, will give the visible geocentric' 

 motion of ^ upon the O with respect to the ecliptick, 

 10". 482 in r48"; and the difference of the parallaxes be- 

 tween the second internal, and the second external contact 

 r=0''. 028, being added to 10" 917, will give 10". 945, for 

 the visible geocentrick motion of ^ upon the O, with respect 

 to the ecliptick, in V 52". ^'s true motion in geocentrick 



latitude, 



=H 



^ 



