MATnEMATICAL PAPERS. 



35 



40' 6r. 1 J but by the tables, it was 7" 13° 41' 0". 0, Mercu- 

 ry's errour therefore, in longitude, was -|- 2". 9. 



For Mercury's heliocentrick latitude, at tlie time of tlie 

 ecliptick conjunction, by observation, and his distance from 

 the node : 



In 2^ 15' 27 



8127 



motion 



geocentrick latitud 



by the tables, was V 56". Oil : Therefore, 8127" : 116. Oil 



8141 



rf 



116". 213 



r 56". 213. 



Thi 



was Mercury's 



which beincr substracted from 



motion in latitude, in 2^ 15' 41" ; 

 9' 20". 595, his geocentrick latitude, at the time of the 

 first external contact, will give 7' 24". 382, for his geocen- 

 trick latitude, at the time of the observed ecliptick conjunc- 

 tion : Then 5 's distance from the Sun : 5 's distance from 

 the earth :: ^'s geocentrick latitude, 7' 24". 382 = 444". 382 : 



^'s heliocentrick latitude, 952". 578 = 15' 52". 578. 

 Let Q E. Fig. 9. be a portion of the ecliptick j the point 



Q the place 



of 5 's ascending 



node ; Q ^, a portion of 



5's heliocentrick orbit ; the point at 5?, his heliocentrick 

 place in his orbit; at the time, of the ecliptick conjunction; 

 and E, his place reduced to the ecliptick ; E ^ , his helio- 

 centrick latitude ; the angle 'E 9> ^ , the inchnation of his 

 orbit = 7° 0' 0". In the right angled spherick triangle, right 

 angled at E, there are given the angle E 8 ^, and the per- 



Mor- 



pendicular or side E ^, to find the base or side Q E 



cury's distance from the ascendiug node : 



Eadius 



Tan 



/r 



E 



15' 52". 678 



EG 5 , 83° 0' 0" : Sine, Q E, 2° 9' 20" 



: Tangent co <[, 

 ^'s distance from 



the ascending node. 



At 



f 



• 



4 



• 



