294 ReducitoH of the Observation of the 



ecliptic =z (p^ m p will be = tt cos <p + ^ sine (p^ and p p 



= /3 cos ^ — TT sine ^ : consequently 



M ^« = s- C^Mp ^ <p) X ir cos (|u, M p ~ (^) /3 



sinep^Mp "^ sine fj, Up ^''^■'^ 



will give the value of M ?n with the utmost accuracy. Now 

 as in the transit of Mercury D ^ must he very small, the 

 angle /x O D may be safely supposed = M O D, and there- 

 fore ju- M p = M O D ; whence we have this rule for finding 

 the effect or parallax. 



Rule. The least ciistances of the centres divided by the 

 Sun's semidiameter give the cosine of an angle which call 

 w, from which subtract the inclination of the relative path 

 of Mercury to the ecliptic,' and call the difference %. Let 

 'Tf be the parallax by which the apparent longitude is di- 

 minished, (3 that by which the apparent latitude is increased, 

 m the horary motion of Mercury in its path in seconds and 



3600'^ 



= T, then will the number of seconds by which the 



m 



ecvress is retarded be expressed 



^sine CO sine w 



In order to express this rule in numbers, we must find 

 from the tables the relative geocentric horary motions of 

 Mercury in latitude and longitude, and hence the angle <p. 

 Now Lalande's tables give us at the egress the relative 

 horary motion in longitude = 361^^ '455, and in latitude 

 5 1''* 7355 <p = 8"" 22^ 26"; and the semidiameter of the 

 Sun corrected for eradiation = 969": consequently m — 86^ 

 17' 22", V = 77° 54f 5C)'' '. and the formula expressing thq 

 number of seconds by which the egress is retarded 9'93 * 

 -\- 2*126^ : from which having given the parallaxes in lati- 

 tude and longitude, the apparent egress for the centre of the 

 Earth may be easily computed, and hence the difference of 

 meridians of two places where the transit has been observed 

 may be found. The parallaxes may be calculated by the 

 common methods, or by the following formula, which will 

 be found sufficiently accurate for that purpose. Let A = the 

 latitude of th^ place of observation, R = the ARoi the mid- 



heaveii;^ 



