and the Methods of calculating their Results. 269 



case of the eclipsed body being a fixed star, not for the centre 

 of the eclipsing body but for the point of the limb where the 

 occultation or emersion takes place, that is to say, for a point 

 whose apparent place is the same with that of the star, in con- 

 sequence of which, instead of the apparent diameter the true 

 one is introduced into the calculation, and the calculation of 

 the former as well as of the true longitude at the time of the 

 observation is avoided. This method has called forth the 

 various attempts to find more convenient formulae for the effects 

 of parallax: I do not deem it necessary to give an account of 

 the numerous essays written with a view to this purpose." 



The second method, on the contrary, does not take notice 

 of the single parts of the phaenomenon ; but consists in making 

 the apparent distance of the celestial bodies, expressed by 

 their geocentric places and those of the place of observation, 

 equal to the sum or the difference of the apparent diameters 

 of the bodies (according as the external or internal contact 

 has been observed), thus producing an equation whose un- 

 known quantity is the time of the conjunction. We are in- 

 debted for this method to Lagrange*, in whose memoir on 

 this subject the unknown quantity of the equation is the mo- 

 ment in which both bodies have the same longitude. This 

 method has been less frequently applied than the other; but 

 its influence has extended far beyond the theory of eclipses, 

 and has given a new form to the problems of astronomy in 

 general. Clausen (in an excellent paper printed in the Astr. 

 Nachr. No. 40) has chosen for the unknown quantity the time 

 of the shortest geometrical distance. 



[2.] The object of all calculations of observed phasnomena of 

 this kind is either to find the corrections required by the ele- 

 ments of the calculation taken from the astronomical tables, or 

 the difference of the meridians of the places of observation. 



With regard to the second object, the first method has not 

 yet been completely developed, as the geocentric distances of 

 the celestial bodies from the pole, and their horizontal paral- 

 laxes at the time of observation at a place whose difference of 

 meridian is unknown, are assumed to be known. The error 

 arising from this circumstance is of practical importance only 

 as far as it affects the latitude (or declination) of the moon; 

 but it may be easily corrected. If we denote the time of con- 

 junction resulting from the calculation by t, and the change 

 which will be produced in it by a correction x of the difference 

 of meridians (d) assumed in the calculation, by a x, the true 

 time of conjunction will be r + a x, the corresponding time for 



* Berlin Ephemeris for the Year 1782, p. 16. 



the 



