Ixxiv 



METHOD PURSUED. 



Available observations. 



For each of the eleven series of equatorial observations, the comparison stars are to be deter- 

 mined in order to obtain absolute positions from the relative measurements. Those meridian 

 observations are to be referred to the same category, which are essentially differential compari- 

 sons, and, in fact, dependent upon a micrometer. In such cases the relative measurement is 

 almost always accompanied by an observation of the absolute position of the comparison star, 

 wbich observation is to be used with such other determinations as may be accessible for deriving 

 a final and adopted place from the mean of all, taken by weight. 



These absolute positions may then be combined directly with the meridian observations, and 

 we shall then obtain one resultant normal equation for each series and each place of observation, 

 the coefficient/ having different signs at the 7 northern and the 2 southern observatories, respec- 

 tively. Of these normal equations there will be 



For Mars, I series, 6 For Venus, I series, 4 



" II series, 4 " II series, 4. 



The terms containing t, u, and v, must, necessarily, be eliminated from the normals before 

 these can be combined for solution. To this end, they may, in most cases, be approximately 

 determined by means of a different combination of the data employed, and indeed the value of 

 V being independent of the object observed, it may be advantageously deduced from the conjoint 

 use of different series of observations. 



The only unknown quantities will then be x, y, z, and w, the first three being necessarily 

 different for each of the four series. 



The means of the several comparisons which constitute a single observation may, by a slight 

 artifice, be so corrected that the influence of the second differences of the parallaxes belonging 

 to these comparisons will be obviated without entailing the necessity of any reduction of the 

 comparisons singly. The period over which the largest series extends is but about five hours, 

 and in all the Santiago observations, which are the only ones sufficiently prolonged to call for 

 any consideration of this point, the comparisons follow one another at intervals so nearly equi- 

 distant that we may assume these intervals to be equal without thereby introducing any 

 appreciable error into the correction. 



Putting, as before, 



the observed apparent declination of the limb 8 

 computed true declination of the center = d 

 parallax in declination =p 



semi-diameter r 



