Cclviii WEIGHTS AND MEAN ERRORS. 



This table has been employed alike to furnish weights for the determination of the places of 

 a planet's center deduced from observations of the two limbs, and for the weight of positions 

 depending on comparisons with a star. In the former case n and n! are the respective numbers 

 of observations of each limb ; in the latter the one denotes the number of observations upon 

 which the adopted declination of the star rests, and the other the number of comparisons. 



In order to combine the additional equations resulting from diameter-measurements with the 

 other equations of condition, we may consider the weight of a pointing to a planet's limb as 

 one-half that of a setting upon a star. Inasmuch as the equations are all formed with reference 

 to the semidiameters, or one half the quantity actually measured, it is evident that we have 

 merely to assign the unit of weight to each additional equation derived from a direct measure- 

 ment. 



From the same assumption as to the relative precision of the two kinds of setting we perceive 

 that the equations derived from indirect measurement are each entitled to one half the weight 

 which belongs to the primary equations of condition to which they correspond." 



The same principles regulate the weights of the supplementary equations derived from 

 micrometric observations upon the meridian. In these observations, however, it will be borne in 

 mind that, from the nature of the case, only one comparison was possible. 



In combining absolute meridian determinations with the comparative measurements furnished 

 by the micrometers of the equatorials, new difficulties arose. The most reasonable, as well as 

 the simplest, course seemed to be to assign the weight unity to each meridian observation, con- 

 sidering the resultant position as dependent upon the combination of one pointing to the object 

 with one observation of the nadir. The errors of graduation are necessarily ignored. In the 

 meridian observations at Athens the equator-point was deduced from the J/ars-culminating 

 stars, and the consideration of the latitude thus eliminated. Yet an inspection of the various 

 values of the equator-point will show that the resultant determinations can scarcely be entitled 

 to claim a weight greater than unity. All consideration of the latitude is here eliminated. But 

 for the other places at which meridian observations were made, any error in the adopted latitude 

 will affect our result by its full amount. To obviate this difficulty as far as possible the same 

 constant correction is applied to the meridian observations of the planet's declination which 

 was previously found applicable to the measured declination of stars. These corrections are : 



Santiago Marsll O."12 



Cape of Good Hope, Mara I 0."59 

 Cape of Good Hope, Mara II l."32 



Greenwich ITarsI-f O."10 



Greenwich Mars II O."06 



For both series of Fcntw-observations the corrections have been applied which were found for 

 the .Jfara-series. 



There remain the observations at Kremsmiinster and Cracow, and the two of Venus I at 

 Altona, for which no details whatsoever are given. These are necessarily to be omitted from 

 the fundamental equations for the preliminary solutions. 



