cclxxxiv 



EESULTS. 



15.-RESULTS. 



The fruit of all the preceding researches may be presented in narrow compass. It consists of 

 new values for the semi-diameters of Mars and Venus, and of the final value for the solar parallax. 



First, as regards the diameters : 



Were it possible to separate the two unknown quantities t and u, so that it might be palpable 

 what portion of the apparent correction to the semi-diameters should be attributed to terrestrial 

 influences, the determination of the magnitudes of Mars and Venus would be attended with 

 comparatively small difficulty, so copious are the observations from which the semi-diameters 

 might be deduced. But this obstacle interferes at the very outset ; and although the collection 

 and consolidation of all the values of such quantities as may be supposed constant for any one 

 instrument has been essayed in every form, the accordance of the results is in no degree com 

 mensurate with a priori theory. 



The determination of t (which comprises, I 6t , the effect of personal equation in pointing ; 2 nd , 

 any error in the assumed thickness of the micrometer-threads ; and 3 rd , any spurious increase of 

 diameter by irradiation depending upon the instrument or other local causes) is only needed, 

 apart from its interest and usefulness for analogous future investigations, in order that the 

 influence of this source of error may be eliminated from our measurement of the actual semi- 

 diameters. This measurement depends, in fact, upon our unknown quantity u ; which is the 

 correction to the semi-diameter at the unit of distance, including, of course, any irradiation 

 which, being proportional to the distance, may only be detected by means of occultations or 

 transits across the solar disk. 



Confining the computation to observations made at Santiago and Washington, we may obtain 

 final values for u by the adoption of either one of two different principles. First, and most naturally, 

 we may combine according to their weights the values of u deduced from actual solution of the 

 normal equations ; or, secondly, we may in like manner combine those values which correspond 

 to the assumption t= o, and which are given in the last columns of the tables of solution in 

 14 ; the weights being, in both cases, proportional to xe~ 2 . I give the results of each method 

 of combination. 



First method. 



