PRELIMINAEY SOLUTIONS, Cclxix 



12.-PEELIMINARY SOLUTIONS. 



The consideration of the respective weights to be attributed to the groups of observations 

 made by different observers, with different instruments, and at different places, has been 

 postponed until a critical investigation of the mean errors and average discordances should 

 render it possible to deduce a measure of precision from the observations themselves. And 

 since it was clearly evident that at least two solutions of the fundamental equations would 

 thus become imperative, the definite substitution of the values adopted for several of the 

 comparatively unimportant unknown quantities, has been delayed as long as possible. Using 

 now closely approximate determinations of , y, z, and w? these other terms may be deduced 

 with tolerable precision, and their influence then eliminated. 



The value of v x -f- 0&quot;.57 being adopted and substituted in all the equations derived from 

 the micrometer-observations with the Santiago Equatorial, there remain only the quantities t 

 for divers instruments, which may be numerically deduced from those equations in each set, 

 which contain terms multiplied by [dd~\. For some cases this appears the only practical 

 method ; in all it is the most convenient. The only exception is furnished by the equations 

 deduced from Santiago equatorial observations ;&quot; in these those values of t have been employed, 

 which result from the combination of all measurements of the semi-diameter made with the 

 instrument either directly or indirectly during both oppositions or conjunctions ; so that 



for Mars, t = + 1&quot;.450 

 for Venus, i= + 0&quot;.745. 



In the second Greenwich series of meridian observations of Mars, the terms dependent upon 

 the apparent semidiameter do not appear. The other Greenwich series give the following 

 equations : 



Mars I. 



24.000 x + 4.677 y + 26.950 z + 17.000 t 14.584 w 11.50 = 



whence t = 0&quot;.1915. 



Venus I. 



17.000x+ 8.781 y + 32.410 z + 9.000 t 38.509 w + 39.92 = 



whence t = 2&quot;. 9 047. 



Venus II. 



17.000 x + 10.176 y + 16.798 z 7.000 t 26.922 w + 41.51 = 



whence t = 0&quot;.3231. 



These values of t for the Greenwich Circle are, of course, to be substituted in their respective 

 groups of equations. 



Finally inasmuch as sundry discrepancies between the results of the Supplementary 

 Equations&quot; (derived from meridian comparisons of Mars II at Santiago) and those from nearly 

 simultaneous observations with the equatorial, and moreover the large negative values of the 

 corrections to the semidiameter, all seemed to imply some unknown source of discordance 



