RESULTS. 

 Second method. 



cclxxxv 





It is manifest, at the first glance, that the results of the first method are those which we must 

 employ ; and the remarkable discordance of the sign in the Fenws-measures with the meridian- 

 circle illustrates the importance of allowing for the influence of the quantity t, even despite the 

 embarrassments which attend the endeavor. 



We thus arrive at the definite values : 



// // // 



Semi-diameter of Mars = 4.6639 + 1.9681 = 6.63 

 Semi-diameter of Venus = 8.6625 0.3118 = 8.35, 



values which, although affected with a very large probable error, would appear to be more trust- 

 worthy than those heretofore employed. 



Lastly, the resultant value of the solar parallax is to be deduced, thus attaining the 

 prominent end of the national Astronomical Expedition, in the prosecution of which its 

 earnest and devoted Superintendent has expended such unremitting effort and unceasing 

 toil rewarded by a mass of observations of high usefulness for the advancement of science, 

 and most honorable to himself and his assistants and among whose incidental results was 

 the establishment and national adoption of the first permanent observatory in one of the great 

 divisions of our globe. 



The four resultant values of w = 1-* (the correction to Encke's determination) are now 

 presented, together with the subsidiary quantities. Their diversity is striking ; but to me 

 they seem to point unquestionably toward a decided diminution of the adopted value. The 

 following table presents the case in a succinct form. The first column contains the deduced 

 correction to be applied to the quantity, S". 57116. The number e in the second column is 



the mean error as given by the ordinary formula e= -^- ; where p = [gg .3], and e = J J-" 



is the mean error of a single observation whose weight is unity. It is evident that, since, in 

 the primitive equations of condition, we had uniformly aa = a = 1, the sum [aa] taken after 

 the multiplication of each equation by its weight, as explained in 10, is equal to the whole 

 number of these standard or unitary observations employed. This quantity e is, therefore, a 

 much larger number than what is commonly called the mean error, being undivided by the 



