EESULTS. 



cclxxxvii 



Let v be the number of observations requisite for attaining the degree of accuracy possessed 

 by a given determination. We have then 



P v = ^ , and P v = - 

 v + 5 e 2 



where C denotes a constant, to be experimentally determined. 



Taking the first JSfars-series as the standard, and putting v 111, (the number of northern 



observations,) we find 



P m = 5.741 = 259.2(7; (7=0.022. 



With this value we determine y 2 from the formula 



6v2 = i 0.022 = 56.194 0.022, 



i j* 



whence, y 2 =:1.30 



or the worth of the value w given by the second Jfars-series is only 1.30 of just such standard 



observations as those of which 111 measure the worth of the value derived from Mars I. 



In like manner we shall find the value of w derived from the first Venus-series to be 

 worth 1.4*7, and that from the second series 1.55 standard observations of the weight unity. 



The difference of methods would afford a ground for the introduction of still another element 

 of relative weight, the two planets being manifestly adapted in very different degrees for 

 enabling an investigation of this kind to be successfully prosecuted. Indeed, the difference in 

 the geocentric distance of the planets during the four series of observations is such as to render 

 it quite warrantable to bring this also into the scale. 



If we determine the weights according to the ordinary method we shall have for the four series, 

 respactively, 286, 34, 22 and 25, provided that we consider the number of actual northern 

 observations as being that upon which the determinations rest. But if, more strictly, we con 

 sider this number as being that of the unitary standard observations whose weight is unity, we 

 find the weights of the four series to be, respectively, 613, 35, 44 and 30. 



These several principles of combination are illustrated in the annexed table, which gives the 

 relative weights resulting from each. Calling the number of northern observations n } the 

 number of southern ones n&quot;, and retaining the former notation in other respects, we have in 

 round numbers : 



Relative Weights of the deduced values of the Solar Parallax. 



How entirely disproportionate are the relative values of the several series, is sufficiently evident, 

 even from the first column of the foregoing table, although this is the one which presents the 

 heterogeneousness in the least unfavorable light. 



If, in the estimated relative weights, we introduce a factor to represent the opportunities for 

 accurate measurement of the parallax which are afforded by the respective series, exclusive of 



