ccltxxvi 



square root of the number of observations. The next columns show, first, the number of 

 actual northern and southern observations, upon which the determination rests, irrespective of 

 the relative value of these observations and of the number of comparisons from which they are 

 severally derived ; and secondly, under the heading -, the number of observations having the 

 weight unity to which these are respectively equivalent. Lastly, the table shows the values of 

 , the mean error of a unitary observation, and the quantity -\j, or weight of the corresponding 







value of )w : 



The first of these values, that derived from the observations of Mars during the first 

 opposition, appears so far superior to the others in all the elements which can insure, and in all 

 the indications which can manifest, precision, that I should feel far less hesitation in adopting 

 it, to the exclusion of all the rest than in attempting to combine the values of the several series 

 by any principle which I can devise. The determination necessarily depends, not upon 

 individual observations, but upon what we may consider as couples of observations ; and no 

 amount of thorough and careful work in the southern hemisphere can suffice to furnish means 

 for a trustworthy deduction of the parallax beyond the limit which is prescribed by the number 

 and quality of the y northern observations. Only for the first opposition of Mars does the 

 material furnished by the northern hemisphere suffice for a respectable determination ; and, 

 with the sole exception of the Naval Observatory at Washington, no northern observatory 

 has provided a single rnicronietric observation for any of the other series. The meridian 

 observations, if they are to be compared for such delicate purposes, require corrections for 

 error in latitude, or some form of personal equation ; corrections which, if omitted or wrongly 

 applied, leave our resultant values affected by their full amount, but which we have, nevertheless, 

 no means of determining except from inadequate data, and by processes not very much better 

 than groping. For all these reasons, no less than for the great intrinsic superiority of the 

 observations as indicated by the mean error of an observation whose weight is unity, this first 

 value 



i- = 0".0762 0".0621 



seems to be of a different order of excellence from the rest, and not likely to be brought nearer 

 to the truth by any combination with the others. 



Nevertheless, should it be thought best to combine the several values, the principles already 

 developed in 10 will assign to the three other series relative weights so insignificant as to 

 amount to a practical corroboration of the views just expressed. We may namely determine 

 the relative worth of the several determinations, as expressed by the number of standard obser- 

 vations of the weight unity which would bo requisite in order to attain the precision which 

 belongs to each determination. For this purpose we will retain the hypothesis of 10, b = 6 ; 



so that P,= -_, , P denoting the weight of a result deduced from n observations. 



