821 



mean rarely coincides with any of its constituents, all the evidence 



goes to show that it is not the true result. Without, however, 



stopping to examine the logical, I proceed to weigh the logistic, 



argument which bears upon the matter. 



In order to have a case before me, I shall take, as a fair example 



of this method, the determination of the latitude of Padua by the 



celebrated astronomer, Giovani Santini, in 1811. His process was 



to observe the instants when several stars of various declinations 



reached a fixed altitude ; by which means ho depended only on the 



going of his clock and the verticality of the axis of his instrument. 



From sixteen sets of such observations he obtained the following re- 

 ts 



suits with their mean. 



Now, on glancing at these numbers, we observe that two of them 

 are no less than 6''*16 below, and one 5" above the mean ; and 

 these variations would seem to show, not that we have obtained a 

 latitude which can be depended upon to the nearest second, but that 

 the observations are not to be trusted to nearer than ten seconds ; 

 and amid these disagreements, Signer Santini's concluding remark 

 sounds strangely, 



'*Si puo pertanto stabilire la latudine dell' osservatorio di Padova 

 in numeri rotondi 45" 24' 2"." 



It would seem that, unless these results have been connected to- 

 gether by some law that would insure the compensation of errors, 

 the only conclusion that we are entitled to come to is, that the lati- 

 tude of the Observatory of Padua is between 45° 23' 56" and 

 45° 24' 0-7". 



Taking, then, this example as a general type of such proceedings ; 

 I observe that there are two distinct sets of cases ; viz., those where 



