dr. gkkgory's strictures on don Rodriguez. 257 



4. This writer infers, that mistakes mu6t have occurred in Don R.'s 4th 

 the (jbjerrafipns, because the sum of other " errors will he™™^^™' 

 found in the estimate of the entire arch, and will increase in place, 

 proportion to the extent of the are measured j but in the 



English measurement, we find exactly the reverse of this." 

 Here he assumes the principle proposed by Boscovich, but 

 condemned by Laplace, for a reason thus briefly assigned by 

 Puissant : — ' J, a solution donnee d'abord par Boscovich est 

 vicituse en ce quelle est fondee sur une hypothese inadmissible, 

 savoir, que leserreurs dans le mesure des arcs du meridien sont 

 proportioned a leurs longueurs." 



5. He concludes that there must be "an error of some Don R.'s 5ih 



seconds in the observations of the fixed stars," because " the r(H . so i n ot ' n< > 



weight* 

 results of the observations made on different stars, differ no 



Loss than 4 second* from each other." Now, what are the facts 

 on which this inference rests ? Simply these : that the only 

 two. stars which indicate any such difference in the whole 

 series of observations, are p Draconis and f Ursae ; that they because the 

 give a difference of 4"'l(j, not in the amplitude of the arc stars » where 

 between Dunnose and Arbury Hill, but of that between Dun- regularity do* 

 nose and Clifton ; and that, whether these two stars be rejected, ,lot apply to 

 or retained with the other fifteen employed in finding that cHfto£ 

 amplitude, they will not occasion a difference of a quarter of 

 a second in the result. How, then, can a fair investigation, 

 bring this as a reason for an alleged inaccuracy, when it obvi- 

 ously cannot apply to the ease? And what must be thought of 

 his impartiality, if it shall appear, that even in this respect, the 

 observations of the French and of Major Lambton, which he 

 so manifestly prefers to the English observations, are far more* 

 open. to censure ? Allow me, therefore, just to make the com- 

 parison . • 



Of the English observations, none are suppressed, (the ob- 

 servers going upon the principle explained by Simpson, in his 

 "Tracts," which clearly establishes the propriety, if not the. Much greater 

 necessity, of taking the mean of a number of observations) j n r « 8ul F r,tl<! j 1 

 and yet, no irregularity of consequence, except the one above observations; 



specified, appears. But, it maybe seen from p, 72, Discourse f ,,e -Y , ev,nr I f' , 

 ' ,. . . „ , o i »,, . besides, a httle. 



rrelimmaire, tome, i. Base du. bysteme Mttlnque Decimal, " coaxing ." 



that no less than sixty-eight of the French observations upon 



# Ursae* majoris were rejected, and termed lad } for no other 



reason 



