46 Capt. E. Sabine's Notices occasioned by the 



not have deemed the observations made with it, under circum- 

 stances that necessarily rendered the readings of the level an 

 approximate instead of an exact record, a specimen of what 

 the circle was capable of performing when an attention should 

 be given to the level, commensurate with the greater value of 

 its divisions. 



The circumstance noticed by Mr. Babbage, that some of 

 the latitudes observed with the circle agree better together 

 when computed with the smaller and erroneous value of the 

 level, than when computed with the larger and more correct 

 value, is a natural consequence of the readings of the level 

 being approximate and not exact. 



To exemplify this, let it be supposed that the sum of the 

 readings of the level may have had an accumulated error, in 

 an extreme case, of ten divisions ; that is to say, an error of 

 + 10 divisions, or of —10 divisions from the truth. Now let 

 there be observations of two stars, in all respects precisely ex- 

 act, except that the one star be charged with the positive, and 

 the other with the negative, error ; let the number of repe- 

 titions be 10 : then will the resulting latitudes be charged, 

 in the one case with an error of -f 1 division of the level, and 

 in the other case of —1 division. When the divisions are 

 reckoned as single seconds, the effect of this error will be to 

 remove the latitudes 2 seconds apart ; but with the greater 

 multiplier of 10*9, they will be removed nearly 22 seconds 

 apart. 



Hence if there are several observations at a station, and the 

 observations are good in all respects except in the liability 

 to error, within the above named limits, in the record of the 

 level, the latitudes will have very small differences when com- 

 puted with the small but erroneous value of the level; and 

 the differences will be increased tenfold in amount when the 

 larger and more correct value is introduced. 



As might be expected the differences in the recalculated 

 latitudes are most remarkable at the stations where the sup- 

 port of the circle was least stable : at New York, where it 

 stood in the window of the cupola of Columbia Cottage; at 

 Bahia, where it was placed upon a garden table; and at Ma- 

 ranham, where, although great care was taken in all respects 

 then deemed of most importance, — the position of the circle on 

 the window sill of the apartment was unfavourable in regard 

 to stability, and probably influenced the two observations of 

 aLyrae, which depart each about 10 seconds from the mean*. 

 At Spitsbergen, on the contrary, where in addition to the same 



case 



* The observations at Maranham, recalculated with 109, and employing 



the 



