128 On the North Polar Distances 



pears to have put an end to all questions, as to the mstruments 

 having changed their figure, or to any apprehension of error 

 fi'om the bending of the telescopes. We may safely assume, 

 for our present purpose, that the three circles of Greenwich, 

 Dublin, and Konigsberg, are perfect, as to their divisions, &c.; 

 particularly as M. Bessel mentions that he has made allowance 

 ibr the small effect produced by the bending of the tube of the 

 telescope. It may, however, be satisfactory to some, to com- 

 pare the two arches of interval between the adjacent stars of 

 the catalogues of Dr. Brinkley and M. Bessel. This compa- 

 rison is given in columns A and B of the subjoined table. 

 Although we have not the means of comparing large arches, 

 for want of stars north of the zenith, yet these will serve to 

 prove the care that was used in dividing these instruments. 

 But it is right to remark, that the agreement between corre- 

 sponding arches, large as well as small, of the Dublin and 

 Greenwich circles, is even closer. 



Column C gives the excess of M. Bessel's North Polar di- 

 stances above those of Dr. Brinkley, inserted in the Journal 

 of Science for September 1822; after having added 0",3tothe 

 latter North Polar distances. These North Polar distances 

 were computed from the co-latitude 36° 36' 46",5, the same as 

 Dr. Brinkley had adopted in 1813: but lately he is inclined 

 to adopt 36° 36' 46", 8, as probably more exact. 



The excess in column C may (assuming the divisions of the 

 circles exact) be supposed to arise fi'om the combinations of 

 errors in the constants of refi-action ; and in the determination 

 of the co-latitude, or Polar point. If, k being the constant of 

 refraction (^ "'^~ui ) ^^ mean temperature and mean barometer, 

 we suppose e+tk tan. Z.D. to represent the quantity to be 

 appUed to each Polar distance of M. Bessel, to agree with 

 those of Dr. Brinkley, we shall have 27 equations ; which, by 

 the method of making the sum of tlie squares of the errors a 

 minimum, give 



(? = — 1 ", 49 and ^k= 0", 70 

 According to the recent determination of M. Bessel (Ast. 

 Fund. p. 36. and Phil. Mag. for January) the mean refraction 

 at 45° = 57",35 x 1,00328 = 57",53. Hence ^■=:57",68 for the 

 exter7ial thermometer. Dr. Brinkley's value for the internal 

 thermometer is ^=57",72. Now, if we suppose, in M. Bessel's 

 determination of k, an error in excess =0",35; and in Dr. 

 Brinkley's an error of 0", 3 5 in defect; the whole quantity Ik is 

 accounted for : and the mean difference of the North Polar di- 

 stance of Dr. Brinkley and M. Bessel will be reduced to rather 



less 



