OCR Text |
Show [ 148] 48 determination of the equatoreal intervals of the transit wires was necessary. These wires were originally seven in number; their intervals are given below (I.) They were broken out after the 21st of October, 1845, and were replaced by a set of five (II,) which in their turn were broken, and the last set (III) inserted. Of these last, the ~econd wire .was broken before the commencement of observations, and the reduction of the mean to the middle wire, of course includes the correction for the deficiency. The following, then, are the adopted intervals of the several }Vires and the mean of the whole from the middle wire: No. Dates. A. B. c. Mean. E. F. G. - • 1845. s. s. s. s. s. s. s. I. Aug. 12 to Oct. 21 +55~49 +36.78 +18.52 +o0.69 -18.12 -34.63 -53.18 1846. I JI. April 14 to April 23 ........ 36.59 17.99 00.00 18.14 36.45 III. June 4 to June 6 ..•. +54.96 ' ........ +18.84 -05.17 -17.41 -35.19 -51.95 From t~is table, the corrections to. t~e. mean of wires for imper· feet transits h.ave been deduced by thvHhng the sum of the ·inter· yals for the ~1res observed by the product of the number of wires ~nto the cosme. of the star's declination·. In the single case of an Imperfect transtt of the moon, 'allowance has been made for the ~oon's motion during the interval of time indicated by the correc· hon. I~ deducing the instrumental and chronometer errors by. com· panson of the observed and computetl times of transit the formula of M .. Hansen has been employed. ' Denotmg by L the latitude of the place. D the declination of the star. Z the zenith distance of the star. i the correction of instrument for error of level. n the correct~on of ~nstrument for deviation at the pole. c the .correction of mstrument for error of collimation.' Then the reduction of the observed transit to the meridian has the form i sec L-n sin Z sec L sec D+c sec D. The value of one division of the level tube accompanying the in· s~rume~t. was unknown; and the instrument itself being in Califor· nia, .this value could not b.e determined; but, knowing from the ob· servmg~books that the axis was always kept as nearly horizontal as po.sstble, ~e .may neglect the constant term i sec L, or rather may ~nclude 1t m the chronometer correction and this without affectmg the observed right ascensions. ' Denote also by A the computed mean time of star's transit. T the observed mean time of star's transit. t:::. T the correction of the chronometer. 49 [ 148] / Then every observation will give an equation of the following form: Q=T+~T-A-sin Z sec L sec D n+sec D c. Or for bre vity: O=T+t:::.T-A-a n+b c. putting a antl b [or the co-efficients of ? and c. By help of this formula, approx1mate values wer~ obtatn eu for n <lnd c from two or more obst->rva:ions. These were generally taken on different days, <ln~l . the equations furnished by them were ouly limited by the condttlon that the value of c should remain constant for these d.ays, all ow an ce being afterwards m<ld e. for the error of this assum ptwn. The values ot n and c thus obtatnt:d, were substituted in the equation furnished by ea~..:h observation. Tbe mean of the cnronomt> ter correL:tions thus determined, being comp<lred with the inoividual results, a new set of equations of condttiou was arranged of the following form: · ' 0=rl6. T-a. rln+b. de. wh~ r e dt:.T is the : esidual quant1~y ob~ained by the above companson. Th e solutiOn of these cldierenttal equations by the metho 11 of least squrtres, gave the corrections of nand 1:, whi eh, applied to the Clssutued, gave the most pr:.obable values. T11e as sumed a 111l adopted n and c are given below. The application ot these final values to the or.igiual equ~tions K_ave now the most probable ehronollleter <·orrect1on, and this, applied to the corrl'dt>d transit of the moou'~ limb, gave tlle rotan time of transit, and finally the right ascens10n. Table of assumed and adopted values of n and c. • Assumed. Adopted. Date. n. c. ' n. a:. • s. 8 . 8. s. 18-15, August 2 I, 22 ...•...• . + 3.i02 -3.237 + 3. 702 -3.237 October 20 ......•.••.. + I. 6:iJ -:L '.!.:i7 + I. 3-.l:i - :l. 062 1846, Apnl I .1 .••••••••••••• + l.Ol +o. IIH + I .H~'{ +11.8~0 16 . ..••.•.•.•.• . +52.07 +u. 183 + 52.265 -0.0"-l June 4 .. .............. ~ + 0.574 -0.145 ~ + 0.57-J -0. 14:) 5 ........... t ••• + O.otHI -0.183 ~he following longituJes were as:-umed as the basis of the compatlson of the observed with the tabulated nJoon culminations: h . m. s. I. 184,5, Augnst 22 .••• •••o•• oo•o•• II. H4\0r.tober20 ............... . 6,., 58 30 I 29 31 I I I . 1 ~-! 6, A p r 1 I 14: . • • • • • . . o • • • • ••••• 8 08 21' l Y. 1846, J u n e 4. 0 •• 0 • • • • •• • • • • • ••••• 8 01 41 J b~ |