LONGITUDE. ] 



ASTRONOMY. 



1019 



The following examples will show the methods of determining azimuthal errors of the transit instrument at the 

 Royal Observatory, Greenwich. 



Approximate 



Solar Time. 



IMS. 



d. h. 



April 28, 9 



April 28, 10| 



June 13, 8 

 20 



Transits Corrected for Error of Colllmation and Level Error, with the Corrections 

 for Clock Rate and Change of B. A., and inferred Azimuthal Errors. 



r ) h ' m " !'. 



Tabular Right Ascension . . 11 41 1974 



X 0-041 



Clock Slow . . . 

 s. h. m. 



Rate [1-25] for 1 20 



Transit of Polaris S P. . 

 Tabular Right Ascension 



+ 8-55 

 l-597 



34-29 

 + 07 



3436 z X 0-041 



h. m. s. 



13 3 25-85 + z X TC38 

 . 1 4 8-76 



42-91 z X 1-638 



Transit of Polaris S. P. . 

 Transit of Polaris . . . 



8. h. 



Clock Rate [1-06J for 12 

 Subtract Increase of 

 R. A.inl2h. 



h. m. s. 

 . 13 4 5-46 + z X 1.638 



1 4 15-84 z x 1-533 



+ 0-53 

 0-40 



1 4 15-97 + z + 1-533 



The practical directions for using them, as given in the 

 Qreenwuh, Observations, are as follows (1848, p. xx.) : 



"If two consecutive transits of Polaris have been 

 observed, the first transit (as corrected for error of colli- 

 mation and level error) is altered by the change of the 

 star's right ascension, and by the estimated clock error 

 for 12h. ; nnd the difference, in seconds of time, between 

 the altered first transit and the second transit (rejecting 

 12h.) is divided by 3 '171 to obtain the azimuthal error in 

 seconds of space. 



" If tluree transits have been observed, the difference 

 between the first and second is taken (rejecting 12h.), 

 and the difference between the second and third in like 

 manner ; and the mean between these is supposed to be 

 independent of the change of right ascension and the 

 clock's rate, and is then divided by 3-171. 



" If several transits have been observed, the same 

 process is used for every successive set of three, and the 

 results are used separately, or the mean of the results 

 is taken, according as there appears reason to think that 

 the position of the instrument has or has not undergone 

 change." 



Example of the Determination of Azimuthal Error by 

 Three Consecutive Transits of Polaris : 



Transit corrected for two errors. 

 h. in. s. 



1846. Dec. 15. Polaris ... 1 4 49 39 



Dec. 15. Polaris, S.P. . 13 4 35 30 



+ 14-09 



Dec. 10. Polaris 



1 4 47-08 



+ 1178 



.Z = 



+ 12-94 

 3-148 : 



+ 4-12. 



ON THE DETERMINATION OF TERRESTRIAL LONGI- 

 TUDES. In this section we shall explain the principal 

 methods used in the determination of terrestrial longi- 

 tudes : 



Longitudes by transits of the moon and moon culmi- 

 nating stars. 



The first introduction of this method appears to be 

 entirely due to the German astronomers. About tho 

 year 1820, it was agreed on by Gauss, Bessel, Struve, 

 Nicolai, and others, to observe transits of the moon, and 

 certain prearranged stars lying in its parallel, for the 

 purpose of determining longitudes. The celebrated 

 Schumacher gave his zealous co-operation by the imme- 

 diate publication of the results in the Astronomisch Nach- 

 richtett. In these kingdoms, the method was cultivated 

 by Dr. Brinkley and the late Mr. Baily ; the latter astro- 

 nomer having contributed to its advancement by his 

 memoir on the subject, in the Transactions of the Royal 

 Astronomical Society, which led to the insertion of the 

 requisite data in the pages of the Nautical Almanac. 



The stars with which the moon is to be compared, are 

 selected in the same parallel of declination, for the pur- 

 pose of nullifying any small errors which may be left on 

 the transit instrument ; but, notwithstanding all the care 

 which was taken by these refinements, there are still un- 

 certainties produced by irradiation and a peculiar per- 

 sonal equation of the limbs of the moon, which tend to 

 throw doubt on the results. The former quantity, or 

 "irradiation," may be eliminated by the results of the 

 moon's 1 L. and 2 L. ; but the latter is a variable and 

 unknown quantity, in some instances affecting the tran- 

 sits of the tirst and second limb in a different proportion. 

 In the following pages we will show the method pur- 

 sued by the Astronomer Royal in the longitudes of the 

 North American boundary, and also those of MM. Rum - 

 ker and Struve. The method of the Astronomer Royal 

 is to be used in cases where there are no corresponding 



