113 



[237] 



In the Proceedings of the American Philosophical Society, (No. 5, vol. 1, 

 p. 231,) are to be found the positions of several American places of observa- 

 tion liirnished by Messrs. Walker and Kendall. The following are here in- 

 troduced, as stations of comparison : 



TABLE II. 



Places. 



Hudson observatory, Ohio 

 Wai^hington Ciiy observatory, D. C. - 

 Philadelpliia High School observ'y, Pa. 

 Dorches-ter, Mass. - . . 



Observers. 



Professor Loom is 

 Lieul.Giilit^, U. S. N. - 

 Professor Kendall 

 IMr. Boud,(privateobs'y) 



North lati- 

 tudes. 



410 14' 37" 



38 53 31 



39 57 8 

 42 19 15 



West of 

 Greenwich 

 longitudes. 



h. m. 

 5 25 



47.46 



6.08 



41.90 



17.81 



The method used in making the rednctions is that of Bessel, given in the 

 Astronom. Nachricht, No. 321. The sun's semi-diameter there given has 

 been employed ; the other elements are taken from the Nautical Almanac. 

 Bessel's semi-diameter of the sun is less than that in the Nautical Almanac 

 by ]".112. The ellipticityof the earth is assumed at 0.00324. Then, after 

 Bessel, we have 



Wherein 

 d = corrected longitude-}- when east, — when west of Greenwich. 

 c/'= resulting longitude, not corrected for the errors of the tables. 

 ( = the correction of the tabular place of the moon on its true orbit. 

 ^ = [he correction of the tabular place of the moon on a perpendicular 



to its orbit. 

 9j =the correction of the tabular sum of the semi-diameters of the sun 



and moon, in the case of a solar eclipse ; or, merely the correction 



for this error of the moon's semi diameter in the case of a star's 



occultation. 



With these elements and co ordinates, the values of </', and the co-efficients- 

 a, 6, c, have been computed as given in the above table. 



With these preliminary remarks, 1 shall proceed to indicate in what man- 

 ner the corrected longitude has been deduced for each place, where the errors 

 of the tables and corresponding observations could be procured ; and to 

 show, at the same time, in what manner these longitudes have concurred 

 with other deductions to a final and adopted value, for the longitude of such 

 place. 



But, it must be remarked, that, in combining several partial results, with 

 the view of obtaining the final longitude, I have not paid any regard to what 

 is called the due weight of each observation ; satisfying myself with taking 

 the arithmetical mean of all the partial results. Indeed, in most of the cases, 

 1 should be at a loss how to determine such a proper weight. I therefore 

 leave to everybody the care of doing, in that respect, what they may think 

 the besti 



8 



