EPHEMERIDES AND AUXILIARY TABLES. XCV1 



The Cambridge observations were given without any correction for refraction. The series is 

 not sufficiently extensive to warrant the computation of tables for this purpose ; but manuscript 

 tables computed for the Cloverden observatory, which is only about half a mile distant from the 

 Harvard observatory and differs but a few seconds in latitude, furnished values of the requisite 

 auxiliary quantities. These tables are omitted here, on account of the disproportionate length to 

 which it would be necessary to print them, inasmuch as of all the twenty-six Cambridge observa 

 tions of Mars, (only seventeen of which were contemporaneous with the Santiago series,) there 

 are but three when the hour-angle was less than 2 !l , and but four others when the planet was 

 within 3 h of the meridian The remainder were at very low altitudes, the meridian distances 

 ranging from 3 h to 6 h 53 m , and the differential refraction in declination amounting in one 

 instance to 1&quot;.45. These values are, moreover, uncertain, to some extent, from the absence of 

 the corresponding readings of any meteorological instrument, excepting the external ther 

 mometer. 



At the Cape of Good Hope observatory, forty-seven determinations and forty-nine compari 

 sons were made, the hour-angle exceeding 4G n in only five instances, and approaching the 

 maximum l h 35 m in but a single isolated case. And since the latitude of this observatory differs 

 from that of Santiago by less than half a degree, and the whole differential retraction for the 

 observations of the Cape series exceeds 0&quot;.75 in only two instances, we may without sensible 

 error employ, in reducing this series, the tables computed for (Santiago, with slight modifica 

 tion in extreme cases. Thus, since 



cos n = cos (p sin (6 a) 



sin n cos N =. sin &amp;lt;p 

 and, consequently, 



1 cos 2 &amp;lt;p sin 2 (# ) 

 =. cotg &amp;lt;p cos (6 ) 

 UV = _ cos(0 ) _ , 



&quot; 1 cos 2 &amp;lt;p sin 2 (0 a) 

 we have even when (6 a) 15 



)N= 1,013 )&amp;lt;p = Q 30 0&quot; 



The observations of Mr. Maclear having been thoroughly reduced under the personal super 

 vision of that eminent astronomer, the labor was very considerably lightened, since the two 

 computations served reciprocally as checks. 



5. COMPARISON STABS. 



The determination of the comparison-stars, by far the most laborious and time-consuming 

 portion of the work, and one entirely foreign to the original plan of investigation, became 

 unexpectedly but imperatively necessary, in consequence of the circumstances already narrated, 

 which entailed the necessity of a thorough examination of all the observations which could be 

 found. In the quest of measured declinations of these stars, no accessible source has been left 

 unexplored ; still, the attempt to identity the objects employed for comparison has offered 

 problems of much difficulty, and has, in some instances, proved altogether unavailing. For 

 instance, out of the twenty-six comparisons at Cambridge eleven were with stars not merely 

 different from those selected by Lieut. Gilliss and proposed in his ephemeris, but quite unknown 

 even to the observer, and only capable of detection by groping, as it were, in zones and cata 

 logues ; and of these, two were of magnitudes as low as the loth. Eight of them have not been 

 found, although sought for with extreme diligence. In other cases, especially among the 

 southern stars of the first Venus- series, the determinations on record have been found so dis 

 cordant as to preclude any reliance upon them, until new observations should be made, to 

 decide which were to be considered erroneous. 

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