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ANNALS NEW YORK ACADEMY OF SCIENCES 



which four were taken in 1870, eight in the spring and summer of 1871, 

 and ten in the spring and summer of 1872. The measures were all made 

 on the Repsold measuring-machine of Columbia University, and all meas- 

 ures were made in duplicate by Miss Harpham and Miss Davis of the 

 Observatory computing staff. On each plate twenty-eight points on the 

 sun's limb were measured, — seven points at or near each pole, and seven 

 points at or near each extremity of the equator. In each of these four 

 groups the separate points were five degrees apart, each group thus covering 

 an arc of 30°, or 15° on each side of the pole or equator respectively. The 

 measurement of each point consisted in the determination of its polar co- 

 ordinates, position angle and distance, as referred to the center of revolution 

 of the plate in the machine. This center of revolution does not coincide 

 with the center of the sun's disk, but the plates can be quite accurately 

 adjusted in the machine. In no case did the center of revolution differ 

 from the true center of the disk by more than 0.05 mm. or 1^.2. 



The measures were corrected for differential refraction, the formulas 

 as given by Chauvenet being used. From these corrected measures were 

 then found the co-ordinates of the center of the sun and the most probable 

 value of the sun's radius. The measured co-ordinates were then trans- 

 ferred from the center of revolution to the center of the sun's disk as origin; 

 and thus were found, for each plate, the values of twenty-eight radii of the 

 sun. 



The mean of the fourteen polar radii, as thus found, for each plate, was 

 taken as the value of the polar radius; and the mean of the fourteen equa- 

 torial radii, as the value of the equatorial radius for that plate. The dif- 

 ference between these values of the polar and equatorial radii was then 

 formed, in the sense polar minus equatorial, and the results for the various 

 plates are exhibited in the following tables: 



Table VI. 

 1870. 



