534 The Astronomer Royal on the Circularity 



the Nautical Almanac, and if we omit consideration of chance 

 errors of observation, the effect of which may be supposed to be 

 nearly eliminated in the mean of many observations, the follow- 

 ing results ought to hold : — If the Sun's disc is really circular, 

 and if the Nautical-Almanac assumed diameter at mean distance 

 is correct, then the observed vertical diameter will agree with the 

 Nautical-Almanac diameter for the day, and the observed dura- 

 tion of passage will agree with that of the Nautical Almanac. 

 If the Sun's disc is really circular, but the assumed diameter in- 

 correct, then neither of the compared measures will agree with 

 the corresponding computation of the Nautical Almanac ; each 

 discordance (one of vertical diameter, the other of duration of 

 passage of horizontal diameter) will indicate a numerical value 

 of correction to be applied to the assumed diameter; but the two 

 numerical values will absolutely agree. But if the Sun's disc is 

 not really circular, then it is impossible that the comparison of 

 observed vertical diameters on the one hand, and of observed 

 durations of passage of horizontal diameters on the other hand, 

 with elements computed on the supposition that the Sun is cir- 

 cular, can indicate the same correction to the assumed semi- 

 diameter. 



All that is necessary, therefore, for ascertaining whether the 

 Sun's horizontal diameter and the Sun's vertical diameter are 

 equal, is every day to compare the Sun's observed vertical dia- 

 meter with the Nautical-Almanac diameter, and the observed 

 duration of passage of Sun's horizontal diameter with the Nau- 

 tical-Almanac duration, and to infer separately from these the 

 correction to be made to the Nautical-Almanac assumed dia- 

 meter. If the two results agree, the horizontal and vertical 

 diameters are equal. 



Now these comparisons are made every day in the routine of 

 the Royal Observatory ; and their results will be found in one of 

 the late sections of each volume of the printed ' Greenwich Obser- 

 vations,' as well as in the more extensively distributed ' Results 

 of the Greenwich Observations,' which contain that section ; and 

 the means of the numbers for each year are given in the Intro- 

 duction to each volume. By extracting these numbers, the fol- 

 lowing Table is formed. I have thought it necessary to divide 

 the Table into three parts, distinguished by the following cir- 

 cumstances : — From 1836 to 1850 the 4-inch telescope (I believe 

 Dollond's) of the Mural Circle was used for the vertical diame- 

 ters, and the 5-inch telescope (Dollond's) of the Transit for the 

 horizontal passages; the diameter used in the computations of 

 the Nautical Almanac was 32' l"-80. Through 1851 and 1852 

 the 8-inch telescope (Simms's) of the Transit Circle was used 

 for both measures,, the Nautical- Almanac assumed diameter 



