of the Sun's Disc. 533 



reduced, and how the comparison of the reduced observations 

 with the numbers of the Nautical Almanac bears upon the sub- 

 ject now before us. 



For the calculations of the Nautical Almanac, an assumption 

 is made as to the numerical value of the Sun's diameter as seen 

 when the Earth is at its mean distance from the Sun. It mat- 

 ters not whether this assumed diameter is or is not correct, pro- 

 vided that it be used consistently in all the calculations of each 

 year ; and it matters not whether it be or be not changed from 

 year to yeai', provided that each volume contain a statement of 

 the assumed diameter which has actually been used in the calcu- 

 lations of that volume. Thus the assumed value of Sun's dia- 

 meter, as seen at Earth's mean distance, in the Nautical 

 Almanacs from 1836 to 1852 was 32' l"-80; that in the subse- 

 quent Nautical Almanacs is 32' 3""64. 



With the diameter thus assumed, two sets of numbers are 

 computed in the Nautical Almanac. One is the apparent dia- 

 meter (or semidiameter) of the Sun at noon on every day ; this 

 is found by merely altering the assumed diameter in the inverse 

 proportion of the Earth's varying distance from the Sun. The 

 other is the duration of passage of the Sun's diameter across 

 the meridian, or the measure of the sidereal time which elapses 

 between the passage of the Sun's western limb and its eastern 

 limb ; this is found from the apparent diameter of the day, by 

 introducing the consideration of the Sun's declination and of the 

 Sun's motion in right ascension. And these numbers being 

 prepared, it is evident that we have elements which correspond 

 very closely with facts that may be observed, the elements being 

 essentially based on the supposition that the Sun's disc is 

 circular. 



Corresponding to these two classes of computed elements, we 

 have two classes of facts observed at the Royal Observatory and 

 at other observatories. One is the zenith distance of the Sun's 

 upper limb and that of the Sun's lower limb. When each of 

 these is corrected separately for refraction and parallax, the true 

 results of geocentric observation are obtained ; and the difference 

 between them gives the observed vertical diameter of the Sun on 

 the day of observation. The other is the sidereal time shown by 

 the transit-clock at the instant of transit of the Sun's western 

 limb, and that at the transit of the Sun's eastern limb ; the dif- 

 ference between these gives the observed duration of passage of 

 the Sun's horizontal diameter across the meridian on the day of 

 observation. 



Now if we compare each of these numbers separately (namely, 

 the observed vertical diameter and the observed duration of pas- 

 sage of horizontal diameter) with the corresponding numbers in 



