1878.] Dr Pearson, On a series of lunar distances. 173 



two small corrections, that for the contraction of the Moon's semi- 

 diameter, because in most cases it will not amount to 10", and 

 would generally operate to increase the error ; that for the sphe- 

 roidal figure of the earth, because I feel no security that the 

 methods usually given for correcting this are to be relied on ; at 

 any rate, a method formerly given in the Nautical Almanac, 1829,-32, 

 has been since omitted, and on reducing the examples given there 

 by Chauvenet's method, I obtain quite different results. But it 

 should be clearly understood that no mode of reducing the distance 

 which will give a really different result to that employed in com- 

 puting these observations has yet been published; it is not stated 

 on what principle the system adopted in the folio volume of 1772 

 was based ^; but by working out the examples given there according 

 ta the formula adopted in the example which I have printed, it 

 will be found that the results are as nearly as could be expected 

 identical. Nor does it seem that better success can be expected 

 from the method given by Bessel in the Astronomische NachricJiten 

 of 1832. 



Bessel's plan is very elaborate ; assuming a Greenwich date as 

 nearly exact as possible, the true apparent distance must then be 

 computed, the result compared with the observed distance, and 

 the error in the assumed Greenwich time thus ascertained; but on 

 reducing two examples, first by the common, and then by Bessel's 

 method, the discrepancy in the two results, in one case was (— ) 15", 

 in the other (+) 5": though the difference between the theoretical 

 and observed distances in the first case was 1' 9" (24"), in the 

 other 1' 37" (32"), both in defect. It is also to be noted that Bessel 

 introduces a correction for the earth's double centre, and elimi- 

 nates the contraction of the Moon's semi-diameter by making the 

 limb, not the centre, of the Moon, and also of the Sun, his point of 

 departure in computing the apparent distance. It has, no doubt, 

 generally been taken for granted that the errors occurring in prac- 

 tice have always been errors of observation ; the late Mr Godfray, 

 who frequently discussed the question with me, always expressed 

 himself entirely satisfied with the existing methods of computa- 

 tion, and no one Avill question his havmg been quite competent to 

 pronounce on the question. But on the other hand, the results 

 hitherto obtained have never, as far as I know, been comparable 



1 I refer to the folio volume of Tables for correcting the Apparent Distance of 

 the Moon and a Star from the effects of Parallax and Refraction, published by 

 Order of the Commissioners of Longitude published at Cambridge in 1772. Thej' 

 are said in the preface to have been computed by Dr Maske'lyue, then Astronomer 

 Eoyal, Mr Parkinson, Senior Wrangler in 1769, and a Mr Williams of Christ's 

 College ; and were edited by Mr Shepherd, Plumian Professor, 1760 — 1796. _ They 

 are extremely long and must have involved a vast amount of laboiir : but it does 

 not quite appear on what principles the computations were made, though I imagine 

 that they have been the basis of the various concise methods which have been 

 published since. 



