174 Dr Pearson, On a series of lunar distances. [Oct. 21, 



in precision with those obtained from another simple method, and, 

 one somewhat similar in the amount of calculation needed, viz. 

 the Occultations of planets, or fixed stars, by the Moon, as I 

 pointed out in my former paper {Cambridge PMlosopkical Pro- 

 ceedings, II. 418); and, considering that more than a century has 

 passed since the question was thoroughly taken in hand, it seems 

 not unreasonable to suggest that it might be re-opened with ad- 

 vantage. It is certainly, with the chronometers of the present 

 day, not of great practical importance, local time being always 

 obtainable with great precision ; but it is generally available on 

 three out of four days in any month, and is, in itself, so neat and 

 scientific, that it almost deserves to be practised for its own sake. 

 It may be remembered, that the inventor of the formula which I 

 have employed — which is, probably the best one available ; at any 

 rate, it is stated to be perfectly general, and to require no distinction 

 of cases — also devised a circle specially for the purpose of making 

 this observation ; in it the limbs supporting the telescope and 

 the mirrors are both moveable on the centre, so that the measure- 

 ment commences from any point whatever in the graduated circle, 

 and reckons continuously onwards until the series of observations 

 is finished (so as to avoid any constant or casual error in the 

 graduation of the circle) ; yet we read in Herschel's Astronomy, 

 that "the abstract beauty and advantage of this principle seem 

 to be counterbalanced in practice by some unknown cause, which 

 probably must be sought for in imperfect clamping ;" may it not 

 be retorted, that we are risking our reputation as theoretical astro- 

 nomers, if we always charge the blame on those who construct our 

 instruments ? 



To myself it seems that the problem is simply one of Spherical 

 Trigonometry, but at the same time somewhat complex ; and not 

 quite so straightforward as has hitherto been assumed. The 

 situation of the observed luminaries towards the meridian, and 

 the difference between their geocentric and geographical altitudes, 

 are also the most hopeful points on which to discover a new cor- 

 rection: the former, on account of the observed errors, and the 

 latter because it affects the position of bodies so differently at 

 different points of the azimuth. 



It is to be hoped that if these two difficulties be thoroughly 

 reconsidered, together with any others which may suggest them- 

 selves to experienced mathematicians, means may be found of 

 introducing a new correction of the observed distance which will 

 give a really accurate result. 



Postscript. Subjoined is an example of an observation worked 

 out after Bessel's method; this is not ordinarily given in treatises 

 bearing on the subject, but the theory will be found explained at 



