1878.] Dr Pearson, On a series of I ancu' distances. 171 



deduced in India, a fair evidence that Lunars taken in the simplest 

 and easiest way will generally give this result north of the Line. 



It has been already remarked that by taking Lunars E. and W. 

 of the Moon, a writer on this subject has stated that the mean of 

 the sets had given him a satisfactory result; and he adds with 

 truth, that in this way the effects of a constant error in his sextant 

 would be eliminated: errors in observation taken E. and W. affecting 

 Green v/ich Time in opposite ways. I venture to think that the meri- 

 dian only is the true point of reference, as I stated in my previous 

 paper ; and that, if both the luminaries are on the same side of it, 

 the error will generally be in defect or excess, according as the 

 Moon is nearer to or more distant from it : when they are on 

 different sides, I am unable as yet to give any decided view, but 

 it seems to me that the same principle generally rules. Hitherto 

 the problem has been always treated as depending only on the 

 altitudes of the two bodies : and that this is very fairly exact can- 

 not be questioned ; but it is not entirely so, as far as I can see ; 

 and I believe that by considering their positions with reference to 

 the meridian, we obtain a neAV point of departure which may 

 perhaps lead to a sa,tisfactory conclusion. 



Now of the observations in question, in about 92 out of 200 

 cases, both the luminaries were on the same side of the meridian; 

 in 38 towards the East, in 54 towards the West : while of those 

 in which they were on opposite sides, in 58 the Moon was to the 

 West, and in 48 to the East : and by giving the errors in defect or 

 excess in each of these ca,tegories, we shall have an approximately 

 accurate means of deciding how far the rule proposed above may 

 be considered true. Let us then take first those cases in which 

 the Sun or star, and also the Moon, were both to the West of the 

 meridian, as it, was mainly from these cases that the rule suggested 

 itself. Of these there are 28 instances in which the Moon was 

 nearest to the meridian: and in 24 of these the measured distance 

 is in defect of what it ought theoretically to be, while in three out 

 out of the four exceptions her altitude was under 10° and less 

 than that of the Sun. On the other hand, of 23 cases in which 

 she was the more remote of the two bodies, in 21 cases the error 

 is in excess, and the two exceptions can cause no surprise, even 

 supposing them to be errors of observation. We will take next 

 the examples in which the Moon was to the East of the meridian, 

 the Sun or star being on the opposite side. Out of 43 cases in 

 which the hour angle of the Moon was less than that of the other 

 luminary, I find only seven in which the measured distance was 

 in excess : and in 4 of these the distance was very great, viz. 128^" 

 and 129", while in two others it was about 116", nor did the error 

 in any case amount to more than 31". As there are only four 

 examples in which the Sun or star was nearest to the meridian, 



