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



but little can be inferred from the fact that two cases make for and 

 two against the rule holding for distances across the meridian. 

 Thirdly, when the Moon has been to the West, and the Sun or 

 star to the East, there are 25 cases when the error has been in 

 defect, the Moon being nearest to the meridian ; and nine in 

 which it has been in excess ; on the other hand, the Moon being 

 the more remote of the two luminaries, the error is (correctly) in 

 excess in only eleven against ten cases : but these ten exceptions 

 are nearly all taken from the Sun, and demand a special allowance 

 which will be noticed farther on. It will thus result that the 

 rule which seemed almost universally to hold when both the 

 heavenly bodies were on the West of the meridian, frequently 

 applies when they are on opposite sides, though with less cer- 

 tainty. We now come lastly to the observations in which both 

 the luminaries were to the East of the meridian. And of these it 

 must be premised that they are much the least convenient to take 

 in practice. When the Moon is near its rising and more distant 

 from the meridian, the stars nearer to the meridian will seldom 

 reflect distinctly; while the construction of any instrument like a 

 sextant, requires the object viewed directly to be the one to the 

 left hand ; and again to work on the Moon in its last quarter, 

 when its light is become tolerably weak, involves using the ' small ' 

 hours of the morning; nor have the observations I have taken on 

 the Sun viewed directly been very satisfactory, as the construction 

 of my circle prevents the reflected Moon being very distinct. For 

 these reasons the E. observations are the least conformable of all 

 to any rule, but the special analysis of them which is subjoined 

 will shew that the discrepancies are not wholly unaccountable. 

 Of 25 cases in which the Moon was nearer to the meridian, 14, 

 with an average error of 48", gave the measured distance too 

 small, and 12, with an average error of 42", gave the distance too 

 large ; most of these last, however, were taken on Arcturus, a Arie- 

 tis, and Pollux, which have respectively a N. Dec. of 20", 22", 29" 

 nearly, an important element in the reduction of the observations. 

 On the other hand, of 10 cases in which the Moon was farthest 

 from the meridian, 7 gave a mean error of 37" agreeable to the 

 rule, and 3 a mean error of 82" in a contrary sense. If the incon- 

 venience of taking these Eastern observations referred to above 

 be taken into account, the result cannot be fairly said to negative 

 the conclusions drawn from those taken in the West. 



It is not pretended that the observations themselves are rigidly 

 exact ; most of the distances taken on the Sun ought to be aug- 

 mented by a small amount, perhaps 10" — 15", on account of the 

 fact that the diameter of the Sun as measured by a small instru- 

 ment is generally too great: this error seems to be due to the break- 

 ing up of the rays in the telescope. I have also entirely neglected 



