Astronomical and Nautical Collections. Ill 



0'» 29' 8" mean time of the moon passing meridian of second place ; 

 at which time the sun's mean longitude will be found to be 

 0" 2' 4.8", the moon's right ascension O** 31' 12"-8, the difTerence 

 between which 0** '29' 8" is the mean time of the moon's passing 

 the meridian already found, and therefore confirms the calculation. 

 The increase of the moon's right ascension in passing between 

 the two meridians is 31' 12"'8, from which M. Bouvard's formula 

 makes the difference of longitude 1 1** 58' 0", being 2' 0" erroneous, 

 as the annexed calculation shows. 



Log. of a, 31' 12''8 32724914 



Log. of r, "2 9-9987953 



15° 0' 0" 

 + wi + 2 30 

 - h -37 30 



Log of 14 25 4-7151674 



A. C. Log. of A ... . 37 30 6-6478175 



Log. of d 11»'58 4-6342716 



The corrected formula is the same as M. Bouvard's, with the ex- 

 ception of r being expunged. It consequently makes the logarithm 

 of d 4.6354763, and d = IP 59' 59'.3, which is as accurate as 

 the data will admit of. The same result is obtained from the rules 

 given by Professors Vince and Woodhouse, in their Treatises on 

 Astronomy. 



It therefore follows that M. Bouvard's calculations of the dif- 

 ference of longitude between Greenwich and Paris must be cor- 

 rected, by adding to each result r'-53, the amount of the error oc- 

 casioned by his introducing r into the calculations. 



It should be attended to, that different observers and different 

 instruments do not always give the same measurements of the 

 moon's diameter, and consequently that the mean longitude de- 

 duced from a number of observations of one limb of the moon, may 

 differ from that deduced from observations of the other. The mean 

 result of the whole observations, taken together, will be somewhat 

 affected by the error arising from this cause, unless an equal num- 

 ber of observations of each limb has been made. When this has 



