o8 Longitude determined 



after an interval of twelve hours apparent time, and EB the 

 diftance of the moon, or, in other words, the increafe of their 

 Tefpe£tive right afcenfions : and fince ED and EB are known 

 from the Nautical Almanac, if we fubtraft the firft from the 

 laft, we haveDB, equal to the difterence between the in- 

 creafe of the fun's and moon's right afcenfion in twelve 

 hours apparent time. Now the difterence of longitude be- 

 tween the two meridians A P and B P is the arc x\.0B, equal 

 to A0D lefs the arc DB; that is, equal to 180" lefs the dif- 

 ference between the increafe of the fun's and moon's right 

 afcenfion in twelve hours : and, fince the increafe of the 

 moon's right afcenfion from the time of its pafling the me- 

 ridian A P to the time of its pafling B P is known from ob- 

 fervation, and equal to EB, we can make the following pro- 

 portion for finding the difference of longitude between any 

 other two meridians, AP and |3P, from the obfervcd increafe 

 of the moon's right afcenfion £i3. 



As EB : A^D — D B : : E^ : A|3 the difference of longi- 

 tude ; or, in more familiar language, as the increafe of the 

 moon's right afcenfion in twelve hours apparent time is to 

 180° or 1 2"' lefs the difference between the increafe of the 

 fun's and moon's right alcenfion in that time : :, fo is any 

 other ohferved increaie of the moon's right afcenfion between 

 two meridians : to their difference of longitude. Q. E. D.* 



If the increafe of the moon's right afcenfion in twelve hours 

 were uniform, or fuch that equal parts of it would be pro- 

 duced in equal times, the above rule would be ftritlly accu- 

 rate; but as that increafe arifcs from a motion continually 

 accelerated or retarded, and feldoni uniform but for a Ihort 

 fpace of time, it will therefore be neceffary to find the mean 

 increafe of the moon's right afcenfion when it is at the inter- 

 mediate point between A and (3, in order to determine their 

 difference of longitude with the greateft precifion ; and for 

 that purpofe, Taylor's Tables of Second Difference are very 

 ufeful. 



EXAMPLE. 



April the 8lh, 1800, the tranfit of the moon's firft limb 

 was obferved at the royal obfcrvatory (A) ; and, allowance 

 being made for the error of the clock, its right afcenfion 

 %vas° - - - -. . 12'' 35"" 1 8*22' 



Add the time that the moon's femi-dia- 

 meier took to pifs the meridian - o i 8-38 



Rioht afcenfion of the moon's centre 12 36 a6'6 



• DemOTilrated for the firft time by the author in 1770, 



On 



