hy the Moon's Tranjlts, loi 



Then, '* As twice the moon's retardation in twelve hours : 

 is to twentv-foLir hours : : 



" So is the mean time later at ^ than at A : to the differ- 

 ence of longitude weft from A." 



After doubling 24"' 13 "35% and alfo 12, which is totally, 

 unneceflary, as the refult would be the fame if they ftood 

 fiugle, we ftate the following proportion : 



As 48"" 267' : 24'' : : lo'" 37-9' to--5'' 15'" i'3% the dif- 

 ference of longitude between A and S. 



But as the third term is improperly reduced to mean time, 

 we (hall take the apparent time above found, and then 48"" 

 267' : 24^ : : 10™ 41-69' to--^'' ly"" 537*; the fame as re- 

 fuhs from Mackay's and Pigott's rul^s. 



We {hall only remark, that 5*^ 17"' 53*7^ is the apparent 

 time that the moon took in paffing from the meridian of A 

 to the meridian of jS; but from what has been demonftrated, 

 the apparent lime at /3 will be equal to the difference betxveen 

 the increafe of the fun's and moon's right afcenfion in that 

 interval of apparent time ; for DB, or 24"^ 13 '35' is the dif- 

 ference for twelve hours, and therefore by proportion op, or 

 io'"4i*69'' will be the difference for ^'^ 17'"53"7''; fubtrafting 

 the former from the latter, we have 5** 7"" 12% the difference 

 of longitude as before, and a clear proof that the authors 

 above meiitioned have omitted to dedu6l the apparent time 

 at the diftant place or ftation f>, from the apparent time at 

 Greenwich. 



If it fliould be thought eafier to employ ffdereal time in 

 refolving the difference of longitude between A and /3, let ED, 

 the increafe of the fun's right afcenfion in twelve hours, be 

 added to twelve hours, and we have then the arc of fidereal 

 timeABDF^; from which fubtracling EB, there remains 

 AjSB, equal to the difference of longitude. By proportion 

 we can therefore fay. As EB, the increafe of the moon's right 

 afcenfion in twelve hours; is to ABD + DE, or twelve 

 hours + the increafe of the fun's right afcenfion ; fo is any 

 other obferved increafe of the moon's right afcenfion as tjS; 

 to the arc of fidereal time A /3 s; and if from this we fubtra6t 

 f /3, then Ap is the difference of longitude required. 



To apply this rule for finding the difference of longitude 

 from the above obfervations and data, we lay, 



As 26'" 3' : 12'' l"M9-65'' ; : ll'"30-l'to A/Je 5'' l8"'42-l» 



From this fubtra^t £/3, the obferved increafe o n 30*i. 



The difference of longitude between X and /3 is 5 71a 



Q. E. r. 



n 3 Although 



