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APPENDIX. 

 " I have calculated the longitude from each fet of 

 " obfervations feparately, to (hew how near they agree 

 *' with each other, and what degree of precifion one 

 ** may exped in fimilar cafes. 



" Obfervations of the diftances of the Moon and Sun, or 

 " Stars, may be ufeful to inform us if the time- keepers 

 " have fuffered any coniiderable change in their rate of 

 " going. For if the longitude deduced from the moon 

 " differs above two degrees from that found by the 

 '' watches, it is reafonable to imagine, that this difference 

 " is owing to fome fault in the watch, as the longitude 

 "'found by lunar obfervations can hardly vary this 

 " quantity from the truth: but if the difference is much 

 *' lefs, as about half a degree, it is more probable that the 

 *' watch is right, fince a fmall error in the diftancc will 

 ** produce this difference. 



" The diftances of the Moon from Jupiter were ob- 

 ** fervcd, becaufe Jupiter is a very bright objed; and the 

 *' obfervations are eafier and lefs fallacious, particularly 

 " that of the altitude, than thofe of a fixed liar, whofe 

 " light is much fainter. This method, however, requires 

 *' a different form of calculation, from that of the obferved 

 *' diflance of the Moon from a fixed ftar, whofe diftances 

 ** are computed for every three hours, in the Nautical 

 *' Almanac. The principal difficulty in the calculation 

 *' is to find the Moon's longitude from the obfervation of 



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