all right do you remember phileas fog counted 80 days where only 79 passed by since he made a east revolution to erath?
sun and moon rotate opposite,sun is faster than moon in sky
so:
from greenwich a person counts sunsets and moonsets
he counts 28 sunsets and 29 moonsets
a sailor makes a revolution east to earth along which he counted 27 sunsets and 30 moonsets
so you make a device in whcih one nedel aims the sun
and a disc aims the moon in which theres a needle which you delay 1/28 every day
from greenwhich both neeldes will always coincide
after a revolution to earth along almost a month needles will delay TWO REVOLUTIONS along 360ยบ
so if you can get a precision of 10th of the disc yyou can measure longitude with a precision of 5 degrees by measuring both needles difference
edit:
well travel around the wrold in 80 days anyone?
phileas fog counted 80 days where only 79 passed by since he made a east revolution to earth, from his point of view travelling one revolution to earth counted as one day
if you take a picture of the moon every day at same hour and animate it as a movie the moon will be moving contrary to the sun
so you go east travelling for one revolution so youll count one more sunset that if you didnt move, as phileas fog
but your following the moon orbit so you count one less moon
so travelling one revolution around earth makes you percieve a difference of sunset and moonset of 3 per evry 28 days while if you didnt move the diference would be of just one per 28, from here easy obtaining longitude just with a calnedar