NavList:

The navigator is making an a.m. chronometer check while passing 3 miles west of the southern point of Brava Island in the Cape Verdes. The latitude of that point is N 14°50' and that close to the equator the 3 miles of departure corresponds to 3' of longitude, using integer minutes of arc. With the Sun bearing SE-by-E he (or she?) takes a series of five timed sights and calculates the mean value of times and altitudes. The date given, December 8th 1840 seems to be the civil date as he uses a declination of S 22°46' and an equation of time of 7^m42^s. The altitude is corrected by 10', indicating a fairly large height of eye or possibly some index error is included. He arrives at a local apparent time of 8^h46^m59^s (civil time). Adding the equation of time the LMT becomes 8^h39^m17^s. He then calculates his longitude using the "old" chronometer correction and compare the result with the known longitude. 

A more direct approach would be to add the known longitude of W 24°46' or 1^h39^m4^s to LMT, thus getting GMT 10^h18^m21^s and comparing it with the uncorrected chronometer reading of 10^h13^m38^s, giving a chronometer correction of 4^m43^s slow.

The difference of 50^s when compared to the "old" correction from 35 days ago indicates that the used daily rate should be adjusted by 1.4^s per day.

Lars