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From the logbook of the ship Challenge in 1853:
"At 10 AM off Macau, Here we discharged our Pilot and proceeded on our way 
with fine North & easterly breezes and pleasant weather. At 11.20 am Potoe 
island bore east from which we take our departure. At 12 meridian Potoe 
island bore NE 1/2 N & Lienchien WSW Ends with fine breezes and pleasant 
weather. Latt by Bearings 21d 48 North Long " do 113d 25 East"
["Long " do" means "Long ditto" or in other words in this particular case "Longitude by bearings"]

That "from which we take our departure" above is typical in the logbooks. You 
pick some point just as you're about to head offshore, and you call it. 
That's the reference point for the dead reckoning that follows.

Here's an example from the logbook of the Charles W. Morgan from 1841:
"kept the Ship off N West, at sunset the West End of Oahu bore NE Dist 15 
miles from which I take a departure"

And from the logbook of the schooner Gazelle in 1850:
"Wednesday August 21st sea Account we commence this day by getting the Gazelle 
underweigh and beating out of the harbor of san francisco. at dark we are 
clear of the headlands the southern most head bears N by W. dist 6. miles 
from which I take my departure it being in Lat 37d 49 N Long 122d 18 W."

And that's a complete "departure" notation: the name of the place, bearing, 
distance off, and the assumed lat/lon of the place. 

These are typical cases. Distances of five to fifteen miles seem to have been 
common for switching from piloting to ocean navigation in the 19th century.

You mentioned the "discontinuity" between the last celestial fix and the fix 
found by bearings upon reaching land. In the early part of the 19th century 
there are often explicit comments on the difference in position. For example, 
you might see something like 'saw the north end of Oahu this morning at 
daybreak thus proving my lunar longitude of two days ago nearly exact'. On 
the other hand, you might see a substantial recorded discrepancy, and the 
navigator frequently doesn't know who or what to blame since the 
charted/listed position might well be wrong in published sources for many 
decades.

-FER




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