NavList:

Hi George

You wrote:

[If] the altitudes are obtained by observation, as they presumably were in all these cases

 we are considering, the altitudes are what they are.

....

Clearing the lunar distance itself corrects for refraction and parallax of  both bodies. So to

obtain GMT the corrections to make beforehand are for index error, dip, and semidiameter.

-----

Firstly, thanks for keeping me on the path!  I do run off into the weeds from time to time!

Secondly, your spot on observation has has been the very heart of the matter for me.

Exactly what does Bayly (and therefore Cook) mean by the altitude entries?  They are specified to a limb,

and therefore not corrected for SD, however, the remainder of the definition eludes us.  Before I am ready

to run off and examine these all of these historical lunars, I would like to understand the definition of terms.

What does ‘altitude’ mean, within the context of this log? 

As to calculated vs observed.  I have come to the same conclusion as you George, they are observed.

Why would someone go to all the trouble to calculate the altitude and then specify it to a Limb, with

the upper or lower limb being an additional complication?  It just doesn't seem probable.  These altitudes

are measured. 

And in being measured, they can have error!  Low altitude refraction for the sun.  The moon’s altitude

is notoriously hard to measure with the glitter off the sea.  In running Frank’s calculator, I find that the

altitude error for each object runs in OPPOSITE directions.

In my first example, I assumed that the altitude was corrected for dip and index error.  I merely included

the SD for each object to the 'altitude' as given.  This resulted in a mere 9 minute error in longitude, well

under the threshold of 30 minutes you mentioned.  {As a side note then, shouldn’t we be setting the

HoE in Frank’s calculator to zero?}

In simple fact, for the trials I have been running, I have been varying only the TIME (as Bayly had no

idea of GMT or GAT, for that matter) and subsequently, the way in which the altitude is included, to

determine what is the definition of altitude in the log.

I do believe we are reaching consensus about the meaning of the term ‘altitude’ in the log.

Kermit: 

Yes, you hit my worry about the latitude quite precisely.  Thank you kindly for your answer.

While I share your admiration of the ability of historical navigators to perform these calculations, seemingly

without error, I do have a caution.  They did it often, and in this case, using notation that they created.

They were very familiar with their own work and methods.  I strongly suspect that all they did was

take observations and perform calculations.  Each and every day, all day.  They should be good at

it, when you get that much practice!!!!  For this log, we are dealing with very skilled navigators and

astronomers.  It’s a scientific expedition, for heaven’s sake.  It would be astonishing to me if we ever

found an arithmetic mistake or a procedural error.  What we will find is, as George points out, that

the ephemeris of the day was imperfect.

Best Regards

Brad