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Robin you wrote:  Moreover on the face it's not clear to me that proportional logarithms based on one hour intervals have much to offer since they would presumably be defined as plog(x) = log(1) - log(x) and log(1) = 0. Could it really be that there were distinct tables of plogs of this type?! Regards, Robin Stuart

David.  Now ‘plog’ I like.  I was going to congratulate you on inventing a new word, but a Google search shows there’re lots of things called ‘plog’ including people called Plog, but well done anyway.  

If you look at Table XXIX in Riddle I think the value of ‘plogs’ is more in the way the tables are laid out than in the algebra.  It’s a bit like the value of the ‘Air Almanac’ to the air navigator cf using the ‘Nautical Almanac’.  The ‘Air Almanac’ gives 10 minute GHAs, so if the air navigator plans to shoot on 10 minutes, he can miss out the step of calculating GHA from the hourly GHAs in the ‘Nautical Almanac’.  Returning to Table XXIX, e.g. If I wanted a log or plog for 1hour, 20 minutes, and 15 seconds, I wouldn’t have to turn it all to seconds or decimals of a minute or hour first; I can dive straight in.  Riddles Plog Tables are based on 3 hours.  They seem to work like this.  One hour is 1/3 of three hours and the log of 0.3333 is - 0.4772.  In Table XXIX the plog of one hour is also 4772.  Similarly, two hours is 2/3 of three hours.  2/3 is 0.6667.  Log 0.6667 is – 0.1761, and in Table XXIX, plog two hours is 1761.

Things I’m still thinking about are:

1.  There has to be a reason for working in proportions cf ordinary numbers.  What is it?

2.  How would you deal with four hours using Riddles Table XXIX?

3.  Why did Riddle settle on three hours to base Table XXIX on?

DaveP