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Sean,

I have it written in my notebook from my early days of reading everything in sight learning on my own.....I forget who I pilfered it from.

Checking it, I have an 1868 editon of Bowditch and if I go to the augmentation table it has a range of values from 0 augmentation  @ 0 alt to 16 seconds augmentation  @ 90 alt.  (which =.2667 @ 90 degrees) (sin value of 1) 

From there a check with the sin of the altitude say at 45 degrees:   (bowditch augmentation 11 seconds=.183)  (my filched formula .26 sin 45 =.184)  so it matches within any rational quest the Bowditch table.

I note the Bowditch table is an approximation, Augmentation  varies with a horizontal paralax, and the Bowditch table i believe is calculated on the average of HP @ about 57.7 HP  which comes out to the .26 number which varies a bit with rounding.  

My notes comment that actual augmentation factors vary from .299 at an HP of 61.4 to .230 @ at an HP 53.9'.  (A min max scenario).  which gives me an average of .26 by inspection (hence my use of it)  Round to 1 decimal and back to old .3 agian.

Based on what we are doing in a lunar as I understand it, heck its close enough. 

I recall the whole calculation is based on the 27.24% ratio SD to HP, and the factor of added size for the radius of the earth in NM 3438? (based on using the 21,600 circ.)

Someone cooked up a rule long ago that adds a bit of perspective on all my futzing with extra decimals....  Measure with a micrometer,  Mark with chalk, Cut with an axe.......