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Art Leung you wrote:  I have checked index error on 4 Kollsman periscopic sextants by just doing simple sight reductions using the 2 minute averager (yes, not necessary, but fun!).  Corrections ranged from -27' to +10'.

Art
For clockwork averagers, I’d treat the index system and averager separately.  I’ve no experience with roller or digital averagers.  I’d set the index mirror to a straight value, 6 degrees in the case of a Smiths and select the averager to one or two minutes.  Then I’d press the trigger and touch nothing else until the sextant had run down.  I’ve never known an averager to be more than 1 second out for a one minute shot or two seconds out for a two minute shot.  If it was, I’d compensate by starting the shot early or late to keep mid-time correct.  I'm not sure if it was the same company, but Smiths also made jolly good alarm clocks in the UK. https://www.gracesguide.co.uk/Smiths_English_Clocks & https://www.gracesguide.co.uk/Smiths_Aircraft_Instruments .  Similarly, I’ve never known the averager counters to differ from the index counters by more than one minute.  If they were, I’d allow for it.  I understand the Kollsman averager can be stopped at any time, which must really mess up knowing mid-time.

On the other hand, for a Smiths Kelvin Hughes sextant, the index system needs calibrating for each 10degree index stop.

Unless I’m demonstrating, I rarely use the averager in a static situation.  The averager is only there to average out the effects of acceleration and adds an unnecessary extra layer of errors.  However, as you say, it is more fun, and guests love it. DaveP