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Three points:

1)The curvature of the upper bubble chamber lens is equal to that of the focal 
length of the lens/mirror arrangement so the bubble is in focus at all times 
in all positions.

2) The bubble chamber is circular so the bubble chamber/sextant can have 
lateral movement (roll) as well as the important movement in pitch, to allow 
some degree of lateral movement not easily possible in a straight (standard) 
bubble tube arrangement. This is probably why the straight tube bubble 
chamber was abandoned on marine sextants, or at least, not developed further 
in favour of other methods.

3) The argument seems to be - if I have it right: to attempt to eliminate side 
accelerations affecting the bubble.  You cannot escape side (horizontal) 
accelerations affecting the apparent gravitational vertical whatever you do, 
as the 'compensating mechanisms'  will be referenced to the local 
gravitational field too. Even if some hysteriesis is present between bubble 
and 'compensator' mechanism,  both will have to come to the same conclusion 
as to where the gravitational field is pointing. In other words you are back 
to square one. 

Eary type aircraft artificial horizons are such a mechanism that uses local 
gravitational field to provide an horizon (or hence vertical whichever you 
prefer) - they have a long time constant errecting mechanism using small 
pivoted vanes on four points around the gyro. The vanes 'dangle' downwards 
due to gravity and provide precessional forces to bring the gyro to an 
horizontal plane.

Coriolis force is such an example of horizontal acceleration that cannot be 
eliminated; it has to be allowed for - luckily because it is a constant 
feature and thus a known quantity.

Douglas Denny.  Chichester. England.


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