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Francis

The most obvious improvement would be to replace the sextant arc with a rotary encoder.

An encoder consists of two parts.  A readerhead and a scale.  As one rotates past the other, a measurement of angle is produced.  There are incremental (not directly suitable) and absolute encoders.  The absolute encoder "knows" where it it at the moment it is powered on with out the need to reference the device.

The index arm would rotate the scale, while the reader head would remain fixed to the body of the sextant. 

On a recent device, I installed a rotary encoder from Heidenhain which has ~134,000,000 counts per revolution.  A count is the smallest integral unit of measure.  Therefore  the resolution of that high quality encoder is ~0.00967 arc SECONDS per count, or very roughly one one hundredth of an arc second. 

While this encoder may be a bit pricey for some, lower resolution encoders are available.

Press a button and get your reading.  No more gear lash or micrometer nonsense.  The reading is directly off of the index arm, similar to vernier arc sextants.

Now add a little bit of memory and a stop watch feature to the electronics, and you can get time and altitude at the touch of a button, recorded into memory.  Viola, you are ready for the next observation

Brad