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    Index Correction
    From: Rafal O.
    Date: 2017 Apr 10, 10:31 -0700

    Few days ago I received Astra IIIb marine sextant. The first thing I wanted to do was to make remove side error and evaluate Index Correction. I made two different set of measurments (SD for Sun in both cases was 16.0'):

    • N=3, On: 34.0', 34.6', 34.6'; Off: 30.8', 29.8', 30.4'.
    • N=6, On: 34.0', 34.2', 34.2', 34.0', 34.0, 34.4'; Off: 31.6', 30.6', 31.0', 30.6', 31.0', 31.0'.

    At this moment I did not differentiate between Towar and Away. The well known procedure is to calculate mean values of:

    • <SD> = 1/(4*N) * sum_{i=1}^N (On[i] + (60.0 - Off[i]))
    • IC = 1/(2*N) * sum_{i=1}^N (On[i] - (60.0 - Off[i]))

    My question is as follows: assuming that both On and Off measurments are independant I can also calculate mean values of every possible pairs for On and Off:

    • <SD> = 1/(4*N^2) * sum_{i=1}^N sum_{j=1}^N (On[i] + (60.0 - Off[j]))
    • IC = 1/(2*N^2) * sum_{i=1}^N sum_{j=1}^N (On[i] - (60.0 - Off[j]))

    I did it for both values of N=3 and N=6. Additionally I calculated also confidence level with C=0.99. I got these values:

    • N=3:
      • SD=16.0, 99% interval: (15.9, 16.2)
      • IC=2.4 on, 99% interval: (2.1, 2.7)
    • N=6:
      • SD=15.8, 99% interval: (15.7, 15.8)
      • IC=2.6 on, 99% interval: (2.5, 2.6)
    • N=3 (superset of all cases):
      • SD=15.9, 99% interval: (15.8, 15.9)
      • IC=2.6 on, 99% interval: (2.4, 2.6)

    Taking into account error bars all three cases give the same values for IC and SD. SD is within Astra IIIb accuracy (0.3'). I know that such calculations requires much time and programmable calculator.

    My question are:

    • Can I use all possible pairs of On and Off measurments to estimate IC?
    • As in both cases IC calculation gave statisticall the same value should I try to remove it or leave it as is (Toward and Away analysis is next step)?

    Yours sincerely,

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