# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding

**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,

Rafal