# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Real accuracy of the method of lunar distances**

**From:**Fred Hebard

**Date:**2003 Dec 31, 00:13 -0500

Jan, This is the 99.7% probability that an _individual_ observation will exceed 90". The standard error of the mean would be the standard error as you defined divided by the square root of the number of observations. I believe (not being a statistician) if you divide 90" by the square root of 6 you will get the value that the mean will not exceed with 99.7% probability, namely, 37", or 15 minutes of longitude. That's quite usable for ocean navigation, and is the worst that is obtained once in a thousand times, more or less. Fred On Dec 30, 2003, at 1:24 PM, Jan Kalivoda wrote: > Now let us consider the maximum errors of lunars that should be taken > into account, based on the values given above. If you multiply the > standard error (SE) by 2, you obtain the error that should be not > exceeded in 95% of observations, and you can be statistically sure > that your error won't exceed the value of (SE times 3) in 99,7% of > observations. Therefore, we can accept the maximum possible error in > practice as SE ? 3 = (1/0.6745 ? PE) ? 3 = 4.5 ? PE very nearly. > > For lunars, PE of 20" times 4.5 gives 90" = approximately 180 seconds > of time = approximately 45 minutes of longitude (the exact value > depends on the actual velocity of the Moon in R.A.). For finding your > position at sea, you should accept this maximum value in both E and W > direction and your real position lies somewhere in the arc of > longitude 1,5 degree long. This makes lunars nearly unusable in > practice in my eyes - where I make a mistake? > > Of course, when you take two lunars to the East and to the West from > the Moon simultaneously, the maximum possible error drops to the > usable limits (onboard sailing ship). > > ------------------------- > > It should be noted that the errors of lunar tables were negligible > compared with the errors of measurements only after cca 1880 (after > Newcomb). From cca 1820 to 1880 (from Damoiseau and others to Newcomb) > one had to accept the error of 20-30" in lunar tables and from 1755 to > 1820 (from Mayer to Damoiseau) the possible error was 60" . > > Maybe this fact gives a commentary to the quotation from Cotter (A > History of Nautical Astronomy, p.256), who himself quotes the report > of Parry's Arctic expedition (1821-1823) concerning lunars taken from > the ships caught by ice and staying at the same place for many months > (not drifting!): > > "The mean of 2500 observations in December differed 14' from the mean > of 2500 observations in the following March; ..." > > ================ > > > I want to be refuted, as I like lunars very much. > > > Jan Kalivoda >