# NavList:

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

**Re: Still on LOP's**

**From:**Bill Murdoch

**Date:**2002 May 6, 16:56 EDT

Bill Murdoch wrote:

> I am still having a hard time with the 25% of the time you are inside

> the cocked hat rule. It just does not 'feel right'. I have played

> around with the Excel spreadsheet map that I mentioned a week or so

> ago, and I can not get the calculations to work like I think they

> should.

> We have been discussing LOPs in two-dimensional (surface) navigation.

> I have what may be a simpler question. What rule applies in

> one-dimensional navigation? Let's say you are a tightrope walker,

> getting nervous, and want to know exactly where you are on the rope.

> You whip out your sextant and with a little skill and calculation plot

> two POPs (points of position). The two POPs are not in the same spot

> (naturally). What is the chance that you are between the two POPs?

> What is the chance that you are to one side of both? What is the

> chance that you are on the other side of both?

Then Mike Wescott wrote:

Answers: .5, .25, .25

Usual assumptions apply: no "systemic errors", equally probable that error

is + or -. If both are plus, they're both on one side of you. If both are -

then they're both on the other side of you. If #1 is + and #2 is - then

one is one each side. Likewise, if #1 is - and #2 is +. Four equiprobable

possibilities and 2 of the four have you between the POPs: 50% and 1 in

four (25%) for each of the other two possiblities.

This is where I 'fell off the train'. If we stand to the side and watch the tight rope walker, we see along the rope from left to right POP#1, tight rope walker, and POP#2. It is just as likely that the tight rope walker is to the left or the right of POP#1, and it is also equally likely that he is to the left or the right of POP#2. If he is to the left of both, he is to the left of POP#1. If he is to the right of both, he is to the right of POP#2. If he is to the right of POP#1 and to the left of POP#2, he is between the two POPs. If he is to the left of POP#1 and to the right of POP#2, he is not on the rope. I understand + +, - -, and + -. I do not understand - +. Or, am I missing much more?

Bill Murdoch