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Thanks... I think that is what I tried to say a few days ago ; )
Thomas A. Sult, MD
IntegraCare Clinic
www.icareclinics.com
tsult@mac.com




On Nov 13, 2009, at 7:05 PM, douglas.denny@btopenworld.com wrote:

>
> I'll attempt an answer to this question:
>
> " ....No one has addressed my question of why the St Hilaire method
> calculates an altitude at a location our ship is NOT at, when we've
> just measured the altitude where our ship IS at...."
> ---------
>
> Answer: Because you are not comparing altitudes with the St Hilaire
> method but you are comparing zenith distances.
>
> You -do- know your zenith distance to an astronomical body because
> you have just measured it with a sextant, but you do not have enough
> information to work out the other parameters you want i.e. lat or
> long from that alone.
>
> What you can do however is imagine you are at position you _do_ know
> and work out a zenith distance for that position. Then you can
> compare the difference between them because they will be close
> together in value.
>
> If you go back to basics and consider what you DO know and what do
> NOT know, and what you have available and not available with the PZX
> spherical triangle, it should be clearer,(see diagrams).
>
> You have:
>
> The geographical position of the body from the almanac. Hence:-
>
> 1) co-declination of the body (from Dec in the almanac:-i.e. 90-dec).
> and
> 2)the GHA of the body.  (This not enough to know the local hour
> angle in the PZX triangle because you do not know your longitude).
>
> You also have from your sextant sight the altitude of the body to
> your local horizon, which means you have immediately:-
> 3) the 'true' zenith distance from yourself to the body. (i.e. the
> side ZX of PZX).
>
> And therein lies the problem.  You do not have enough information
> about the PZX triangle to solve it.
> Consider:
>
> a)If you knew the longitude accurately you would know what the angle
> ZPX is (i.e.the local hour angle) and could work out the latitude
> accurately.
>
> b)If you knew the latitude accurately, you would know the side PZ
> accurately - the co-latitude and you could work out the local hour
> angle and hence longitude.
>
> But you do not have either.
>
> Sumner stumbled on the position line principle by making an
> assumption as if he did know the latitude and worked out a
> longitude. He did this three times with three different latitudes
> and suddenly realised that what he had was a line of position where
> the sun could have been along that line found with the three results
> at that instant of the time of the sight - it was the line of equal
> altitude from the body,  and a certain fixed zenith distance from
> the body to the position line is implied, it is an equal zenith
> distance - a circle surrounding the geographical position of the
> body.  (see diagram "position line X at pole).
>
> St Hilare's brilliance is in the realisation that it is not
> necessary to know either either lat or long singly with precision to
> solve the pzx triangle, as you can work out an accurate zenith
> distance if you use an _assumed position_   (this is the correct use
> of this term here) which is _near_  where you are, and using an
> exact lat and long for that assumed position.
>
> .... and then compare the accurate (or 'true') zenith distance you
> have measured with your sextant with the calculated zenith distance
> for the assumed position nearby (which must be similar in value to
> your sextant sight value) - and close by as the assumed position is
> close by.  And hence find the difference.
>
> That difference (the intercept) is easily marked off on the chart
> from the assumed position. You then have a position line along where
> you must lie. (neglecting errors).
>
> In other words you are supplying yourself with the (accurate)
> necessary information of latitude and longitude to work out the PZX
> triangle that you cannot work out normally with insufficiently
> accurate informaation, then using a comparison method with your
> sextant (measured) information you do have in terms of zenith
> distance.
>
> That in a nutshell is the Mark St Hilaire's (or intercept) method.
>
> Douglas Denny.
> Chichester. England.
>
>
> =====================
> Original Posting:-
>
> No one has addressed my question of why the St Hilaire method
> calculates an altitude at a location our ship is NOT at, when we've
> just measured the altitude where our ship IS at.  (For politically
> correct reasons, I'm not using the name of this location.)
>
> Now lets go back to Sumner's 1837 calculation, where he picked three
> different longitudes and calculated three points on the circular LOP.
> This calculation is exact, and the equation for each point is the same
> as the one of the two necessary in the St Hilaire method (thus each
> Sumner point is half the work of a St Hilaire reduction).  And he
> could calculate as many exact points as he wished.
>
> So I'll put my question yet another way:  Why is the St Hilaire method
> superior to Sumner's and consequently the only one used today??
>
> I claim that the answer to this question has been made confusing
> because of the conventional name (names?) used for the location of the
> St Hilaire altitude calculation.  As evidence of this confusion I note
> that some authors write that we need to assume some point because the
> distance between the GP and the LOP is too great to plot, that there's
> insufficient information to plot the LOP, or that iterations are
> required to get exact points on the LOP.  The Sumner calculation
> demonstrates that none of this is correct.
>
> JK
> 
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>
>
> >


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