I am trying to find the lat/long coordinates to the following point
described in a document written in the 1900.  It describes the point
as follows:

Wheeler Mountain bears N. 79 ° 17´ W.
Mount Silverheels bears S. 70° E.
thence N. 66° 29´

I know the coordinates of 
Mount Silverheels NAD27 39.3392/-106.0047 and
Wheeler Mountain NAD27 39.3806/-106.1356

Could you please give me the exact lat/long coordinate of this point
and let me know how you did the calculation.

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Request for Question Clarification by redhoss-ga on 08 Jul 2004 07:23 PDT

The only way the info you have given makes sense to me is this:

A person standing at a point took compass readings to two identifiable
referance points (Wheeler Mountain and Mount Silverheels). This is
enough info to exactly locate the point where he stands. He then
(thence) set out on a compass heading of 66 deg 29 min. How far he
continued on this course you do not know. If you agree with this
logic, I can explain to you how to find the exact spot where he stood
and how to follow the path he then took. You will need a topo map and
a good compass.

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Clarification of Question by curious8-ga on 08 Jul 2004 09:18 PDT

Yes, I agree with this logic.  I understand that we should be able to
triangulate based on those two points.  I have a GPS and a compass. 
So, what I was hoping to do is to identify the GPS coordinates of the
point and then follow the path based on the last compass reading. 
Thanks.

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Request for Question Clarification by redhoss-ga on 08 Jul 2004 15:00 PDT

Okay, we are getting close to being able to find the point in
question. One thing remains. You say you have a compass and GPS, but
you will still need a topo map of the area. That is the only way to
triangulate the point. I do not have a topo map. I have looked at the
area on TerraServer, but can't download a map in enough detail to
locate both locations and lay out the triangle.

It sounds to me like you have a point and then a compass heading from
that point (N. 66° 29´).

You also have to take into account the magnetic declination and how it
changes over time.  Since the information is from 1900 (over 100 years
ago) the magnetic declination may have changed signifigantly since
then.

Basically you would find a map with these two places on it. (eg
mytopo.com you can  order a highly detailed topo map for about $15.00.
 The nice part about them is you can choose the scale and span USGS
Quadrants.)  Here is what you do:

Get a topomap with the two locations on it.  Find one of the locations
on the map.  (assuming your compass has a square base, a direction of
travel, and a rotating bezel with lines) (for Wheeler Mountain) Rotate
the bezel to 79 °.  Position the base of the compass so the direction
of travel is towards Wheeler Mountain.  Slide the base of the compass
around until the lines attached to the rotating bezel are parrellel to
Magnetic north. (I draw the magnetic north lines right on the map so I
don't have to add or subtract based upon where I am in the country.) 
Once you have done that draw a line on the map from Wheeler Mountain
in the direction opposite the direction of travel.

Repeat the above procedure for Mount Silverheels and 70° .  Where the
two lines intersect is where the person was standing to take the
original bearings.

You do not need a topo map.  You have the coordinates of the peaks and
the directions to them, which is all you need.  It is important to
know whether the numbers refer to true north or magnetic north.  If
magnetic north, you need to know the magnetic declination at the
location and time the bearings were taken.  However, it is likely that
the bearings are true, in which case you don't have to worry about it.
 If we assume the bearings are true, the point from which the bearings
were taken was (39.3616, -106.0647).  I figured this out by finding
the equation of the line through each peak with the proper slope, and
solving for their intersection. The slope of the line through Wheeler
is -0.3469, and through  Silverheels -.4823.  When doing the
calculation, you have to remember to divide differences in longitude
by the cosine of the latitude when computing distances.  At this small
scale, the errors introduced by not using spherical geometry are
negligible.  It is unfortunate that the two peaks were in very nearly
opposite directions (about 171 degrees apart) because a small error in
the bearing will cause a large error in the location.

I am sorry, I made an error in the calculation above.  (for some
reason when I subtracted 70 from 90 I got 30).  When I do the
calculation correctly, it turns out that the two lines intersect
northwest of Wheeler, which means that the bearings must either be
incorrect, or uncorrected for magnetic declination.  From

http://www.ngdc.noaa.gov/seg/geomag/jsp/Declination.jsp

the magnetic declination at your location in 1900 was 14 deg 11 min E.
 So the true bearings would be N 65 06' W to Wheeler and S 55 49' E to
Silverheels.  Using these numbers, the lines intersect just southeast
of Silverheels.  So my conclusion is that the bearings are crap. 
There is no possible place you could have stood in 1900 and obtained
those bearings to those places, whether the bearings are true or
relative to magnetic north.