great paper david
& i am pleased jacks fantastic discovery here satisfies your needs
also i realize you are working from a theoretical basis
& that your modeling is intended to smooth over any rough edges
& indeed it seems to me to be successful for that very reason
yet from a punctological point of view
a primary thalweg line can only be traced to its true source
experientially
naturally
inch by inch
& in the upstream direction only
& cant simply be declared to fall by extra fiat as it were
defined as a course line now & no longer even a true thalweg
from any particularly convenient point
including even the low point of a saddle
deliciously simplifying & satisfying as that is
because in reality waters are shed from above the saddle as well
& unless you actually perform the sawanabori uphill you can never be
sure you are upon the main stem at any given moment
from my own observations & tries at doing just this sort of thing
i believe if we stood at naches pass in a heavy rain we would even be
able to see the trickles that fall in both directions from the saddle
there as tributaries to larger trickles that fall from elsewhere on
the transverse ridge
so you may pronounce your extra fiat that will make this a perfect
quadripoint
but i still dont see how there is a true natural fiat quadripoint by
your earlier definition
as indeed there might well have been at a mountain peak
m
--- In BoundaryPoint@y..., David Mark <dmark@g...> wrote:
> Thanks, Jack, this IS an instance of what I was looking for,
although I
> was imagining 4 ridges coming to a peak, and not two ridges and two
> course lines coming to a saddle.
>
> There is a theory of continuous, smooth surfaces laid our by Alred
Cayley
> in 1859, and the famous physicist James Clerk Maxwell in 1870, that
shows
> that at any saddle point (such as Naches pass), there in fact are
two
> course lines that must emanate from the exact point of the saddle,
as well
> as two ridge lines running up to peaks. According to that theory
this
> should indeed be a perfect quadripoint.
>
> Cayley, A., 1859. On contour lines and slope lines. Philosophical
> Magazine, 18, 264-268.
>
> Maxwell, J. C., 1870. On hills and dales. Philosophical Magazine,
vol. 40,
> 421-427.
>
> For far more on this topic, see the appropriate section in
>
http://wings.buffalo.edu/philosophy/faculty/smith/articles/topography.
pdf
>
> David
>
> On Sat, 6 Apr 2002, acroorca2002 wrote:
>
> > jack
> > apologies
> > as my library computer was shooting blanks that day
> >
> > but i think the message was simply that even if kikipiya isnt a
> > perfect fiat quadripoint there might still be a washington statute
> > that makes it a legal quadripoint
> >
> > & probably nobody but us would think of drawing such fine
> > distinctions anyway
> > so lets not write it off yet from our list of true megapoints
> >
> >
> > also in the unlikely event that it or they are marked
> > i still doubt anyone would think of erecting 2 monuments
> > especially on public land & in such a remote place
> > when even a small marker would probably suffice to physically
cover
> > both points so close together
> > if they are even distinguishable
> > which they probably arent
> >
> > all in all a pretty ridiculous situation
> > & i am sure glad we discovered it
> >
> > m
> >
> > --- In BoundaryPoint@y..., "Jack Parsell" <jparsell@n...> wrote:
> > > Michael,
> > > I agree that it is not highly probable that there is a little
pool
> > > of water in the pass with the water having difficulty deciding
> > > which way to descend, although I've seen that in the
Adirondacks.
> > > The distance between the 4920 ft. contour lines on each side of
the
> > > pass is less than 200 ft. and the drainages line up
> > cartographically,
> > > but I guess a single precise point is too much to hope for. It
> > looks
> > > like pretty rough terrain with 2000 ft gain in elevation from
the
> > > nearest paved road so I don't plan to check it out. It would be
> > > nice to know though.
> > > Jack
> > >
> > > -----Original Message-----
> > > From: acroorca2002 [mailto:orc@o...]
> > > Sent: Wednesday, April 03, 2002 5:18 PM
> > > To: BoundaryPoint@y...
> > > Subject: [BoundaryPoint] Re: TopoZone - Washington quad county
point
> > >
> > >
> > > jack
> > > i still like this just as much but my nearsightedness had missed
> > the
> > > fact that these are 2 opposite watersheds descending from that
pass
> > > for i was imagining it was just one river running thru a gap
> > > oops
> > >
> > > now that you have said this tho
> > > i have to think a purely fiat quadripoint is technically as
> > unlikely
> > > here as on that mountaintop in france without a little fudging
or
> > > coaxing
> > > because it is almost inconceivable that 2 sawanaboris should
ascend
> > > to meet at a single precise point along a crest line
> > > but they would by their nature produce 2 distinct fiat tripoints
> > > however close together
> > > m
> > >
> > > --- In BoundaryPoint@y..., "Jack Parsell" <jparsell@n...> wrote:
> > > > This quad-county point of King - Kittitas - Pierce - Yakima
> > > > counties is at N 47 05' 14", W 121 22' 42" at Naches Pass at
> > > > about 4920 ft. National Forest Development Rd.#70 from Naches
> > > > Pass Campground runs to within a little over a mile from the
> > > > quad-point. The Naches Trail and a jeep road cross the pass
and
> > > > the Pacific Crest trail passes about 1/2 mile west. It appears
> > > > the King-Kittitas and Pierce-Yakima lines are on a ridge. The
> > > > King-Pierce line is the beginning of Meadow Creek drainage and
> > > > the Kittitas-Yakima line is the beginning of Middle Fork
Little
> > > > Naches River drainage. Thus it is an intersection of a ridge
> > > > line and two drainages all of which are natural features.
> > > > I belive that is what David was looking for.
> > > >
> > > > Jack
> >
> >
> >
> >
> >
> > Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
> >
> >
> >