All discussions are based on the interpretation of the "the high peaks that divide waters ".

Let us imagine that the land is something so simple as a rectangular pitched or double-sloped roof (plant drawing: fig. 1). The sidewalls are 10 feet high and the summit (the line where the two slopes meet) is 15 feet high. The summit is seen in the drawing as a horizontal line (C-C'). Rain falling in any point that is above this line in the drawing drains to the North side and if it falls below it drains to the South side. It seems evident that the summit. (C-C') is the line that divides waters.

The line joining the stacks (W-Z) would be the "high peak line" and has no relation to summit line and does not divide waters; rain falling South of X (between X and C-C') drains to the North, and that falling North of Y (between Y and C-C') runs southwards.

It seems therefore that the "high peak line" is one thing and "the line that divides waters" is another thing. Roca and Errázuriz the Argentinean and Chilean presidents that signed the treatise seem to have written an ambiguous statement. According to what we know about these characters it seems unlikely that they did it by ignorance, and less by inadvertence. This ambiguity might have been intentional to be able to solve the most important problem and kick forward the difficult cases. As a matter of fact a war was avoided and in many spots of the border an agreement was reached.

But now comes the worse. The "high peak line" is in itself a meaningless sentence. In our figure 1 we have drawn the four stacks in a straight line, that can happen with chimneystacks, but very seldom with mountain peaks. If the 4 chimneys are not aligned (as it happens in figures 2 or 3) what line do they define: RSTU as in fig. 2 or RTSU as in fig. 3? (Mountains are not an well-ordered set)

But we have not reached the bottom. In this simple example of the double-sloped roof the "the line that divides waters" is easy to define.

There is another possible explanation of this strange "mistake" made by so acute diplomats: It is possible that they were really thinking on the technical concept of "continental water divide". This is a known technical concept that will be also in line with the so-called bioceanic principle, also stated in the agreement (Chile towards the Pacific Ocean, Argentina to the Atlantic).

But when the moment came to write the treatise the technical expression "continental water divide" was a strange thing to lawyer's ears, and since lawyers usually advice to avoid technical expressions in legal papers and try to "simplify" them, they invented that nonsense of "the high peaks that divide waters" that sounds better, more diplomatic-like and more understandable by "common men" It is a pity it means nothing.