Location of the Yesod Ramp: Part 2

Last week I came up with the following diagram and accompanying equation which describes where along the main Ramp of the Altar the minor ramp to the Yesod branched off to the west. 

Tiferes Yisrael, in his Temple Diagram §48, indicates that the minor ramps branched off somewhere on the lower half of the main Ramp. When the above equation is solved (I entered it in Grapher, my Mac's built-in graphing program), we get:

e = 13.81

This means that the ramp to the Yesod began 13.81 amos from the foot of the main Ramp, or 2.19 amos below its midpoint, which is indeed on the lower half of the main Ramp.

As for the ramp to the Sovev on the east, it is physically impossible to have it branch off on the lower half of the main Ramp and also conform to the Temple standard of 1 amah of height for every 3 amos of length. Since the slope will, in any case, differ from the standard, it appears that we may have the minor ramp to the east branch off at the same point as the ramp to the Yesod on the west. This not only makes the Altar more symmetrical, but having the two ramps directly across from one another shortens the distance that the Kohen needs to walk when descending from the Sovev to bring excess blood to the Yesod.

Location of the Yesod Ramp: A Mathematical Diversion

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SUMMARY It is possible to determine mathematically where the minor ramp to the Yesod branched off from the Main Ramp based on the dimensions of the Altar.

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Two minor ramps branched off of the Altar's Main Ramp, one on the west leading to the Yesod and the other on the east leading to the Sovev. Tiferes Yisrael states that the "two minor ramps branched off near the foot of the Main Ramp, on its lower part" (Temple Diagram §48), which I take to mean that the minor ramps began somewhere on the lower half of the Main Ramp. In this post I attempt to figure out exactly where the ramp to the Yesod began.

Lighting the Interior of the Antechamber

In an earlier post I included this image of the interior of the Antechamber. Here the large curtain of the main entryway is partially open with the morning sun shining in from the east, a pretty typical lighting scheme.

The Otem

The floor level of the Antechamber stood 6 amos above that of the Courtyard. These first 6 amos of the building’s height were occupied by the Otem, a sturdy foundation of hewn stone which rested upon the bedrock of Mount Moriah and supported the immense weight of the Antechamber and Sanctuary walls. Due to the steps in the east, the Otem was not at all visible on that side but could be seen on the northern, southern, and western sides of the Antechamber. The Otem extended under the Sanctuary as well but was not visible from the outside of the building (it formed the inner wall of the bottom level of tau'im, or small rooms outside the Sanctuary).

Structure and location of the Otem