Kevin,
Note that the drop-in dovetail is also narrower at the throat where it enters the beam. The fact that the shear (not sheer) force rises exponentially as the timber section decreases is just the nature of the beast; I can't explain the derivation of the formula but trust it is so.
EXCEPT that d/dn squared factor is a misprint, I believe. I will consult the editor. This chapter in the book is a reprint from Timber Framing #38, and this section is different than the calculations in the original. The NDS formula calculates the allowable shear rather than the actual shear (like the article)and uses a squared factor. That may be where the confusion (by the author/editor) arises. I'll report back.
Please call me if you have more questions on your original issue.
Also note that the NDS specifies that beam notches should not exceed 1/4 the depth, and I would never go past 1/2 the depth in practice, so notching a 9" joist down to 4" is excessive, IMO, even though the formula might work. Call it intuition, but also the nature of wood,
