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Pole Foundation Embedment

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I have difficulty in interpreting pole foundation embedment formula given in 
UBC.

Required depth, d, of embedment is a function of S1, which is defined as 
"Allowable lateral soil bearing pressure as set forth in Table 29-B, based on 
a depth of one-third the depth of embedment."

Is it, therefore, correct to say that, S1=Allowable Lateral Bearing X (Depth 
of embedment)/3?  Also, would it not be prudent to discount the frost depth 
in this calculation?

One of the footnotes to table 29-B, states that the lateral bearing value 
"may be increased the amount of the designated value for each additional 
depth to a maximum of 15 times the designated value." So, if d=10 feet in 
clayey soil, is the lateral bearing equal to 1000 psf/ft depth of embedment 
or should it be an average value of (100+1000)/2 = 550 psf/ft depth of 
embedment? Taking advantage of this footnote will make the solution 
iterative, because while 'd' is dependent on S1, S1 itself becomes a function 
of 'd'.

Any comments?  Thanks.

Raj.