MAXIMUM DEPTH and CONTINGENCY DEPTH
DEFINE the Maximum Operating Depth (MOD) for any given Nitrox mix as the depth at which the partial pressure of oxygen in the mix equals 1.4 ata.
Since Partial Pressure is defined as P(r,d) = [1 + d/33] * r, we will have reached the MOD for the mix r when
[1 + d/33] * r = 1.4
Clearing terms, we can restate this expression as MOD(r) = [1.4/r - 1] * 33
This can be further simplified to d = 46.2/r - 33, but doing so obfuscates the logic behind the expression.
Similarly, we define the Contingency Depth (CD) for a Nitrox mix as the depth at which the partial pressure of oxygen in the mix equals 1.6 ata. As above, this will happen when
[1 + d/33] * r = 1.6
Clearing terms, we can restate this as CD(r) = [1.6/r - 1] * 33. (Or, if you want to lose sight of the big picture, simplify further and you will arrive at CD(d) = 52.8/r -33, which is the expression on page 82 of your manual.)
In both of the above cases (MOD or CD), use the constant 34 in place of 33 if you want the answer for fresh water.
NOTE: All of this becomes simple mental arithmetic (for salt water) if you will only think metric instead of imperial. Since 10m of sea water is one atmosphere of pressure, you can use P(r,d) = [1 + d/10] * r to find partial pressure if the depth d is stated in meters. Likewise, the MOD and CD expressions are much easier to calculate if the depth d is given in meters.