How can finding longitude require you to already know your longitude?

"Now, we are not on the exact meridian, though, so we'll need to use the Arc to Time Conversion Tables (Figure 19) to correct the time for our distance from the meridian. We are in the time zone centered at longitude 60 degrees West. At 65 degrees 16 minutes west longitude, we are 5 degrees 16 minutes of arc to the west..." How can we use the Arc to Time Conversion Tables if we don't know our longitude beforehand?