Chester's calculation isn't very far off as you can see; to do a "real" "exact" calculation, one would have to obtain measurements of temperature / pressure / humidity at all elevations between the camera and the peak being photographed ... so of course the formulas use a series of assumptions and simplifications. Which may or may not be right.
Most notably, if you have temperature inversion conditions, the vertical gradient of air density may become more pronounced, and then your distance of sight may be longer than the models predict?