How can you calculate relative humidity using the wet and dry bulb. temperatures of a hygrometer?

This is an interesting question and I have been discussing it without coming to an agreement. Here is what I know: Seafarers have for many years used the wet and dry bulb to forecast fog. As you probably know, the wet bulb has wet cotton wool and both thermometers have to be placed somewhere away from the direct sunlight but open to the wind. Seafarers then do this: They read both thermometers and average the temperature. Then they take a bucket of sea water and plot both on a diagram. When projected to meet in the future then fog can be expected at that time. This happens often when sailing toward the shore. The question then is: What is the dew point temperature? The average of the two or the wet bulb temperature? One thing is for sure: when both thermometers read the same value, the air is 100 percent saturated as it is when fog exists. This is, for example, at 15 degrees Celsius (the average temperature on earth) when one cubic meter of air contains 14 grams of water. 14 grams is then the absolute humidity and 100 percent, the relative humidity. In my opinion, the wet bulb reading is the actual dew point temperature. But not everyone I talked to agree to that. In aviation, we also use the same principle and the dew point temperature is always given on the METAR (aerodrome weather report), together with the OAT (outside atmospheric temperature). I don't know if it is still practiced but not so long ago, the weather man at the airfield would have his wet and dry bulbs at the end of a rope that he/she would rotate in the air in order to have enough air passing on them. As a rule of thumb, we consider this: the temperature decreases at about 2 degree Celsius per thousand feet of altitude. If the METAR says e.g. 15/11, the spread (difference between dew and ambient temperatures) is 4 C and the ceiling can be expected at 2,000 feet. Of course, dew point vary with pressure so it is only a rough estimation.