"Back in the day" when we played outdoor sports, I remember the coach having an ice chest marked ammonia water with hand towels soaking in it. When we would get over heated, she would put one of the back of our neck.
I would like to know the proper ratio…
It was 108 degrees in the shade yesterday here in North Texas.

I can guess that ammonia water was used because ammonia evaporates quickly, and evaporation cools the skin. But it also would burn the eyes and is dissolved in the mucous membranes of the nose and is caustic. So it is not a good idea. Alcohol rubs were given in the hospitals to reduce fevers for the same evaporation reason also. They used isopropyl or denatured alcohol for that.