Ahh, I see your dilemma now, sir. You have been getting markedly different readings for the specific gravity from one end of the tank to the opposite end of the aquarium. You’re right, that certainly shouldn’t be happening — ordinarily the specific gravity of a given solution is homogenous throughout for a small body of water. You can sometimes see some vertical stratification if there is not adequate circulation, since the less dense freshwater may float atop the more dense saltwater momentarily when you’re topping your aquarium off, for instance, but it is most unusual to see a difference from one side of the tank to the other.
That’s unheard of and I can’t imagine that there isn’t enough water movement in any aquarium to prevent such a thing from happening, so I think the difference in the specific gravity must be an artifact of how you are measuring the salinity. For example, if you are using a floating hydrometer, that might erroneously record a different specific gravity at either end of the tank because the water/air mixture nearest the bubble stream of the airstone would be less dense than the pure salt water without any bubbles in it at the other end of the aquarium. In other words, the hydrometer would sink deeper near to the airstone and float higher in the bubble-free saltwater at the end opposite the airstone, whereas in actuality the specific gravity of the water was the same at both ends.
If you are using a swing-arm hydrometer, then you may have gotten some air bubbles attached to the arm when you sampled the water near the airstone, and that’s what is giving you a false reading for the specific gravity. It’s very important to tap the swingarm and free any bubbles that may be clinging to it before you can get an accurate reading. Most likely if you double check the specific gravity readings from both ends of the tank more carefully, you’ll find that they are actually the same.
Is the airstone the only thing that is providing water movement in your 57-gallon aquarium? Do you have an external filter to provide mechanical and chemical filtration, as well as to circulate the water throughout your tank?
If not, I would suggest adding a hang-on-the-back external filter with a waterfall return or a canister filter with a spray bar return rated for an aquarium of 60 gallons in order to increase the water flow and circulation throughout the tank.
Best of luck figuring out the specific gravity quandary, arcprolife.