The idea of compression of a mass was understood and applied as early as 1662. Chemist, physicist, and sometime philosopher and theologian Robert Boyle theorized that any given mass of a gas was inversely proportional to the volume and pressure at any given temperature when confined. Water pressure and the volume of the body of water affect the confined compressed gas that SCUBA divers breath. The air that SCUBA divers breathe is a mix of oxygen and nitrogen, the same gas mix that is breathed by humans above water; only this air is highly compressed inside the cylinder, and breathed through high pressure hoses underwater where the effects of Boyle’s law makes the mass of the gas even smaller and more tightly packed within the cylinder. Here is an example:
I have a friend who drives a semi-truck for a living. He delivers chips and tortillas. These products are sealed into bags at near sea level. One of his deliveries is nearly 9,000 feet above sea level, when he offloads there, the bags appear to have ballooned in size. This is because at sea level the air that was trapped in the bag was at a lower altitude where atmospheric pressure is high, but as he went up in altitude to make his delivery, the atmospheric pressure is lower than at sea level, so the bags expanded, as the mass of the gas trapped inside the bags expanded.
The same happens underwater. The deeper a diver goes the smaller the given mass of a gas will get, which means that the diver breathing that gas will use it quicker at say 70 feet then he/she would at 10 feet, because the gas is more tightly compacted at 70 feet than it is at 10 feet. There are many different techniques and equipment that will allow a diver the maximum time allowable on the No-Decompression Dive Table. Double cylinders, attaining and maintaining neutral buoyancy, and larger cylinders all give a diver more time underwater.
Archimedes Principle is very simple. Any object may buoy itself positively if the object displaces more water relative to its’ size. If it cannot displace that water then it sinks. Obvious enough. In recreational diving neither positive or negative buoyancy is desired, rather neutral buoyancy is desired so that less air is used during the dive, and the diver is able to move about in the water with greater ease. To achieve this a combination of weights and a buoyancy compensator device are worn while diving. There are very simply techniques and skills used to attain and maintain neutral buoyancy underwater so that a diver may achieve good trim while moving underwater. A diver’s trim whether SCUBA or free-diving is the horizontal position that a diver seeks to maintain while moving about at depth.