(Click his picture for more information on GAS laws.)
Boyle has a famous experiment involving a U-shaped glass tube. Here he placed equal amounts of mercury in the tube. One end of the tube was open and the other closed. Under atmosphere pressure the mercury was level and equal. Boyle then started to add mercury to reduce the volume in the closed end. He found that to reduce the volume in the closed end by half, he had to add 30 inches more of mercury. Thus it proved to him that to half the volume in the closed end, a doubling of the atmosphere was needed. In other words, if temperature remains constant, the volume of the gas is inversely proportional to the absolute pressure. If you raise the pressure the volume will decrease proportionately.
Click on pictures to see it better.
Why do I need to know this as a diver ?
The deeper you dive the less volume of air you have in your tank Look at the chart here. Go from 1 ATA( Atmosphere) to 2 ATA you double the ATA but now the tank if 1/2 full. Go to 130 feet or 5 ATA -- 5 times the ATA, but now 1/5 the air volume. Another way. 5 breaths at the surface = to 1 breath at 130 feet. That is pressure and volume relationship. Increase pressure = decrease volume by that amount. This is why your stay at depth is shortened. Click on his picture above for more information on this principle.
Now lets talk about density and pressure. While pressure and volume of a gas are inversely proportional, the pressure and density of a gas are directly proportional. If the gas volume is reduced, the space where the gas molecules are must also be reduced, therefore, the same number of molecules in now a smaller space become compact or denser. Let's get this principle. You reduce the volume (space) by pressure, which reduced the air volume you have to breath. But now the space is smaller for the same number of molecules making them more dense. The relationship is the same as before. If you double the ATA you will double the density because now it is a direct relationship. See chart to help with this relationship. So at depth, you have less air to breath, but the quality of molecules would be increased.
Divers take with them gas-filled containers -Tanks, BCDs, dry suits, mask, - and have have gas filled spaces in their bodies - sinuses, ears, and lungs. Even the tiny bubbles that comprise wet suits continually expand and contract as pressure changes as described by Boyle's Law.