Cascade filling system  A cascade filling system is a high pressure gas cylinder storage system which is used for the refilling of smaller compressed gas cylinders. In some applications, each of the large cylinders is filled by a compressor, otherwise they may be filled remotely and replaced when the pressure is too low for effective transfer. The cascade system allows small cylinders to be filled without a compressor. In addition, a cascade system is useful as a reservoir to allow a low-capacity compressor to meet the demand of filling several small cylinders in close succession, with longer intermediate periods during which the storage cylinders can be recharged. When gas contained in a cylinder at high pressure is allowed to flow to another cylinder containing gas at a lower pressure, the pressures will equalise to a value somewhere between the two initial pressures. The equilibrium pressure is affected by transfer rate as it will be influenced by temperature, but at constant temperature the equilibrium pressure is described by Dalton's law of partial pressures and Boyle's law for ideal gases. The formula for the equilibrium pressure is:  An example could be a 100-litre (internal volume) cylinder (V1) pressurised to 200 bar (P1) filling a 10-litre (internal volume) cylinder (V2) which was unpressurised (P2 = 1 bar) (resulting in both cylinder equalising to approximately 180 bar (P3). If another 100 litre cylinder pressurised this time to 250 bar were then used to "top-up" the 10 litre cylinder, both of these cylinders would equalise to about 240 bar. However, if the higher pressure 100 litre cylinder were used first, the 10 litre cylinder would equalise to about 225 bar and the lower pressure 100 litre cylinder could not be used to top it up. In a cascade storage system, several large cylinders are used to bring a small cylinder up to a desired pressure, by always using the supply cylinder with the lowest usable pressure first, then the cylinder with the next lowest pressure, and so on. In practice the theoretical transfers can only be achieved if the gases are allowed to reach a temperature equilibrium before disconnection. This requires significant time, and a lower efficiency may be accepted to save time. Actual transfer can be calculated using the general gas equation of state if the temperature of the gas in the cylinder is accurately measured. A breathing set cylinder may be filled to its working pressure by decanting from larger (often 50 litre) cylinders. (To make this easy the neck of the cylinder of the Siebe Gorman Salvus rebreather had the same thread as an oxygen storage cylinder, but the opposite gender, for direct decanting.)