similar to polythene, are semi-conical in shape, with integral, hinged sealing caps. Larger samples are spun using centrifuge bottles, which range in capacity from 250 to 1000 millilitres. Although some are made of heavy glass, centrifuge bottles are usually made of shatterproof plastics such as polypropylene or polycarbonate. Sealing closures may be used for added leak-proof assurance. Safety The load in a laboratory centrifuge must be carefully balanced. This is achieved by using a combination of samples and balance tubes which all have the same weight or by using various balancing patterns without balance tubes. It is an interesting mathematical problem to solve the balance pattern given n slots and k tubes with the same weight. It is known that the solution exists if and only if both k and n-k can be expressed as a sum of prime factors of n. Small differences in mass of the load can result in a large force imbalance when the rotor is at high speed. This force imbalance strains the spindle and may result in damage to the centrifuge or personal injury. Some centrifuges have an automatic rotor imbalance detection feature that immediately discontinues the run when an imbalance is detected. Before starting a centrifuge, an accurate check of the rotor and lid locking mechanisms is mandatory. A spinning rotor can cause serious injury if touched. Modern centrifuges generally have features that prevent accidental contact with a moving rotor as the main lid is locked during the run. Centrifuge rotors have tremendous kinetic energy during high speed rotation. Rotor failure, caused by mechanical stress from the high forces imparted by the motor, can occur due to manufacturing defects, routine wear and tear, or improper use and maintenance. Such a failure can be catastrophic failure, especially with larger centrifuges, and generally results in total destruction of the centrifuge. While centrifuges generally have safety shielding to contain these failures, such shielding may be inadequate, especially in older models, or the entire centrifuge unit may be propelled from its position, resulting in damage to nearby personnel and equipment. Uncontained rotor failures have shattered laboratory windows and destroyed refrigerators and cabinetry. To reduce the risk of rotor failures, centrifuge manufacturers specify operating and maintenance procedures to ensure that rotors are regularly inspected and removed from service or derated (only operated at lower speeds) when they are past their expected lifetime. Another potential hazard is the aerosolization