Proper velocity addition formula: where formula_3 is the beta factor given by formula_4. or in terms of logarithms: Proper velocity is useful for comparing the speed of objects with momentum per unit rest mass ("w") greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound. For example, a 45 GeV electron
Mass (mass spectrometry) used to selectively detect compounds with a mass spectrometer based on their chemical composition. The term packing fraction was defined by Aston as the difference of the measured mass "M" and the nearest integer mass "I" (based on the oxygen-16 mass scale) divided by the quantity comprising the mass number multiplied by ten thousand: Aston's early model of nuclear structure (prior to the discovery of the neutron) postulated that the electromagnetic fields of closely packed protons and electrons in the nucleus would interfere and a fraction of the mass would be destroyed. A low packing fraction is indicative of a