"In their calculations, Clausius (and Waterston, for that matter) had imagined all atoms in a gas moving at the same speed. They knew this wasn't true... but they didn't have the mathematical sophistication to tackle the full problem. Maxwell... defined a mathematical function called the distribution of velocities, which kept track of how many atoms were moving at any particular speed relative to the average, and by dealing in terms of this distribution... was able to give his calculations a precision that those of Clausius lacked."