What is meant by “conservation” in practice is not exactly what it means in theory. In theory we say that a quantity is conserved when the amount of it in the world is the same at any one time as at any other. But in practice we cannot survey the whole world, so we have to mean something more manageable. We mean that, taking any given region, if the amount of the quantity in the region has changed, it is because some of the quantity has passed across the boundary of the region. If there were no births and deaths, population would be conserved; in that case the population of a country could only change by emigration or immigration, that is to say, by passing across the boundaries. We might be unable to take an accurate census of China or Central Africa, and, therefore, we might not be able to ascertain the total population of the world. But we should be justified in assuming it to be constant if, wherever statistics were possible, the population never changed except through people crossing the frontiers. In fact, of course, population is not conserved. A physiologist of my acquaintance once put four mice into a thermos. Some hours later, when he went to take them out, there were eleven of them. But mass is not subject to these fluctuations: the mass of the eleven mice at the end of the time was no greater than the mass of the four at the beginning. This brings us back to the problem for the sake of which we have been discussing energy. We stated that, in relativity theory, measured mass and energy are regarded as the same thing, and we undertook to explain why. It is now time to embark upon this explanation. But here, as at the end of Chapter VI, the totally unmathematical reader will do well to skip, and begin again at the following paragraph. Let us take the velocity of light as the unit of velocity; this is always convenient in relativity theory. Let _m_ be the proper mass of a particle, _v_ its velocity relative to the observer. Then its measured mass will be _m_ —————————— √(1 - _v²_) while its kinetic energy, according to the usual formula, will be ½ _mv²_ As we saw before, energy only occurs in a profit-and-loss account, so that we can add any constant quantity to it that we like. We may therefore take the energy to be _m_ + ½(_mv²_). Now if _v_ is a small fraction of the velocity of light, _m_ + ½ _mv²_ is almost exactly equal to _m_ ————————— √(1 - _v²_). Consequently, for velocities such as large bodies have, the energy and the measured mass turn out to be indistinguishable within the limits of accuracy attainable. In fact, it is better to alter our definition of energy, and take it to be _m_ —————————— √(1 - _v²_),