A system is called “conditionally periodic” when its motion is compounded of a number of motions, each of which separately is periodic, but which do not have the same period. For example, the earth has a motion compounded of rotation round its axis, which takes a day, and revolution round the sun, which takes a year. There are not an [Pg 65] exact number of days in a year, if a year is taken in the astronomical and not in the legal sense; that is why we need a complicated system of leap-years to prevent errors from piling up. Thus when we take account of both rotation and revolution, the motion of the earth is “conditionally periodic.” We shall find later that the motions of electrons in their orbits, when we take account of niceties, are, strictly speaking, conditionally periodic and not simply periodic. The quantum-theory in its general form applies to motions that are conditionally periodic in terms of “separated” coordinates. We can now state the generalized quantum-principle. Take some one coordinate of the system, and imagine the motion of the system throughout one period of this coordinate divided into a great number of little bits. In each little bit, take the generalized momentum corresponding to the coordinate in question, and multiply it by the amount of change in the coordinate during that little bit. Add up all these for all the little bits that make up one complete period. Then, in the limit, when the bits are made very small and very numerous, the result of the addition for one complete period will be exactly or or or some other exact multiple of .[4] No one [Pg 66] knows in the least why this should be the case; all we can say is that it is so, in all the cases that can be tested.