Planck’s principle in its original form is as follows. If a body [Pg 61] is undergoing any kind of vibration or periodic motion of frequency (i.e. the body goes through its whole period times in a second), then there is a certain fundamental constant such that the energy of the body owing to this periodic motion is or some exact multiple of . That is to say, is the smallest amount of energy that can exist in any periodic process whose frequency is , and if the energy is greater than it must be exactly twice as great, or three times as great, or four times as great, or etc. The energy was at first supposed to exist in atoms or little indivisible parcels, each of amount . There might be several parcels together, but there could never be a fraction of a parcel. We shall see that this principle has been modified as it has been applied in new fields, so that in its present form it can no longer be stated as involving indivisible parcels of energy. But it is as well to understand its original form before considering the more recent statements of the principle. The quantity , which is called Planck’s “quantum,” is of course very, very small, so small that in all the large-scale processes observable by means of our senses there is an appearance of continuity. It is in fact so small that one unit of it is involved in one revolution of the electron in its minimum orbit round the hydrogen [Pg 62] nucleus. It is difficult to express very large numbers in words, particularly as the word “billion” is sometimes used to mean a thousand million, and sometimes to mean a million million. If we use it to mean a million million, we may say that a billion billion times would be a quantity just appreciable without instruments of precision. Taking the electron in its smallest orbit, is exactly obtained by multiplying the circumference of the orbit by the velocity of the electron and multiplying the result by the mass of the electron.[3] In the second orbit the result of this multiplication is , in the third, , and so on.