In studying the connection between the different lines in the spectrum of an element, it is convenient to characterize a wave, not by its wave-length, but by its “wave-number,” which means the number of waves in a centimetre. Thus if the wave-length is one ten-thousandth of a centimetre, the wave-number is 10,000; if the wave-length is one hundred-thousandth of a centimetre, the wave-number is 100,000, and so on. The shorter the wave-length, the greater is the wave-number. The laws of the spectrum are simpler when they are stated in terms of wave-numbers than when they are stated in terms of wave-lengths. The wave-number is also sometimes called the “frequency,” but this term is more properly employed to express the number of waves that pass a given place in a second. This is obtained by multiplying the wave-number by the number of centimetres that light travels in a second, i.e. thirty thousand million. These three terms, wave-length, wave-number, and frequency must be borne in mind in reading spectroscopic work. In stating the law’s which determine the spectrum of an element, we [Pg 44] shall for the present confine ourselves to hydrogen, because for all other elements the laws are less simple. For many years no progress was made towards finding any connection between the different lines in the spectrum of hydrogen. It was supposed that there must be one fundamental line, and that the others must be like harmonies in music. The atom was supposed to be in a state of complicated vibration, which sent out light-waves having the same frequencies that it had itself. Along these lines, however, the relations between the different lines remained quite undiscoverable.