To illustrate further this kind of deduction, let us consider the spectrum shown in Fig. 9 and see what may be learnt from it. With a little trouble we can disentangle a beautifully regular series of bright lines. The marks above will assist you to pick out the first few lines of the series from the numerous other spectra mixed up with it. Noticing the diminishing spacing from right to left, you will be able to see that the series continues to the left for at least fifteen lines beyond the last one marked, the lines ultimately drawing close together and forming a ‘head’ to the series. This is the famous Balmer Series of hydrogen, and having recognized it we identify hydrogen as one of the elements present in the source of the light. But that is only the first step, and we can proceed to further inferences. Professor Bohr’s theory of the hydrogen atom teaches us that each line of the series is emitted by an atom in a different state. These ‘states of excitation’ can be numbered consecutively, starting from the normal state of the hydrogen atom as No. 1. The light emitted in the first few states comes into the part of the spectrum not reproduced here, and the first line in our picture corresponds to state No. 8. Counting to the left from this you will recognize the successive lines without much difficulty up to state No. 30. Now the successive states correspond to more and more swollen atoms, that is to say, the planet electron[17] makes a wider and wider circuit. The radius (or more strictly the semi-axis) of its orbit is proportional to the square of the number of the state, so that the orbit for state No. 30 is 900 times larger than the orbit for the normal atom No. 1. The diameter of the orbit in No. 30 is approximately a ten-thousandth of a millimetre. One inference can be drawn immediately--the spectrum shown in Fig. 9 was not produced in any terrestrial laboratory. In the highest vacuum that can be used in terrestrial spectroscopy the atoms are still too crowded to leave room for an orbit so large as this. The source must be matter so tenuous that there is vacant space for the electron to make this wide circuit without colliding with or suffering interference from other atoms. Without entering into further detail we can conclude that Fig. 9 is a spectrum of matter more rarefied than the highest vacuum known on the earth.[18]