4 8 
THE QUANTUM 
[iv. i 
It has long been known that certain spectra contain a definite 
series of lines, one of the most striking of the series being that 
found in the spectrum of hydrogen. A number of lines may be 
seen in the spectrum starting with a prominent red line coinci 
dent with the line observed by Fraunhofer in the solar spectrum 
and called the c line of hydrogen. In the solar spectrum this 
occurs as a dark line, in the emission spectrum of hydrogen as a 
bright line generally known as H a . Other bright lines occur in 
the green, in the blue, or in the ultra-violet, and the series is 
indicated by the letters of the Greek alphabet H a , H^, H y . . . 
The spectrum is shown in Fig. 7 and it will be noticed that in 
passing towards the violet end of the spectrum the lines come 
closer together. 
Many attempts had been made to obtain a numerical relation 
between wave-lengths of these lines, but the first that was com 
pletely successful was that made by Balmer in 1885. He found 
that the first nine lines of the elementary spectrum of hydrogen 
violel ultraviolet 
blue 
5000 
6000 
Hi 
15000 20000 25000 —* » iocm' 1 
Fig. 7.—The Balmer Series in the Hydrogen Spectrum. 
can be represented by a simple mathematical formula. The 
wave-length is given by 
4:1 
where m is a positive integer to which we give in succession the 
values 3, 4, 5 ... 11. Within the limits of error of observa 
tion this formula gives A accurately. It was shown later that 
the same formula would account for the lines in the ultra-violet 
observed in the solar eclipse of 1898, as many as twenty-nine 
lines being measured. In modern work on spectra it is usually 
convenient to employ not the wave-length but the wave number. 
The number of complete waves in 1 cm. may be represented by 
N so that N is the reciprocal of A, assuming that A is expressed 
in centimetres.* We may now re-write Balmer’s formula in 
terms of wave numbers, and put it in the form 
and Iceland spar (calcite). The “ initial ” value 2-814 x io -8 cm. = 2-814 
A.U. = 2814 X.U. is employed for rock salt, and the value 3-029 X io _a 
cm. — 3-029 A.U. = 3029 X.U. is proposed for calcite. 
* Or N = io 8 /(A in Angstrom Units).