Music and the Making of Modern Science

248 Chapter 16

contributions by Gustav Kirchhoff, Robert Bunsen, and others).^3 But that still avoids the

question why elemental spectra are discrete, rather than continuous.

To address this, the mysterious thicket of spectral lines needed to be cataloged; Frauen-

hofer himself had noted no fewer than 570 dark lines in the solar spectrum, whose distri-

bution seemed to follow some complex but definite pattern, as did the individual elemental

spectra Å ngstr ö m produced. Nor was the complexity of the pattern the product of random-

ness or experimental uncertainty, for Å ngstr ö m ’ s results were accurate to within one part

in ten thousand, showing the precision that his optical methods could achieve even at the

beginning of spectroscopic analysis. In the case of hydrogen, Å ngstr ö m measured the

wavelengths of the first four spectral lines (all in the visible range), which he called H α ,

H β , H γ , H δ.^4 Efforts to find some mathematical order in the lines began in the late 1860s.

In 1871, the physicist G. Johnstone Stoney argued that “ the lines in the spectra of gases

are to be referred to periodic motions within the individual molecules, and not to the

irregular journeys of the molecules amongst one another ” ; as was common at the time,

he used the word “ molecule ” where we would say “ atom, ” treating it as vibrating in

response to the incoming waves of light. To describe this, Stoney relied on Helmholtz ’ s

work on sound: “ A pendulous vibration, according to the meaning which has been given

to that phrase by Helmholtz, is such a vibration as is executed by the simple cycloidal

pendulum. ”^5 Indeed, Helmholtz began his Tonempfindungen with those pendulous or

simple vibrations “ since they cannot be analyzed into a compound of different tones, ” and

hence form the basis on which musical tones are built.^6 Stoney was not original in describ-

ing atoms in terms of such simple modes of vibration (which Maxwell and others had

explored in the preceding decade), but he was the first to do so in the context of spectra,

for which “ one periodic motion in the molecules of the incandescent gas may be the source

of a whole series of lines in the spectrum of the gas, ” using the exact mathematical form

of the overtone series.^7 Stoney also used the musical analogy of atomic vibrations to

explain why many in the “ overtone series ” of spectral lines seem to be absent, “ analogous

to the familiar case of the suppression of some of the harmonics in music, ” such as the

clarinet, whose characteristic timbre is caused by the suppression of even-numbered over-

tones.^8 Stoney then takes the further step of applying this analogy to hydrogen and its

visible spectral wavelengths H α , H β , H δ , which he describes as “ the 32nd, 27th, and 20th

harmonics of a fundamental vibration, ” whose wavelength he calculates as 131,277.14 Å

(where 1 Å = 10^ – 10 m).^9 Put another way, Stoney expressed the ratio of the wavelengths

of these lines as

HHHαβδ::=^1 ::

20

1

27

1

32

in terms of that implicit fundamental wavelength, which he calculates corresponds to a

fundamental time of 4.4 × 10 – 14 seconds, considered as “ very nearly the periodic time of