General · EdgepediaOctober 10, 20268 min read

Heinrich Kayser

Heinrich Kayser (Johann Heinrich Gustav Kayser; 16 March 1853, Bingen – 14 October 1940, Bonn) was a German physicist who, with the mathematician Carl Runge, mapped the spectra of many elements and established the empirical laws of spectral series, and for whom the CGS wavenumber (reciprocal of wavelength; count of waves per centimeter) unit, the kayser (1 cm⁻¹), was named.¹^•² Arnold Sommerfeld, in his 1941 obituary, called him the "Nestor der deutschen Physik" (dean of German physics).¹

Key fact	Detail
Life dates	Born 16 March 1853 in Bingen; died 14 October 1940 in Bonn¹
Education	Studied under Kundt, Helmholtz, and Kirchhoff from April 1873; Ph.D. Berlin, 13 March 1879³
Chairs	Professor of physics, TH Hannover, 1885; successor to Heinrich Hertz at Bonn, 1894, where he built the first institute wholly devoted to spectroscopy²
Series work	"Über die Spektren der Elemente" with Runge, 1888–1893; alkali spectra resolved into three series with regularly shifting positions³^•⁴
Handbuch der Spectroscopie	Eight volumes, Leipzig 1900–1932, the first six essentially by Kayser alone, vols. VII–VIII with Heinrich Konen³^•⁵
Precision	Iron-arc standards measured with a 21-foot Rowland concave grating; same-line repeatability 0.001–0.002 Å on the same standards⁶
Honors	Foreign Member of the Royal Society, 1909; Honorary Member of the Royal Institution, 1899; LL.D. St Andrews, 1912⁵
Unit	The CGS wavenumber unit cm⁻¹ was named the "kayser"; the NBS line-intensity tables of the mid-20th century still used it⁷

Life and career

Kayser studied from April 1873 to March 1879 under August Kundt, Hermann von Helmholtz, and Gustav Kirchhoff, following Kundt to Berlin, where he took his doctorate on 13 March 1879 with a thesis on how the intensity of sound affects its propagation speed.³ He qualified as an academic lecturer on 26 September 1881 with a dissertation on the condensation of gases on surfaces, the work in which he coined the word "adsorption".³

Professorships. In 1885, on Helmholtz's recommendation, Kayser received the professorship of physics at the Technische Hochschule in Hannover at the age of 32.² In 1894 he succeeded Heinrich Hertz as professor of physics at the University of Bonn and taught there until 1920; in Bonn he established the first institute wholly devoted to spectroscopy.²^•³ More than a hundred doctoral students took their degree under him in Bonn.⁵

Work on spectral series

At Hannover, Kayser began the collaboration that defined his career. He was the experimenter; Carl Runge, his mathematical colleague there, was the theorist.³ After Balmer's 1885 formula for the hydrogen spectrum, Runge sought comparable formulae for other elements, and the two worked together for seven years, until Kayser's move to Bonn.⁸

The alkali result. For the alkali metals lithium, sodium, potassium, rubidium, and cesium, all known spectral lines could be assigned to three series described accurately by equations of the same structure, and the spectra shifted regularly with increasing atomic weight.³ The first paper, "Ueber die Spectren der Alkalien", appeared in Annalen der Physik volume 277 (1890), pages 302–320, with both authors at the Hannover Technische Hochschule; it cites Balmer's 1885 paper and Rydberg's 1890 Comptes rendus note.⁴ The major series "Über die Spektren der Elemente" appeared from 1888 to 1893, partly in the Abhandlungen of the Prussian Academy.²^•³

In his 1893 survey of spectral photography, Kayser reported that photographic methods and Rowland concave gratings had made it possible to order the tangle of spectral lines: he and Runge, and shortly afterward Rydberg, had found that most lines of many elements arrange into series like hydrogen's. Series occurred pairwise among the alkalis and in triplets among the alkaline earths; chemically related elements have similar spectra; and within a group the series shift toward the red end as atomic weight increases. The regularity had then been demonstrated for 5 groups of elements, the last (Al, In, Tl) reaching the photographic limit of 200 nm.⁹

Relation to Rydberg and Balmer. Rydberg's most significant competitors in mathematically ordering spectral data were Kayser and Runge, but their general formulas were of significantly different form; Rydberg's use of wavenumbers enabled a particularly useful form, and his constant N₀ = 109721.6, common to all series and all elements, became the Rydberg constant.¹⁰^•¹¹ Sommerfeld judged that Rydberg's Balmer-anchored form of the series representation proved more fruitful than the more interpolatory Kayser–Runge formulas.¹ Gerhard Herzberg's Royal Society memoir adds that Kayser and Runge missed the real clue to line series supplied by Rydberg's idea of representing a spectral line's frequency as a difference of two terms.⁵ Runge's own approach was to represent spectral series by adding an additional term to Balmer's formula.⁸

Instruments, methods, and wavelength standards

Kayser and Runge acquired a large Rowland grating using private funds as well as Berlin Academy support.² Kayser's key methodological idea was to measure the wavelengths of many spectral lines relative to precisely measured "Normalen", or standard lines.² He recognized the iron spectrum as particularly suitable for wavelength standards and carried out the first determinations of those standards.⁵ The early work was done without a proper comparator, a cathetometer serving instead, and without a calculating machine.⁵

His 1910 paper on standards of the third order on the international system describes the working method: the iron arc spectrum photographed in the second order with a Rowland concave grating of 21-foot radius, plates made partly by Konen, Eversheim, Bachem, and Kayser himself. Each line was measured ten to twenty times and the arithmetical mean with its probable error taken. Measurements of the same line on different plates with the same standards differed by no more than 0.001 to 0.002 Å; with different standards, differences as great as about 0.006 Å occurred, showing that some standards carried errors of 0.004–0.005 Å. Comparison with Rowland's solar spectrum gave differences varying irregularly between 0.15 and 0.22 Å, reducible to the international system by subtracting about 0.19 Å.⁶ The first volume of his Handbuch also reviewed the automatic comparator of Kayser's own design, and adopted Runge's treatment of the curved grating in place of Rowland's original 1883 handling.¹²

The Handbuch der Spectroscopie

Kayser's Handbuch der Spectroscopie, published by S. Hirzel in Leipzig, grew far beyond its plan. The first volume, covering the history of spectroscopy and the description and theory of apparatus, appeared in 1900 at XXIV+784 pages.¹³ Kayser had originally planned to finish in four volumes, but the mass of absorption material forced the third volume to split in two; volume 5 (1910, 48 marks) contained only element spectra down to nitrogen.¹⁴ The Dictionary of Scientific Biography records the completed work as eight volumes (1900–1932), with volumes VII and VIII written with Heinrich Konen, Kayser's Bonn successor.³ HathiTrust's catalog, by contrast, lists 7 volumes dated 1900–34, with volumes 7 onward "von H. Kayser und H. Konen"; the bibliographic record is not settled.¹⁵ Herzberg states that Kayser wrote the first six volumes essentially alone between 1897 and 1912.⁵

Reception. The 1902 Astrophysical Journal review of volume 1, which included a 128-page history from Newton to the Zeeman discovery, judged the survey so comprehensive that a spectroscopic experiment had, or had not, been tried according as it was, or was not, "found in Kayser".¹² Herzberg wrote that the effect of the handbook on spectroscopy "can hardly be exaggerated": the whole earlier literature had been collected in one place and its value assessed.⁵ Sommerfeld noted that spectroscopists worldwide still built on this foundation.¹ The work remained the working reference into the 1930s: volume 7 part 1 appeared in 1923 with data for the elements A to Fe complete up to 1922, and part 2 (1931) treated Ga to Ir with data up to 1928.¹⁶

By the numbers

~65,000 wavenumber values. Kayser's Tabelle der Schwingungszahlen (1925) contains nearly 65,000 eight-digit, vacuum-corrected wavenumber values between 2,000 and 10,000 Ångström, computed with a still primitive electric machine.²
0.001–0.002 Å. Repeatability of a line measured on different plates against the same standards in the 1910 iron-arc work; up to about 0.006 Å against different standards.⁶
21 feet. Radius of the Rowland concave grating used for the international-system standards.⁶
8 volumes (or 7). The Handbuch's extent, 1900–1932 per the Dictionary of Scientific Biography, 1900–34 in 7 volumes per HathiTrust.³^•¹⁵
1 kayser = 1 cm⁻¹. The CGS wavenumber unit named for him; the NBS tables give the conversion 1 eV = 8065 cm⁻¹.⁷

Honors and recognition

Kayser was made an Honorary Member of the Royal Institution at its centenary celebration in 1899 and elected a Foreign Member of the Royal Society in 1909; he received an LL.D. from St Andrews in 1912.⁵ On Runge's death in 1927, Kayser succeeded him on the collaborating editor board of the Astrophysical Journal, where Runge had served since 1903.⁸

References

Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026