Rydberg received his bachelor's degree in 1875 from the University of Lund. He continued his study of mathematics and wrote a main dissertation on conic sections for his doctorate in mathematics with a second thesis on algebraic integrals of algebraic functions. He was awarded his doctorate in 1879. While he was studying mathematics, Rydberg also taught physics at the Lund Physics Institute where he had been appointed as an assistant in 1876. After the award of his doctorate, in 1880 he was appointed to the post of assistant lecturer, or docent, in mathematics at Lund University but his research interests were now turning towards mathematical physics rather than to pure mathematics. During his two years as a lecturer in mathematics he worked on problems relating to electricity. The physics research he undertook at this time was experimental rather than theoretical.
In 1882 Rydberg moved from an assistant lectureship in mathematics to become an assistant lecturer in physics at the University of Lund. In the same year the University of Lund's request for a new physics building to house the Institute of Physics was approved. This new Institute would eventually become Rydberg's place of work for the rest of his career. In 1886 he married Lydia Eleonora Mathilda Carlsson, the daughter of a medical official to the provincial county council; they had two daughters and a son Helge who became a biologist. In 1897 he took over the duties of the professor of physics but this was only on a temporary basis and he remained an assistant lecturer. With an extremely poor salary, Rydberg was forced to take a position as an accountant in a local saving bank so that he could supplement his income sufficiently to allow him to support his family. In 1897 Rydberg applied for the chair of physics at the University of Lund which became vacant when Karl Albert Viktor Holmgren (1824-1905) retired. Six people applied for the chair but the process went on several years and the appointing procedure became almost farcical.
The outcome was that Albert Victor Bäcklund, who was an applicant that the referees had considered as not worth ranking for the position, was appointed. After his appointment, Bäcklund tried to get Rydberg promoted to professor. It is unclear whether Bäcklund was trying to right the wrong of the chair appointment or whether he wanted an additional chair appointment so that he had a lighter teaching load. In March 1901 Rydberg was named as an extraordinary professor but it only became a full professorial appointment in January 1909. From this time until his retirement he held the chair of physics at Lund.
Rydberg's most important work is on spectroscopy where he found a relatively simple expression relating the various lines in the spectra of the elements. We quote from the obituary  (see also ):-
Notwithstanding the imperfect spectroscopic tables then at his disposal Rydberg discovered most of the important properties of series spectra, including the relation between corresponding series in the spectra of related elements, and foreshadowed discoveries which were made later, when experimental work has sufficiently advanced. Some of the features noted by Rydberg were observed about the same time by Kayser and Runge, but his work had the special merit of connecting different series in the spectrum of the same element into one system, which could be represented by a set of simple formulae having but few adjustable constants. He especially insisted that the hydrogen constant, now generally called the "Rydberg constant," should appear in all series and, apart from slight variations from element to element suggested by the theoretical work of Bohr, nearly all subsequent attempts to improve the representation series have involved this supposition, and have had Rydberg's formula as a basis.We know that he had found his results by September 1887 since he wrote to the Royal Swedish Academy of Sciences at this time requesting financial support and attached to his application an appendix listing the results he later announced publicly. His first public announcement of his results was in On the Structure of the Line Spectra of Chemical Elements. Preliminary Notice Communicated by the Author which was published in 1890. In this preliminary notice, he stated that his researches had been only on elements in groups I, II, and III of the periodic table. However, he was certain that the laws he had found applied to all elements. He had presented his main paper Recherches sur la constitution des spectres d'émission des élements chimiques to the Royal Swedish Academy of Sciences on 13 November 1889. It also was published by the Academy in 1890. We now look at some of Rydberg's comments in these papers.
He had been led to study spectral lines of elements because of the work of Dmitri Ivanovich Mendeleyev (1834-1907) who had produced his periodic table of the elements in 1871. Mendeleyev's work was, at first, greeted with little enthusiasm but this changed over the years. Rydberg writes in Recherches:-
With the discovery by Mendeleyev of the periodic table of elements, there has arisen a new point of departure of great importance for all the work which I study here. However, it has been used but little. In 'Om de kemiska' I have concluded that the periodicity of a great number of physical coefficients must depend on the fact that the force which acts between two atoms of the same, or of different elements, is a periodic function of the atomic weight.He states that, except for the Balmer formula for the spectrum of the hydrogen atom, the:-
... problem of the constitution of luminous spectra is still unsolved and most of the attempts that have been made to compare and calculate the spectra of the elements have been done in such a way as to throw discredit on all work of this kind and to exaggerate the difficulties their authors having let their imaginations run so freely in the formation of their hypothesis.He gives a formula based on various constants and notes that:-
... the wave-lengths and wave numbers of corresponding lines, as well as the values of the three constants of the corresponding series of different elements, are periodical functions of the atomic weight. Therefore, if the spectra of two elements in the periodic table are known, the spectrum of the element in between them can be calculated using interpolation.He continued to study the problem of spectral lines and in his paper Lines in the Hydrogen Spectrum (1897) he writes:-
As I have pointed out already in my general exposition of the constitution of line spectra, and have afterwards tried further to confirm, there can be no doubt that these series are really parts of a single group of lines with two variable integral parameters, the general formula of which can be written approximately.He hoped to determine the structure of the atom but, although his work did provide the basis for the structure theory, he himself did not reach his goal. Only after Ernest Rutherford had proposed his model of the atom, and Niels Bohr and Max Planck had added a quantum theory approach to the theory of atomic structure, was the foundation in place to give a correct theoretical account of spectral data.
We have seen above that Rydberg only became a full professor in 1909. He was 54 years old, but sadly his health soon began to deteriorate. He had a stroke in 1911 and, although he recovered sufficiently to return to work, he began to suffer heart and circulation problems. His health continued to deteriorate and he became seriously ill in 1914. Although he continued to hold the chair he took sick leave in 1914 and was absent from the university from that time on. Manne Siegbahn (1886-1978), who had been a student of Rydberg from 1906 to 1911, then Rydberg's assistant from 1911 to 1914, took over his teaching duties in 1914. He carried these out until Rydberg reached the age of 65 in 1919. We note that Siegbahn wrote the biography of Rydberg . Rydberg resigned his position in 1915 and in 1916 he was taken into hospital. He spent three years in hospital before dying from a brain haemorrhage. Siegbahn became a professor in 1915 when Rydberg retired but it was only early in 1920 that he was appointed to Rydberg's chair of physics.
The authors of  write about Rydberg's character:-
Rydberg was considered by many of his contemporaries as a complicated person and his sadness was apparent, but his modesty and kindliness of heart were also appreciated.The author of  writes about:-
... his quiet sense of humour especially when concerned with those who were apparently unable to appreciate him. For years chairman of the 'Fysiska föreningen' in Lund, Rydberg was always interested in discussions with the younger men in the society and the institution, and with graduate students nearing their goal.We have already seen that, despite his groundbreaking work, Rydberg struggled to get a professorial appointment. He also failed to receive the Nobel prize for physics despite being nominated for the 1917 prize (no award was made that year) and again for the 1920 prize (his death in December 1919 meant he was not eligible). Even more surprising is that he failed to get elected to the Royal Swedish Academy of Sciences. However, shortly before his death, on 29 June 1919, he was elected a fellow of the Royal Society of London. Certainly he has achieved more fame after his death than during his lifetime. A conference was held at the University of Lund in July 1954 to celebrate the 100th anniversary of his birth. It was attended by the leading physicists of the day and the proceedings was published (see ). Two of the scientists who attended were Niels Bohr, who contributed the article , and Wolfgang Pauli, who contributed the article . The crater Rydberg on the Moon and asteroid 10506 Rydberg have been named in his honour.
Article by: J J O'Connor and E F Robertson