I arrived at the thoroughly clear conviction that I ought to place Docent Rydberg first on the list. The consideration, that has guided me, was essentially the following: different men can work with equal energy on scientific tasks and nevertheless an extra ordinary difference is noticeable, when the results of their works are examined; a few grasp, with fortunate hand, the great problems, which the works of their antecessors have brought so far, that it has been possible to obtain results of far reaching consequence, which open new possibilities to research, and give to all existing collections of materials a new, often not suspected worth. Others, on the contrary, work perhaps with great assiduity and talent on tasks, which are not yet ripe for solution, the fruit of the labours being isolated results, no doubt of importance, but perhaps only after a time influencing the total. Therefore they soon stand still, because they find the way impracticable and are freed to take new points of departure. Men, belonging to the first category, not only exercise great influence on the progress of science, but are also to a particular extent capable of stimulating their scholars, who feel themselves raised and brought forward, as they find themselves able to contribute to the attaining of great aims. Now it cannot be denied that Docent Rydberg has shown that he is able to set a high aim to himself and to work for it with indefatigable energy. The results, which he has already attained, are indeed highly appreciated by all, who have the necessary pre requirements to value them. ... I do not at all understand that anyone should consider it a deficiency in Docent Rydberg that he has worked up materials already existing. I should think, as a physicist, that it would have been a legitimate reproach, had he not proceeded in this way. It was exactly his duty to work up the extraordinarily great and for the most part excellent material, before he passed over to experimental investigations in this direction. His qualifications as an experimental physicist Docent Rydberg has quite sufficiently evinced through earlier researches and more especially through those of his works, which are connected with the investigations upon diffraction spectra, among the rest through the photographs taken by him of spectra. I deem it unnecessary to give an analysis of the works of Docent Rydberg; their principal results form, however, the basis of all investigations on the regularity in Spectrum Analysis and have as such passed over in the manuals. They can in the main be expressed through a few and simple propositions, but their importance becomes evident only, when we compare the state before and after the publication of his treatise and when we consider the labour it has cost to attain this, whereof the memoir of Docent Rydberg of 1890 bears sufficient witness. I am convinced that those, who have not the pre-requirements to value his works fully, would wonder at the unanimity with which the savants abroad in this department would express themselves in this respect, if given an opportunity of doing so. ... I can on these reasons but remain at my original arrangement, that Docent Rydberg is to be placed first on the list, Lektor Mebius and Dr Grangvist second and third.
Docent Rydberg's scientific authorship is at once various and quantitatively considerable. Thus we find amongst his published works, besides a couple of essays on pure mathematics, several containing theoretical speculations on chemical atomic weight and further a whole series of investigations concerning the constitution of the spectra of the chemical elements. The researches last mentioned, which perhaps ought to be considered the author's most important works, have their centre in his great memoir: "Recherches sur la constitution des spectres d'émission des élements chimiques." In this memoir, on the composition of which a considerable amount of work has been evidently expended, the author, similarly to what has been done by Kayser and Runge nearly at the same time, points out the possibility of arranging the lines of a spectrum in certain regular series, which, although at present without a theoretical foundation, will possibly be of importance for the search of the theory yet unknown of these extremely complicated phenomena. In some particulars one might perhaps have occasion to make remarks upon the author's way of conducting his calculations, but considering the condition of the material of observation at the time of these investigations this has, in every case, no importance as to their main result. A rather great number of smaller memoirs deal, more and less, with particular questions of the same dominion. Now, at the same time as one cannot declare these works to be destitute of a certain degree of interest in a spectroscopical regard, one cannot deny, that they are mainly speculations on materials of observation taken from elsewhere, whose qualitative and quantitative insufficiency, known even before, and proved still more through these investigations, ought to have given the author ample occasion of improvements on them by his own experiments and observations. ...
Docent Rydberg has written a considerable number of works; besides those, which lie completely outside of the dominion of physics, he has in several essays treated the question of the periodical system of the elements, especially the relations between the qualities and the atomic weights of the elements. Of this kind are the following works: "Om de kemiska grundamnenas periodiska system," "Mättningskapacitet och atomvigt," "Die Gesetze der Atomgewichtzahlen," "Ein neues Forshungsgebiet der phys. chem. Wissenschaften," "Studien über Atomgewichtzahlen," and "De enkla kroppamas härdhet," of which the last mentioned has been handed in in manuscript. The main problem of these memoirs, which perhaps ought to be reckoned to the physical chemistry, is to find empirical formulae, through which a certain quality of the elements is expressed as a function of the atomic weight. As the author, however, has in this confined himself to combining, elaborating and calculating the materials of observation in hand, these works of course cannot set forth a very deep knowledge of physics and still less prove any experimental ability and skilfulness. The question, of which Docent Rydberg has made the very greatest merit, is concerning the regular distribution of the (spectral) lines of the spectra of the elements. To this belong the memoirs: "Über den Bau der Linienspectren der chemischen Grundstoffe," "Recherches sur la constitution des spectres d'émission des élements chimiques," "Beiträge zur Kentniss der Linienspectren (I-IV)," "Die neuen Grundstoffe des Cleveitgases," "The New Series in the Spectrum of Hydrogen," "On Triplets with constant Differences in the Line Spectrum of Copper," "On the Constitution of the red Spectrum of Argon," and the memoirs handed in in manuscript: "Studien über die Funktionsform der Spectralserien," and "Einige Liniengruppen mit constanten Schwingungsdifferenzen bei vierwerthigen Grundstoffen." The main problems of these memoirs have been to express the situation of the spectral lines of the elements through empirical formulae. Together with Messrs Kayser and Runge is Mr Rydberg undoubtedly one of those who have gained the greatest merits within this dominion of Spectrum Analysis. But whereas the two first mentioned have, themselves, enriched science with a great number of measurements of the spectra of the elements and then have used these fully comparable determinations for their calculations, Docent Rydberg has, here, also, chiefly used the line determinations of others for his calculations. What has been said previously of Docent Rydberg's works on the qualities of the elements, may be said here too. Docent Rydberg's works on Spectrum Analysis are undoubtedly of a great scientific value and prove also the author's great diligence and interest for the treatment of an often ungrateful problem, but these works cannot completely establish his competency for the appointment in question, as they are not based on his own measurements and researches.
Your work and that of Runge's and mine, have independently aimed at the same goal and have reached it to about equal degrees. You have taken the quickest way in using already-existing measurements. Many before you have tried the same thing in vain. You have succeeded superbly. I have always had to admire your sharp eye, with whose help you discovered all conformities to the spectral law from the faulty material that you had at your disposal. But that sharp eye is the distinctive mark of genuine scientific thinking. Helmholtz used to say: a main requirement for a physicist would be "wit," that is, the ability to recognise similarities that others overlook. This ability you have proven to possess in a superb way in your work "Recherches sur la Constitution."
I state without reservation that I have the highest admiration for your spectro-analytical work. This admiration is to a large measure based on the fact that you discovered the regularities in the spectra of elements through an examination of the then-existing, many-fold deficient observations. Your work proves a very outstanding capability in the art of evaluation of laboratory observations in a proper way, an art, that in my opinion, is equally important both for the experimental as well as the theoretical physicist. For example, I find admirable, that you discovered the second triplet series in the strontium spectrum based on Kayser's and my observations, one that we missed even though we had directed our attention especially to these series. Also, regarding the new series in the spectrum of magnesium, which you announced, I have been convinced by later observations that you were completely correct, and Kayser and I were wrong when we disputed this series.