Colding, Ludvig August

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(b. Holbaek, Denmark, 13 July 1815; d. Copenhagen, Denmark, 21 March 1888)

engineering, physics.

Colding was the second son of Andreas Christian and Anna Sophie Colding. His father, a former sea captain and officer in the privateering service of the Danish navy, unwisely embarked on a new career as farmer and manager of an estate near Copenhagen at about the time of Ludvig’s birth. There the boy was raised under somewhat strained economic circumstances, as a result of difficult times following Denmark’s involvement in the Napoleonic wars and particularly through the elder Colding’s evident lack of talent for agriculture. The deeply religious household reflected his mother, daughter of a prominent clergyman, and left a permanent stamp on the boy. His elementary schooling was rather irregular, although eventually he served an apprenticeship under a well-known craftsman in Copenhagen, on the advice of the physicist Hans Christian Oersted, an old family acquaintance. In 1836 he became journeyman, and the following year enrolled at the Polytechnic Institute in Copenhagen with an engineering career in mind, again following Oersted’s suggestion. After his graduation in 1841, Colding held several modest teaching and tutorial positions before being offered his first important appointment in 1845, as inspector of roads and bridges in Copenhagen. The post enabled him to marry Henriette Louise Lange, a cousin.

Oersted’s influence on his education and, indeed, on his subsequent career and philosophy of life began when Colding was a student at the Copenhagen Polytechnic. There he had easy access to Oersted, who, as director of the institution and professor of physics, took considerable interest in him and aided him. The strength of the curriculum in those years lay in basic and theoretical subjects, although practical application of fundamental knowledge was not neglected, in line with Oersted’s own philosophy. Oersted had himself been instrumental in founding the Institute in 1829 on the pattern of the École Polytechnique.

Commencing with his appointment as inspector in 1845. Colding held a succession of technical and administrative positions with the municipal government of Copenhagen, which culminated in his being named to the specially created post of state engineer for Copenhagen in 1857. During these years he oversaw the planning of public housing and parks, transways and railways, roads and bridges, and harbor and canal projects. He also supervised major improvements in city services, including the introduction of gas illumination and the overhauling of desperately inadequate water and sanitation systems. In addition, he was consultant on many projects in other cities, and acquired a high reputation both within and outside Denmark.

Despite the burden of his official responsibilities, Colding found time to pursue an impressive range of scientific subjects. Some of this research was of a basic nature, while other portions concerned applied aspects, many of them evolving naturally from engineering problems encountered during his regular activities. His work covered fluid dynamics, hydrology, oceanography, meteorology, electromagnetism, and especially thermodynamics. From 1869 he was professor at the Polytechnic in addition to his official duties. He was a member of numerous technical commissions and scientific societies, and received many honors at home and abroad, including the Cross of Honor of the Men of Dannebrog, awarded on his retirement in 1886.

A concept of special and abiding importance to Colding was the notion of a “principle of the imperishability of the forces of nature,” and it is this phase of his scientific and philosophical work that is likely to be of principal interest to scholars outside Denmark. Aside from the general intellectual milieu fostered at the Polytechnic, several specific factors are discernible in the background of this idea. By Colding’s own account the earliest hint of the idea occurred to him in 1839, while still a student, when he was led to contemplate “d’Alembert’s principle concerning lost forces.” The starting point for these speculations was, however, as much of a religious and metaphysical nature:

My first thought concerning the imperishability of the forces of nature I have, as I have mentioned earlier, borrowed from the view that the forces of nature must be related to the spiritual in nature, to the eternal reason as well as to the human soul. Thus it was the religious philosophy of life that led me to the concept of the imperishability of forces. By this line of reasoning I became convinced that just as it is true that the human soul is immortal, so it must also surely be a general law of nature that the forces of nature are imperishable (L. A. Colding, Naturvidenskabelige Betragtninger . . ., 155).

Oersted’s personal influence on Colding’s religiophilosophical development is clear and was repeatedly acknowledged by Colding himself. Moreover, his preoccupation with a fundamental underlying harmony or unity in the material world was a recurrent and dominant contemporary philosophical view, voiced especially in Naturphilosophie, of which Oersted was a firm adherent.

In 1839 Colding finally had the opportunity to assist Oersted in a series of fundamental experiments on the compression of water, a subject that had occupied Oersted off and on for many years. The results were puzzling at the time, and only in the following decade was the underlying effect – the increase in temperature of a liquid when it is adiabatically compressed –recognized as central to the concept of energy and its conservation.

The energy concept was vaguely recognized by 1840, having essentially been anticipated but not published or expounded publicly by Sadi Carnot. The first explicit suggestion of an invariable relationship between heat and mechanical work was put forth by J. R. Mayer in Germany in 1842 and a year later, independently, by J. P. Joule in England and by Colding. The circumstances surrounding this nearly simultaneous enunciation of the principle of the conservation of the “forces” of nature, and its manifold sources, have received considerable attention from historians of nineteenth-century science. Mayer, a physician, was first guided to the principle through metabolic observations on the relationship between heat produced by the human organism and the work expended in producing it. Joule, in contrast, was a physical scientist and brilliant experimenter. Originally concerned with improving the efficiency of electric motors, he employed his gift for precision measurements to yield a long series of determinations of the “mechanical equivalent” of heat with steadily increasing accuracy. Colding appears to have compounded the energy principle from a complex merger of metaphysical speculation and experiment. In 1847 appeared the classic treatise by Helmholtz, which treated the interconversion of forms of energy from a very general point of view. It had considerable influence on the mature formulation of the energy concept, although the systematic development of thermodynamics came in the second half of the century, mainly by R. Clausius, W. J. Rankine, and William Thomson.

Colding’s first paper on the subject, “Nogle Saetninger om Kraefterne” (“Theses Concerning Force”), was read before the Danish Society of Sciences in 1843, although its publication was delayed until 1856. In it he first summarized available data on friction and compressibilities of various materials indicating that the heat evolved is dependent on the compression or friction. Next, he reported on an experiment of his own in which the mechanical work required to move a weighted sled over a track of metal rails was correlated with the linear expansion of rails and sled runners, as a result of the frictional heating. He concluded that “. . . the quantities of heat evolved are, in every case, proportional to the lost moving forces,” although he neglected to condense these preliminary results in a numerical coefficient of proportionality. Consequently, “When a force seems to disappear it merely undergoes a transformation, whereupon it becomes effective in other forms.”

On Oersted’s recommendation, a more elaborate version of this experiment, supported by the Danish Society of Sciences, was subsequently carried out by Colding. The new results were reported at the 1847 meeting of Scandinavian scientists in Copenhagen, and published in the first of two companion papers in 1850, “UndersØgelse om de almindelige Naturkraefter og deres gjensidige Afhaengighed og isaerdeleshed om den ved visse faste Legemers Gnidning udviklede Varme” (“Investigation Concerning the Universal Forces of Nature and Their Mutual Dependence and Especially Concerning the Heat Evolved From the Friction of Certain Solid Bodies”). From these measurements he adopted a value for the mechanical equivalent of heat approximately 14 percent lower than the modern accepted value (by this time Joule was within 1 percent of the accepted value). An alternative derivation of this constant yielding (fortuitously, as it turned out) essentially the same value, based on Oersted’s experiments on the compression of water and on the then available (albeit not very accurate) value for the specific heat of air. appeared in his second paper of 1850. “Om de almindelige Naturkraefter og deres gjensidige Afhaengighed” (“On the Universal Forces of Nature and Their Mutual Dependence”), which is largely theoretical and devoted to a mathematical treatment of thermodynamic relations. A considerably more accurate value (only 3 percent in error) was presented in a fourth paper on the subject (1852), dealing with practical problems of steam engineering: “Undersøgeise over Vanddampene og deres bevaegende Kraft i Dampmaskinen” (“Investigation Concerning Steam and Its Motive Power in Steam Engines”).

The philosophical and religious side of Colding’s thesis was first elaborated in his cumbersome treatise of 1856, “Naturvidenskabelige Betragtninger over Slaegtskabet mellem del aandelige Livs Virk-somheder og de almindelige Naturkraefter” (“Scientific Reflections on the Relationship Between the Intellectual Life’s Activity and the General Forces of Nature”), his last paper on this topic to the Danish Society of Sciences; it was published on the occasion of his being elected member of the Society. It stressed his own philosophical convictions and dwelt at length on the relationship between the material and the spiritual in nature, clearly echoing the intellectual and aesthetic influence of Oersted and in a tone reminiscent of Kant and Schelling. This paper is also of interest for Colding’s discussion of Joule’s experiments, with which he was acquainted by then, and for his passionate priority dispute with Mayer.

Colding returned to thermodynamics and the mechanical theory of heat in an 1863 manuscript, submitted in response to a prize competition on the theme announced that year by the French Academy. “Samlet Fremstilling af Naturkraefternes gjensidige Afhaengighed med Anvendelse paa den mekaniske Varmetheori” (“Unified Presentation of the Mutual Dependence of the Forces of Nature With Application to the Mechanical Theory of Heat”). It failed to win the prize, however, and was not published. His last and only paper on energy published abroad was a memoir in Philosophical Magazine (1864); there was also a translation of his second paper of 1850 in Philosophical Magazine (1871). The former work, “On the History of the Principle of the Conservation of Energy,” is of value chiefly as a summary of his various contributions to the subject.

Among his prolific research the energy concept appears to have most occupied Colding’s mind. Unfortunately, however, this aspect of his scientific productivity went rather unnoticed in his time, even in Denmark; and today Colding remains a somewhat neglected pioneer in the research through which the first law of thermodynamics came to be recognized. His lasting scientific contributions are found elsewhere, particularly in his numerous hydrodynamic and meteorological works. He was, in fact, largely responsible for the establishment of a meteorological institute in Denmark. His major achievement, however, was undoubtedly the extraordinary number of municipal projects started on his initiative and completed in full or in part during his forty years of service to the Danish community.


I. Original Works Colding’s writings include “UndersØge1se om de almindelige Naturkraefter ogderes gjensidige Afhaengighed og isaerdeleshed om den ved visse faste Legemers Gnidning udviklede Varme,” in Det Kongeiige Danske Videnskabernes Selskabs Skrifter, 5th ser.. 2 (1850), 122- 146; “Om de alminde lige Naturkraefter og deres gjensidige Afhaengighed,” ibid., 167–188; “UndersØgelse over Vanddampene og deres bevaegende Kraft I Dampmaskinen” ibid.,3 (1852), 1–35: ,“Nalurvidenskabelige Betragtninger over Slaegtskabet mellem det aandelige Livs Virksomhederog de almindelige Naturkraefter,” in Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhan- dlinger. no. 4–6 (1856), 136–168;” NogIe Saetninger om Kraeftcrne “supp. to ibid., no. 8 (1856), 1–20; and” “On the History of the Principle of the Conservation of Energy,” in London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science,27 (1864), 56–64.

A copy of the MS “Samlet Fremstilling af Naturkraef-ternes gjensidige Afhaengighed med Anvendelse paaden mekaniske Varmetheori“is in the possession of Torben Hoick Colding, in Copenhagen.

II. Secondary Literature See Theodore M. Brown. “Resource Letter EEC-1 on the Evolution of Energy Concepts from Galileo to Helmholtz,” in American Journal of Physics. 3i (J965), 759–765; Torben Andreas Colding, Professor L. A. Coldings Naturviden-skabelige Bctragtninger (Copenhagen, 1924); Per F. Dahl. “Ludvig A. Colding and the Conservation of Energy,” in Centaurus,8 (1963), 174–188; and Ludvig Colding and the Conservation of Energy Principle; Experimental and Philosophical Contributions (New York–London, 1972). “which includes English translations of Colding’s papers relevant to energy conservation:” Erwin N. Hiebert, Historical Roots of the Principle of Conservation of Energy (Madison, Wis., 1962); Thomas S. Kuhn, “Energy Conservation as an Example of Simultaneous Discovery,” in Marshall Clagett, ed., Critical Problems in the History of Science (Madison. Wis., 1959). 321–356; and Asger Lomholt, Fortegnelse over Del Kongelige Danske Videnskabemes Selskabs Publicationer 1742–1930; Saertryk af Oversigt over Det Kgi Danske Videnskabemes Selskabs Forhandtinger 1929–1930 (Copenhagen. 1930), with an index of Colding’s scientific papers published in the journals of the Royal Danish Society of Sciences on 221 – 222 and a list of Oersted’s papers on 361 – 364.

Also see Vilhelm V. Marstrand,“ilngeniøren og Fysi-keren Ludvig August Colding,” in Ingenørvidenskabelige Skriften no. 20 (1929); Hans Christian Oersted, H. C. Oersted, Scientific Papers, Kirstine Bjerrum Meyer, ed., 3 vols. (Copenhagen, 1920), with two essays on Oersted’s work by the editor, I, xiii-clxvi; III, xi-clxvi; George Sarton, “The Discovery of the Law of Conservation of Energy” in Isis, 13 (1929), 18–49; and Povl Vinding, “Colding, Ludvig August” in Dansk Bio-grafisk Leksikon, V (Copenhagen, 1934), 377–383.

Per F. Dahl