Colding, L A

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Ludvig August Colding (1815-1888)


Colding grew up on a farm close to Copenhagen but did not want to become a farmer. Instead, he was trained as a carpenter after advice from Hans Christian Ørsted (the world-renowned physicist who discovered electro-magnetism) to whom his father was acquainted. This first training raised his interest for engineering, and, having passed the entrance examination, he started at the Polytechnic School, where Ørsted was director. During his study, he assisted Ørsted by measuring the heat released from compression of water.

Gradually Colding arrived at the conviction that mechanical forces (the work of forces, i.e. the energy) did not disappear but was transformed into other forms including heat. To prove this idea he established experiments with a sled loaded with different cannon balls that was dragged on rails of different metals. By measuring the heat expansion, he found support for his hypothesis and could estimate the mechanical equivalent of heat. He graduated in 1841, and in 1843 he submitted a treatise on the conservation of energy in parallel to independent works of Julius von Mayer and James Joule on the same hypothesis. All three are recognized as the pioneers of the first law of thermodynamics.

In 1845, Colding was employed by the city of Copenhagen, where he two years later became water inspector. At that time, Copenhagen suffered from insufficient and unhygienic water supply based on wells in the city and uptake from small surrounding lakes. Moreover, there was no sewerage, and the smell was terrible. In 1849, the city launched and international competition on water supply, gas lightning and sewerage projects. Colding won the water supply competition with an innovative project based on establishing of artesian wells in a nearby catchment, utilizing two lakes as reservoirs, introducing sand filtering and building a water works powered by steam engines along with a clean water consumption-equalizing reservoir.

Before the projects were finally decided, a cholera epidemic hit Copenhagen in 1843. Almost 5000 people died. Together with a younger colleague, Julius Thomsen (a later famous chemist), Colding immediately investigated the causes for the spread of the disease, and they found that the spread was strongly correlated to the soil water quality (pollution) and the population density in different city sections. A year later, John Snow in London gave the final proof for the cholera to be water borne . Colding was appointed managing engineer for all three projects. While the water supply and the gas lightning projects were smoothly approved and initiated, the sewage project became heavily delayed despite the tragic cholera epidemic. Colding had to revise the winning far-sighted project based on separation of rainwater and sewage water into a combined sewer without allowance for water closets, however still a significant improvement. In 1857, Colding advanced to chief city engineer in Copenhagen. The new water supply and the gas lightning projects were inaugurated in 1859, while the sewage project was accomplished during the 1860s.

In parallel to the practical work for the city, Colding maintained his interest for scientific investigations. He continued writing treatises on different subjects, and in 1956 he became member of the Royal Danish Society of Science. Most of his works were written in Danish, but a few were translated into English, French and German and printed in journals. The subjects were diverse covering thermodynamics, magnetism, steam power, hydraulics, soil physics, hydrology, heating and ventilation, meteorology and oceanography. He served commissions on the metric system, building project, harbour facilities and meteorological service, and he was consultant to several water supply projects.

During 1865-1883, Colding lectured at the Polytecnic School on the fundamentals on drainage of harmful water, supply of water and gas, and heating and ventilation, and in 1869, he was appointed as Professor at the school. Two years before, in 1967, he was bestowed Knight of the Order of Dannebrog. In 1871, Colding was conferred the honorary degree of Doctor at the University of Edinburgh simultaneously with Joule. He retired in 1886 and died a few years later in 1888. On his tombstone, his four sons put the inscription: “The forces of nature are imperishable 1843”.

Hydrological Achievements

To a certain extent, the hydrological findings of Colding were inspired by his work for the city of Copenhagen. His curiosity, however, led him far beyond the actual needs.

Colding developed a theory for water movement in partly filled, closed conduits. While the theory for stationary flow in pressured conduits was well known, this was not the case for partly filled conduits like sewers. Colding based the theory on cross-sectional mean flow velocities and verified the results by a series of large-scale experiments.

The new water supply to Copenhagen was based on artesian wells in a 5500 ha catchment upstream a 77 ha lake. To estimate the amount of water available for supply, Colding measured precipitation and lake outflow as well as evaporation from a partly submersed sheet metal box placed on a float in a lake and containing either pure water or wetted turf. Additionally, he measured flow in drain systems. He succeeded in getting reliable estimates of the complete water balance including the annual variation.

Using experimental results by Boileau, Darcy and Bazin, Colding developed a theory for the cross-sectional velocity distribution in stationary flow. He considered closed as well as open conduits of various forms and different resistances, including rivers, and obtained close agreement between theory and experiments. Colding expanded the theory to cover free flow in the sea. He examined and described the Golf Stream in detail using all available measurements. He assessed the driving forces including the impacts of the trade winds and the returning polar stream, and he showed the influence of the Earth’s rotation on the flow . Using the theory for a rotating water whirl, Colding showed its applicability for a cyclone assuming that the theory for free water flow is also applicable for flow of air masses. For the cyclone that passed St. Thomas in 1871, he assessed the wind speed based on air pressure observations.

By analysing water level variations in the artesian wells for Copenhagen water supply, Colding found a proportionality between discharge and head difference and the impact of the different soils. Theoretical analysis and a series of experiments with water flowing through a flume filled with soils of different types led him to Darcy’s equation, however without knowledge of the recent discovery by Darcy. Additional theoretical analysis resulted in equations for the parabolic piezometric surface in confined aquifers and the elliptic water table between drainpipes.

Previous theoretical analyses of the wind effect on the surface of flowing water together with observations of air pressure in the Baltic Sea made it possible for Colding to explain the development of the 1872 storm in the Baltic Sea, where the southern islands of Denmark were flooded, 80 people died and 500 ships stranded. Based on Colding’s theory necessary dike heights could be determined.


Reference Material

Marstrand, V. (1929) Ingeniøren og fysikeren Ludvig August Colding (The engineer and physicist Ludvig August Colding), Ingeniørvidenskabelige Skrifter, Series A, No. 20, Gad, 61 pp.

Dahl, P. F. (1972) Ludvig Colding and the Conservation of Energy Principle, The Sources of Science No. 104, Johnson Reprint Cooperation, 1972.

Caneva, K. (1998) Colding, Ørsted, and the meanings of force, Historical Studies in the Physical and Biological Sciences, 28(1), 1-138.

Wisniak, J. (2008) Conservation of Energy, Readings on the origins of the first law of thermodynamics, Part II, Educasión Quimica 19(2), 216-225.

Selected Publications

Colding, L. A. (1843) Nogle Sætninger om Kræfterne (Treatise concerning forces), printed 1856 in Videnskabernes Selskabs Forhandlinger, 3-20.

Colding, A. & Thomsen, J. (1853) Om de sandsynlige Årsager til Choleraens ulige Styrke i de forskellige Dele af Kjøbenhavn (The probable causes of the unequal intensity of cholera in the different parts of Copenhagen and the means for decreasing the intensity of the plague for the future), Reitzel, 112 pp.

Colding, A. (1864) On the history of the principle of the conservation of energy, Philosophical Magazine 4(27), 56-64.

Colding, A. (1864) Sur l’histoire du principe de la conservation de l’énergie, Annales de Chimie et de Physique, 4(1), 466-477.

Colding, A. (1867) De frie Vandspeilsformer i Ledninger med constant Vandføring (The free surface forms in conduits with constant flow), Videnskabernes Selskabs Skrifter, 5(6), 1-96.

Colding, A. (1871) On the universal powers of nature and their mutual dependence, Philosophical Magazine, 4(42), 1-20.

Colding, A. (1871) On the Laws of Currents in Ordinary Conduits and in the Sea; (I), Nature, 5(108), 71-73; (II), Nature, 5(109), 90-92; (III), Nature, 5(110), 112-114.

Colding, A. (1872) Om lovene for Vandets Bevægelse i Jorden (On the laws for movement of water in soil), Videnskabernes Selskabs Skrifter, 5(9), 563-622.

Colding, A. (1875) Einige Bemerkungen zu den Strömungsverhältnissen der Luft, Zeitschrift der Österreichischen Gesellschaft für Meteorologie, 10, 133-142.

Colding, A. (1876) Fremstilling af Resultaterne af nogle Undersøgelser over de ved Vindens Kraft fremkaldte Strømninger i Havet (The resulting sea water flow caused by the wind friction), Videnskabernes Selskabs Skrifter, 5(11), 246-274.

Colding, A. (1881) Nogle Undersøgelser over Stormen over Nord- og Mellemeuropa af 12te-14de November 1872 og over den dermed fremkaldte Vandflod i Østersøen (The 1972 storm in the Baltic Sea and resulting flooding of the southern Danish islands), Videnskabernes Selskabs Skrifter, 6(1), 243-304.