Cato Maximilian Guldberg was born on August 11, 1836, in Christiania (now Oslo), Norway, the eldest of nine children of Carl August Guldberg, a minister and owner of a bookstore and printing office, and Hanna Sophie Teresia Bull Guldberg, who came from a highly esteemed and wealthy merchant family of Fredrikstad. When young Cato w as 11 years old, his father was appointed minister at Nannestad, about 50 miles north of Christiania. The foundation for Cato's later interest in the outdoors, hunting, and fishing was laid in his father's remote parish, but he could not receive a satisfactory education there. Therefore, at the age of 13, Cato was sent to live with his maternal gr andmother, Catharina Ohlson, in Fredrikstad, where he attended secondary school and excelled in mathematics. This school could not grant admission certificates to the university so Cato returned to Christiania and spent his last year of secondary education at a private Latin school.
Guldberg entered the University of Christiania in 1854, the same year as his close friend Peter Waage, with whom he began a close lifetime friendship. Together with a number of other fellow students, the two founded a small, informal club whose members met on Saturday afternoons to discuss chemistry and physics problem s. Guldberg majored in mathematics and prepared for secondary examinations in physics and chemistry. He worked independently on advanced mathematical problems, and his first published scientific article, "On the Contact of Circles" (published in 1861), won the Crown Prince's Gold Medal in 1859.
Guldberg graduated in 1859 and became a teacher at Nissen's secondary school in Christiania. He was appointed a mathematics teacher at the Royal Military Academy in 1860. In 1861 he made a one-year study tour of France, Switzerland, and Germany by means of a scholarship. Upon his return to Norway Cato became Professor of Applied Mechanics i n 1862 and Professor of Advanced Mechanics the following year at the Royal Military College, two positions he held until his death in Christiania on January 14, 1902. In 1867, Cato was awarded a scholarship at the University of Christiania, where he became Professor of Applied Mathematics in 1869.
Guldberg's name is intimately linked with that of his friend Waage primarily for their joint discovery of the law of mass action. This fundamental law of chemistry, which today is known to every beginning chemistry student, had several forerunners, but the combined efforts of the theorist Guldberg and the empiricist Waage were ne eded to produce the first general, exact, mathematical formulation of the role of the amounts of reactants in chemical equilibrium systems.
But Guldberg and Waage were also related through two marriages; Guldberg married his cousin Bodil Mathea Riddervold, daughter of cabinet minister Hans Riddervold, and the couple had three daughters. Waage married Bodil's sister, Johanne Christiane Tandberg Riddervold by whom he had five children, and after her death in 1869, he became Guldb erg's brother-in-law a second time, in 1870, by marrying one of Guldberg's sisters, Mathilde Sofie Guldberg, by whom he had six children.
Guldberg and Waage's collaboration on the studies of chemical affinity that led to the law of mass action began immediately after Guldberg's return from abroad in 1862. Waage presented their findings to the Division of Science of the Norwegian Academy of Science and Letters on March 14, 1864, where it elicited little response. Even after it s publication the following year in Norwegian in the academy's journal--which was not accessible to many scientists--it failed to attract attention. Moreover, their work remained almost completely unknown to scientists as did the more detailed description of their theory published in 1867 in French. The theory did not become generally known until 1877, when German chemist Wilhelm Ostwald published an article that adopted the law of mass action and proved its validity by experiments of his own. The following year Dutch chemist Jacobus Henricus van't Hoff derived the law from reaction kinetics, apparently without any awareness of Guldberg and Waage's previous work. Bec ause their work was not become universally known and van't Hoff had not recognized their priority, Guldberg and Waage published their previous work for a third time, this time in the German journal Annalen der Chemie and in German, the lingua franca of 19th-century chemistry. In 1884, in his Études de Dynamique Chimique, van't Hoff finally mentioned their work, thus assuring their priority.
The law of mass action is Guldberg's most significant contribution to physical chemistry, but not his only one, for much of his early work, published in Norwegian, did not receive the attention that it deserved. He spent much time on a search for a general equation of state for gases, liquids, and solids from a kinetic-molecular approach. In 1867, 19 years before van't Hoff, he introduced the ideal gas equation in the form: pV = 2T. In 1869 he developed the concept of "corresponding temperatures" and derived an equation of state valid for all liquids of certain types. In 1890, he formulated the rule (Guldberg's rule) that the re duced boiling temperatures of most liquids are close to 2/3, a relationship discovered independently by the French- Swiss chemist Philippe Auguste Guye that same year. Guldberg also made a number of contributions to the thermodynamics of solution and of dissociation, and he discovered and explained cryohydrates. He wrote many articles on various practical problems as well as several textbooks on mechanics and mathematics.
Guldberg served as co-editor (1860-61) and Editor-in- Chief (1863-73) of Polyteknisk Tidsskrift, a journal devoted mainly to applications of science. The topics of some of his articles in this journal show the breadth of his interests: melting points of alloys (1860), fuels and their heat values (1860), specific weights (1860), a new system of weights and measures (1862), the cheapest form of lighting (1863), the mechanical theory of heat (1864), the steam engine (1870, 1871, 1872), the movement of water in tubes (1871), the theory of the movement of water and air on the Earth's surface (1872), superheated steam (1872), and new theori es of the flow of gases and vapors (1873).
Guldberg served three terms as Chairman of the Polytechnical Society (1866- 68, 1869-72, 1874-75), was an active member and officer of many scientific societies and commisions, and received several domestic and foreign honors. His work with the Norwegian Royal Commision of 1873 resulted in Norway's becoming the first Scandinavian country leg ally to adopt the metric system (1875).
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