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He was born at Jedburgh, Scotland, where his father, a teacher of high reputation, was rector of the grammar school. At the age of twelve he was sent to the University of Edinburgh, being intended for the clergy. However, he had already shown a strong inclination for natural science, and this had been fostered by his intimacy with a "self-taught philosopher, astronomer and mathematician," as Sir Walter Scott called him, of great local fame—James Veitch of Inchbonny, who was particularly skilful in making telescopes.
Though he duly finished his theological course and was licensed to preach, Brewster's other interests distracted him from the duties of his profession. In 1799 he was persuaded by his fellow-student, Henry Brougham, to study the diffraction of light. The results of his investigations were communicated from time to time in papers to the Philosophical Transactions of London and other scientific journals. The fact that other philosophers, notably Etienne Louis Malus and Augustin Fresnel, were pursuing the same investigations contemporaneously in France does not invalidate Brewster's claim to independent discovery, even though in one or two cases the priority must be assigned to others.
The most important subjects of his inquiries can be enumerated under the following five headings: (1) The laws of polarization by reflection and refraction, and other quantitative laws of phenomena; (2) The discovery of the polarizing structure induced by heat and pressure; (3) The discovery of crystals with two axes of double refraction, and many of the laws of their phenomena, including the connection between optical structure and crystalline forms; (4) The laws of metallic reflection; (5) Experiments on the absorption of light. In this line of investigation the prime importance belongs to the discovery (1) of the connection between the refractive index and the polarizing angle, (2) of biaxial crystals, and (3) of the production of double refraction by irregular heating.
These discoveries were promptly recognized. So early as the year 1807 the degree of LL.D. was conferred upon Brewster by Marischal College, Aberdeen; in 1815 he was made a member of the Royal Society of London, and received the Copley medal; in 1818 he received the Rumford medal of the society; and in 1816 the French Institute awarded him one-half of the prize of three thousand francs for the two most important discoveries in physical science made in Europe during the two preceding years.
Among the non-scientific public his fame was spread more effectually by his rediscovery in about 1815 of the kaleidoscope, for which there was a great demand in both England and America. An instrument of higher interest, the stereoscope, which, though of much later date (1849—1850), may be mentioned here, since along with the kaleidoscope it did more than anything else to popularize his name, was not, as has often been asserted, the invention of Brewster. Sir Charles Wheatstone discovered its principle and applied it as early as 1838 to the construction of a cumbersome but effective instrument, in which the binocular pictures were made to combine by means of mirrors. To Brewster is due the merit of suggesting the use of lenses for the purpose of uniting the dissimilar pictures; and accordingly the lenticular stereo-scope may fairly be said to be his invention.
A much more valuable practical result of Brewster's optical researches was the improvement of the British lighthouse system. It is true that the dioptric apparatus was perfected independently by Fresnel, who had also the satisfaction of being the first to put it into operation. But it is indisputable that Brewster was earlier in the field than Fresnel; that he described the dioptric apparatus in 1812; that he pressed its adoption on those in authority at least as early as 1820, two years before Fresnel suggested it; and that it was finally introduced into British lighthouses mainly by his persistent efforts.
Brewster's own discoveries, important though they were, were not his only, perhaps not even his chief, service to science. He began literary work in 1799 as a regular contributor to the Edinburgh Magazine, of which he acted as editor at the age of twenty. In 1807 he undertook the editorship of the newly projected Edinburgh Encyclopaedia, of which the first part appeared in 1808, and the last not until 1830. The work was strongest in the scientific department, and many of its most valuable articles were from the pen of the editor. At a later period he was one of the leading contributors to the Encyclopaedia Britannica (seventh and eighth editions), the articles on electricity, hydrodynamics, magnetism, microscope, optics, stereoscope, voltaic electricity, etc., being from his pen.
In 1819 Brewster undertook further editorial work by establishing, in conjunction with Robert Jameson (1774—1854), the Edinburgh Philosophical Journal, which took the place of the Edinburgh magazine. The first ten volumes (1819—1824) were published under the joint editorship of Brewster and Jameson, the remaining four volumes (1825—1826) being edited by Jameson alone. After parting company with Jameson, Brewster started the Edinburgh Journal of Science in 1824, sixteen volumes of which appeared under his editorship during the years 1824—1832, with very many articles from his own pen.
To the transactions of various learned societies he contributed from first to last between three and four hundred papers, and few of his contemporaries wrote so much for the various reviews. In the North British Review alone seventy-five articles of his appeared. A list of his larger separate works will be found below. Special mention, however, must be made of the most important of them all–his biography of Sir Isaac Newton. In 1831 he published a short popular account of the philosopher's life in Murray's Family Library; but it was not until 1855 that he was able to issue the much fuller Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton, a work which embodied the results of more than twenty years' patient investigation of original manuscripts and all other available sources.
Brewster's relations as editor brought him into frequent communication with the most eminent scientific men, and he was naturally among the first to recognize the benefit that would accrue from regular intercourse among workers in the field of science. In an article in the Quarterly Review he made a suggestion for "an association of our nobility, clergy, gentry and philosophers," which was taken up by others and found speedy realization in the British Association for the Advancement of Science. Its first meeting was held at York in 1831; and Brewster, along with Charles Babbage and Sir John F. W. Herschel, had the chief part in shaping its constitution.
In the same year in which the British Association held its first meeting, Brewster received the honour of knighthood and the decoration of the Guelphic order of Hanover. In 1838 he was appointed principal of the united colleges of St Salvator and St Leonard, St Andrews. In 1849 he acted as president of the British Association and was elected one of the eight foreign associates of the Institute of France in succession to J. J. Berzelius; and ten years later he accepted the office of principal of the university of Edinburgh, the duties of which he discharged until within a few months of his death.
In estimating Brewster's place among scientific discoverers the chief thing to be borne in mind is that the bent of his genius was not characteristically mathematical. His method was empirical, and the laws which he established were generally the result of repeated experiment. To the ultimate explanation of the phenomena with which he dealt he, contributed nothing, and it is noteworthy in this connection that if he did not maintain to the end of his life the corpuscular theory he never explicitly adopted the wave theory of light. Few would dispute the verdict of James D. Forbes, an editor of the eighth edition of the Encyclopaedia Britannica: "His scientific glory is different in kind from that of Young and Fresnel; but the discoverer of the law of polarization of biaxial crystals, of optical mineralogy, and of double refraction by compression, will always occupy a foremost rank in the intellectual history of the age." In addition to the various works of Brewster already mentioned, the following may be added: Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry (1824); Treatise on Optics (1831); Letters on Natural Magic, addressed to Sir Walter Scott (1831); The Martyrs of Science, or the Lives of Galileo, Tycho Brahe, and Kepler (1841); More Worlds than One (1854).
See also Brewster's angle.