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 accompanied on his journeys as representative of the foreign office. He was present with the king during the campaigns of 1866 and 1870–71. In 1851 he published anonymously Babylon und Jerusalem, a slashing criticism of the views of the (q.v.).

ABEL (Hebrew for breath), the second son of Adam, slain by Cain, his elder brother (Gen. iv. 1-16). The narrative in Genesis which tells us that “the Lord had respect unto Abel and to his offering, but unto Cain and to his offering he had not respect,” is supplemented by the statement of the New Testament, that “by faith Abel offered unto God a more excellent sacrifice than Cain” (Heb. xi. 4), and that Cain slew Abel “because his own works were evil and his brother’s righteous” (1 John iii. 12). See further under. The name has been identified with the Assyrian ablu, “son,” but this is far from certain. It more probably means “herdsman” (cf. the name Jabal), and a distinction is drawn between the pastoral Abel and the agriculturist Cain. If Cain is the eponym of the Kenites it is quite possible that Abel was originally a South Judaean demigod or hero; on this, see Winckler, ''Gesch. Israels'', ii. p. 189; E. Meyer, Israeliten, p. 395. A sect of Abelitae, who seem to have lived in North Africa, is mentioned by Augustine (De Haeresibus, lxxxvi.). ABEL, SIR FREDERICK AUGUSTUS, (1827–1902), English chemist, was born in London on the 17th of July 1827. After studying chemistry for six years under A. W. von Hofmann at the Royal College of Chemistry (established in London in 1845), he became professor of chemistry at the Royal Military Academy in 1851, and three years later was appointed chemist to the War Department and chemical referee to the government. During his tenure of this office, which lasted until 1888, he carried out a large amount of work in connexion with the chemistry of explosives. One of the most important of his investigations had to do with the manufacture of gun-cotton, and he developed a process, consisting essentially of reducing the nitrated cotton to fine pulp, which enabled it to be prepared with practically no danger and at the same time yielded the product in a form that increased its usefulness. This work to an important extent prepared the way for the “smokeless powders” which came into general use towards the end of the 19th century; cordite, the particular form adopted by the British government in 1891, was invented jointly by him and Professor James Dewar. Our knowledge of the explosion of ordinary black powder was also greatly added to by him, and in conjunction with Sir Andrew Noble he carried out one of the most complete inquiries on record into its behaviour when fired. The invention of the apparatus, legalized in 1879, for the determination of the flash-point of petroleum, was another piece of work which fell to him by virtue of his official position. His first instrument, the open-test apparatus, was prescribed by the act of 1868, but, being found to possess certain defects, it was superseded in 1879 by the Abel close-test instrument (see ). In electricity Abel studied the construction of electrical fuses and other applications of electricity to warlike purposes, and his work on problems of steel manufacture won him in 1897 the Bessemer medal of the Iron and Steel Institute, of which from 1891 to 1893 he was president. He was president of the Institution of Electrical Engineers (then the Society of Telegraph Engineers) in 1877. He became a member of the Royal Society in 1860, and received a royal medal in 1887. He took an important part in the work of the Inventions Exhibition (London) in 1885, and in 1887 became organizing secretary and first director of the Imperial Institute, a position he held till his death, which occurred in London on the 6th of September 1902. He was knighted in 1891, and created a baronet in 1893.

Among his books were—Handbook of Chemistry (with C. L. Bloxam), Modern History of Gunpowder (1866), Gun-cotton (1866), On Explosive Agents (1872), Researches in Explosives (1875), and Electricity applied to Explosive Purposes (1884). He also wrote several important articles in the ninth edition of the Encyclopaedia Britannica. ABEL, KARL FRIEDRICH (1725–1787), German musician, was born in Köthen in 1725, and died on the 20th of June 1787 in London. He was a great player on the viola da gamba, and composed much music of importance in its day for that instrument. He studied under Johann Sebastian Bach at the Leipzig Thomasschule; played for ten years (1748–1758) under A. Hasse in the band formed at Dresden by the elector of Saxony; and then, going to England, became (in 1759) chamber-musician to Queen Charlotte. He gave a concert of his own compositions in London, performing on various instruments, one of which, the pentachord, was newly invented. In 1762 Johann Christian Bach, the eleventh son of Sebastian, came to London, and the friendship between him and Abel led, in 1764 or 1765, to the establishment of the famous concerts subsequently known as the Bach and Abel concerts. For ten years these were organized by Mrs Cornelys, whose enterprises were then the height of fashion. In 1775 the concerts became independent of her, and were continued by Abel unsuccessfully for a year after Bach’s death in 1782. At them the works of Haydn were first produced in England. After the failure of his concert undertakings Abel still remained in great request as a player on various instruments new and old, but he took to drink and thereby hastened his death. He was a man of striking presence, of whom several fine portraits, including two by Gainsborough, exist. ABEL, NIELS HENRIK (1802–1829), Norwegian mathematician, was born at Findöe on the 25th of August 1802. In 1815 he entered the cathedral school at Christiania, and three years later he gave proof of his mathematical genius by his brilliant solutions of the original problems proposed by B. Holmboë. About this time, his father, a poor Protestant minister, died, and the family was left in straitened circumstances; but a small pension from the state allowed Abel to enter Christiania University in 1821. His first notable work was a proof of the impossibility of solving the quintic equation by radicals. This investigation was first published in 1824 and in abstruse and difficult form, and afterwards (1826) more elaborately in the first volume of Crelle’s Journal. Further state aid enabled him to visit Germany and France in 1825, and having visited the astronomer Heinrich Schumacher (1780–1850) at Hamburg, he spent six months in Berlin, where he became intimate with August Leopold Crelle, who was then about to publish his mathematical journal. This project was warmly encouraged by Abel, who contributed much to the success of the venture. From Berlin he passed to Freiberg, and here he made his brilliant researches in the theory of functions, elliptic, hyperelliptic and a new class known as Abelians being particularly studied. In 1826 he moved to Paris, and during a ten months’ stay he met the leading mathematicians of France; but he was little appreciated, for his work was scarcely known, and his modesty restrained him from proclaiming his researches. Pecuniary embarrassments, from which he had never been free, finally compelled him to abandon his tour, and on his return to Norway he taught for some time at Christiania. In 1829 Crelle obtained a post for him at Berlin, but the offer did not reach Norway until after his death near Arendal on the 6th of April.

The early death of this talented mathematician, of whom Legendre said “quelle tête celle du jeune Norvegien!”, cut short a career of extraordinary brilliance and promise. Under Abel’s guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made. His works, the greater part of which originally appeared in Crelle’s Journal, were edited by Holmboë and published in 1839 by the Swedish government, and a more complete edition by L. Sylow and S. Lie was published in 1881.

For further details of his mathematical investigations see