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 GRASSMANtf There are many other species in different parts of the world, but none merit attention for their destructiveness in comparison with the locusts; war is rarely waged against grass- hoppers, as their natural enemies, birds, do- mestic fowls, and sand wasps, keep them down in proper limits. GRASSMAM, Hermann Giinther, a German mathematician, born in Stettin, Prussia, April 15, 1809. His father was professor of mathe- matics in the gymnasium of Stettin and the author of several mathematical text books. Hermann studied theology and mathematics, and from 1834 to 1852 was a teacher in the Otto-Schule in Stettin, when he succeeded his father as professor of mathematics in the gym- nasium. In 1844 he published the first part of Die Wissenschaft der extensiven Grosse, eine neue mathematische Disciplin. This part also bore the special title Die lineale Ausdehnungs- lehre, ein neuer Zweig der Maihematik, darge- stellt und durch Anwendungen avf die ubrigen Zweige der MathematiTe, wie auch auf die Statik, Mechanifc, die LeJire vom Magnetismus und die Krystallonomie erlautert. In the preface to this work he gave a short account of his discovery, and declared his intention to make its development and application the chief object of his life. He further developed his theory in Geometrische Analyse (1847), which obtained the prize offered by the Prince Jablo- novvski scientific society of Leipsic, and in arti- cles in Oelle's mathematical journal treating the higher classes of curves. In 1853 Cauchy published in the Comptes rendus of the French academy a method of resolving algebraical equa- tions and other problems by means of certain symbolical quantities, which he called clefs alge- bralques. The method was identical with that employed by Grassmann, and the latter imme- diately addressed a " claim of priority " to the academy. A committee was appointed to ex- amine the question, but it never made any re- port, and Cauchy abruptly broke off the publi- cation of his articles. In 1862 Grassmann completed the development of his theory by publishing Die Ausdehnungslehre volhtandig und in strenger Form "bearbeitet. This work is in strict mathematical form, after the model of Euclid's Elements, consisting almost entire- ly of propositions and demonstrations. In it he develops the connection of his theory with every branch of mathematics, from arithmetic to the integral calculus, and discusses its appli- cation to geometry. The profoundly meta- physical character of his first work and the ex- ceedingly abstract form of the last, together with the total absence of all geometrical fig- ures and all simple illustrations, have very much retarded the progress of his doctrine among professed mathematicians, and have pre- vented its comprehension by any others. It has many striking analogies to the quaternions of Sir William Rowan Hamilton. There can be little doubt that the theory of Grassmann, or one essentially the same, and only differing GRATIAtf 171 somewhat in form, will in time supersede the whole system of analytical geometry as founded by Descartes and so greatly developed by the labors of subsequent mathematicians. Grass- mann has been a frequent contributor to the leading scientific journals of Germany, and has published text books on various branches of science. He has an extensive knowledge of languages, published in 1870 a work on the German names of plants, and is now (1874) en- gaged in publishing a Sanskrit-German diction- ary to the Rig Veda. GRASS TREE, one of the English names given to plants of the genus xanthorrhcea, which are also called grass-gum trees and black-boys. They belong to the order liliacece, and are es- pecially distinguished by their crowns of long, pendulous, grass-like leaves, from the centre of which arises a long stem bearing at its summit a dense flower spike looking somewhat like a large cat-tail (typha). Some species have very short stems, while others have trunks 6 to 18 ft. high, which, with their singular tufts of leaves, form a striking feature in the Australian landscape. X. arlorea, X. australis, both ar- borescent, and X. hastilis. nearly stemless, are the best known species, as they are the prin- cipal ones in cultivation as ornamental green- house plants. Two resins obtained from these plants have been known for some time ; one is yellow and called Botany Bay resin and gum acaroides, and the other red, resembling drag- on's blood, and known as black-boy gum. They are aromatic, contain cinnamic and ben- zoic acids, and have the general properties of the balsams proper. No important use seems to have been found for these products. GRATIAN (AUGUSTUS GKATIANUS), emperor of Rome, born in Pannonia in 359, slain at Lugdunum (Lyons) in 383. His father, Valen- tinian I., bestowed upon him the title of Au- gustus in his childhood, but when he died in 375 the officers of the army compelled Gratian to give his half brother Valentinian II., then a young child, a share in the western empire, the East being in the hands of his uncle Valens. Gratian received Gaul, Spain, and Britain, and reigned over Italy, Illyricum, and Africa as guardian of his brother. Great severity marked the beginning of his reign. When the East was attacked by the Goths, Gratian was de- layed in aiding his uncle by another incursion of barbarians from the north; and when he finally marched to his rescue, he received the news of his defeat and death (378), which made him the ruler of both parts of the empire. In the next year he ceded the East to the younger Theodosius, Several wars with bar- barous tribes on the Rhine and Danube were successfully terminated, and Gratian, who is praised by both Christian and pagan historians as just, moderate, and virtuous, now enjoyed a few years of repose at his residence in Milan, where he became the friend of St. Ambrose. By the confiscation of the property of the temples and the abolition of the privileges of