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* LOGIC. 412 LOGOGBAPHEKS. out in great detail, ami some of them at least claim that there is no really scientific logic ex- cept of this algorismic sort. But they have not succeeded in converting many logicians to their wav of thinking. Tlic tendency has Ijeen to con- sider logic as an independent science which can only in a very artilicial and inadequate way be reduced to algebraic exjircssion. BinLioGBAPJiY. For history of ancient and media;- val logic, consult Prantl's great work, (jcschiclile der Logik im Abeiidlnnde (4 vols., Leipzig, 1855- 70). For a general history, consult Harms, Ge- schichie der Lo(jik (Berlin, 1881). Ueberweg, System der Lorjik (Bonn, 1857; 5th cd. 1882; Eng. trans, of 3d ed., London, 1874) ; Hamilton, Lectures on Lotjic (London, 1859) ; and ilansel's annotated editicm of Aldrirli's Artis Lof/iea' Hudi- mcnln (London, 1S51) give valuable historical material. Laird, Lcs loyicieus anglais coiitem- porains (Paris, 1878), may be consulted with ad- vantage by students desiring to obtain a general survey of English work done up to the time of publication of that book. Of systematic treatises on logic, the following may be mentioned; Aris- totle's various writings now known collectively as the Onjanon ; Kant. Lof/iA- (Konigsberg, 1800) ; Hegel, W'issenschoft dtr Logik (Greater Logic, 2d ed., Berlin, 1831) ; id.. Eneyklopidie der philosophisclwn IVissrnschaften iiii Gnindrisse. Erster Theil. Die Logik (Lesser Logic. Heidel- berg, 1817) ; Jlill, A System of Logic, lintiocina- live and Inductive (London, 1843: 'sth ed. 1872) ; Whately. Elements of Logic (ib.. 1825; many subsequent editions) ; Thomson, Outline of the Necessary Laus of Thought (ib., 1842) ; JIansel, Prolegomena Logica (O.xford, 1851); Jevons, Elementary Lessonsi in- Logic (London, 1870) ; id., Pure Logic (ib., 18G3) ; id., Substitution on Similars (ib., 18G9) ; id., The Principles of Science (ib., 1874; 2d ed. 1877) ; id.. Studies in Deductive Logic (ib., 1880); Venn, Symbolic Logic (ib., 1881) ; id.. Principles of Empirical or Inductive Logic (ib.. 1889) ; Fowler. The Ele- ments of Deductive Logic and The Elements of Inductive Logic (ib., lS(i!l) ; .Jones, Elements of Logic as a Science of Proportions, (ib., 1800) ; Bain, Logic, Inductive and Deductive {ih.. 1870) ; Bradley, The Principles of Logic (ib., 1883) ; Bosanquet, Logic (ib., 1888) ; id., The Essentials of Logic (ib., 1895) ; Sidgsvick, The Process of Argument (ib., 1893) ; Minto, Logic. Inductive and Deductive (New York, 1894); Hibben, In- ductive Logic (ib., 189G) ; Hobhouse, The Theory of Knowledge (London, 1896) ; Welton, Manual of Logic (ib., 1891-9(1) ; Hyslop, Elements of Logic (New York, 1892) ; C'reighton. An Intro- ductory Logic (ib., 1898) ; Trendelenburg, Logische Untersuchungcn (Leipzig, 3d ed. 1870) ; ^igwart, Lofft'A- (Freiburg; 2d ed. 1889-93; trans, by Denby, London, 1895) ; Lotze, System der Philosophic, I. Theil. Logik (Leipzig; 2d ed. 1880; trans, ed. by Bosanquet, Oxford, 1881); Schuppe. Erkenntnisstheorelisehe Loqik (Bonn, 1878); Wundt. Logik (Stuttgart. 2d ed. 1893- 95) ; Erdmann, Logik (Halle, 1892) : Bergmaun, Die (Irundprohleme der Logik (Berlin, 1895). LOGIER, l.'i'zhya'. .TonAXX BERxnAKD (1777- 1846). A Oerman-English musician and inven- tor, born at Cassel. Germany. He was of a musical fa.niily, and when, at ten years of age, he was taken to England he studied the flute and piano, and subsequently became flutist in the band of an Irish regiment. When it was dis- banded he obtained the post of organist at West- port, Ireland. He now invented the 'chiroplast,' an apjiaratus designed to help beginners to ac- quire the correct position in playing the piano. It consisted of two wooden bars, parallel to the keybo;nd, and a pair of open gloves, and by means of this arrangement the wrists were kept elevated, and the fingers were obliged to strike vertically. The chiroplast was later simplified by Kalkbrcnner. Both this contrivance and a new system of instruction, by which Logier had several pupils play at once on separate instru- ments, aroused widespread interest and contro- versy. Their inventor was quick to take advan- tage of the notoriety and soon acquired a fortune. In 1821 the Prussian Government invited him to Berlin to teach his system, and he remained there for three years. In 1826 he gave up teach- ing and settled near Dublin. His compositions, largely for the piano, are unimportant. Init his books, A Complete Introduction to the Keyed Bugle (an instrument he is said to have in- vented) ; An Explanution and Discussion of the lioyal Patent Chiroplast, or Hand-Director for the Piano: and The First Companion to the Royal Patent Cliiroplast, are rather interesting. The chiroplast. which Liszt condemned, has been abandoned by musicians, but the 'Logier system' is still somewhat used. LOGISTICS ( Gk. Xoyio-TiitTi [ic. r^x*'')]. iogis- tike [sc. iechnel, art of calculation, from oyur- T^s, logistcs, calculator, from oyij;e<T6ai, logixs- ihai. to compute, from X670S, logos, speech, word, I'eason). In military science, the branch whiiOi deals with all estimates for supplies of ammuni- tion and transportation. It is one of the most important details of general staff (q.v. ) duties in connection with an army in the field, because of its special reference to all matters affecting the arranging and timing of concentration or other marches, and the direction of transportation, etc. It is a leading factor in the art of strategy so far as its provisions are concerned, and with 'tactics' in respect to the actual carrj-ing out of pre- arranged plans. LOG'OGRAM: ( Gk. Uyos, logos, word + ypd/i. /ia, gramma, letter). A complicated or multi- plied form of the anagram (q.v.), where the puz- zle-maker, instead of contenting liimself with the formation of a single new word or sentence out of the old, by the transposition of the letters, endeavors to discover all the words that may be extracted from the whole or from any portion of the letters, and throws the whole into a series of verses in which synonymous expressions for these words must be used. The puzzle lies ia ascertaining what the concealed words are. and, through them, what is the primary word out of which they have all been extracted. LOGOGTIAPHERS (Gk. Xo7o7pd0os, logogra- phos. historian, from u70s, logos, word -i- ypdcpeiv, graphcin, to write). The name by which the Greek historians previous to Herodotus aredesig- nateil. The logographers. chiefly Ionian, described in prose the mythological subjects and traditions whic'li had been treated of by the epic poets, sup- plementing them by material derived from family traditions and tho.se dealing with the founding of cities, so as to form, at least in appearance, a connected history; their works, however, were wholly imcritical. The fragments are published, by JIueller, Fragmcnta Historicorum Grcscorunv