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* CLEAVAGE. 15 CLEBSCH. CLEAVAGE (from cleave, AS. cleofan, Gcr. kliebrii, to ilcavo. Lat. t/luberc, to peel. Gk. yMifxtv, !jl!/i>lieiit, to hollow out). In geolog}', a ]>iuperty induced, under eertiiiii eonditions. dur- ing deformation in a rock by virtvu' of which the rock may lie readily split into parallel layers or rods, i.e. parallel to a jilanp or line. It is a property possessed also by certain original gneisses that have not undergone deformation since their first soliditication. Cleavage, in rare cases, may be parallel to planes of bedding that may be i)re.sent in the roek-mass. The essential condition of rock-cleaage is a parallel dimen- sional arrangement of the constituent mineral particles of the rock. In certain minerals, such as mica, parallel dimensional arrangement car- ries with it a parallelism of the mineral cleav- age. The cleavage of a rock may be observed to occur parallel to the greater diameters of the mineral particles, or to tlie parallel mineral- cleavages. When the two coincide, as in the case of mica, the rock-cleavage produced is parallel to one plane. Where they do not coincide, two rock-cleavages may be produced at angles to each other, as in the ca.se of feldspar, although one may be conspicuous and the other obscure. The property of rock-cleavage is observed in rocks that have yielded to pressure by deformation M-ithout conspicuous fracture. This deformation can be induced only where the rock is under such great pressure from all sides that it flows rather than fractures. The planes or lines of rock- cleavage are further observed to be normal to the directions in which the rock-masses have been most shortened. A number of processes probably cooperate to induce the parallel arrangement of mineral par- ticles during the shortening of the rock-mass. Chief among these is the reerystallization of old mineral particles and the crystallization of new particles thiough the agency of contained water. This process results in the elongation of the mineral particles of the rock in the plane or line of greatest elongation of the rock-mass as a whole, and in shortening nonnal to this direc- tion; in other words, it resiilts in the flattening of the mineral particles through solution and deposition of mineral material. Other processes which produce rock-cleavage axe the rotation into parallel position of previously existing par- ticles whose axes liave unequal length, and the flattening in situ of original mineral particles through the process known as gliding — i.e. dif- ferential movement along certain definite planes and crystals without fracture. Cleavage is found in almost all varieties of rocks which, under pressure, have been made to flow, al- though as a rule it is showTi to best advantage in the finer-grained rocks. Rocics possessing the property of cleavage are called 'slates' or 'schists.' Bibliography. Phillips. "Cleavage and Folia-" tion in Rocks," in Report of Britixh Association for the Advancement of Science (London. 18.56) ; Heim, Mechanismiis der Gehirqshildunq. vol. ii. (Basel, 1878): Tyndall, "Comparative View of the Cleavage of Crystals and Slate-Rocks," in Philosophical Maga::ine, 4th series, vol. xii. (London. IS,")*)) ; Daubree. Geoloqie expcrimcn- tale, vol. i. (Paris. 187i1) ; Vaii Hise, "Prin- ciples of Xorth .merican Pre-Cambrian Geol- ogy," in Sixteenth Annual Report of the United States Geological Survey (Washington, 1896). CLEAVAGE OF CRYSTALS. Most crys- tals, owing to the regular arrangement of the molecules, possess directions along which co- hesion is at a minimum. They, therefore, tend to fracture along planes normal to these direc- tions, which are called 'planes of cleavage.' The tendency of a crystal to cleave is necessarily the same for any plane as for any other parallel ]ilane: in other words. cleavagc-])lanes have direction rather than position. Cleavage-planes, in their relative perfection and number, conform to the symmetry of the crystal in which they occur. Tendency to cleave along special planes determined in position as well as in direction is described as 'parting.' See Cry.stai.i,ogr.puy; .MiNKKAI.OC.V. CLEAVE'LAND, Mose.s (1754-1806). An American pioneer, the founder of Cleveland, Ohio. He was born in Canterbury, Conn.: prac- ticed law, served in the Revolutionary War. and became a brigadier-general of militia in 17M6. In 1795 he joined a number of others in pur- chasing from Connecticut, for $1,200,000. the tract in Ohio known as the 'Connecticut Western Reserve.' He directed the surveyors who laid out the site of the present Cleveland, which was named after him. The form of the name was al- tered, in 1S31, to Cleveland, by a newspaper edit- or, who wished to economize space for a headline. CLEAVELAND, Parker (1780-1858). A distinguished mineralogist. He was born in Rowley. Mass.: graduated at Harvard in 1799, was tutor in mathematics there from 1803 to 1805, was chosen professor of mathematics and natural philosophy and lecturer on chemistry and mineralogy- in Bowdoin College — a position which he retained until his death, although many professorships in other colleges and the presi- dency of his o"n were offered to him. He gathered a valuable collection of minerals, and published a treatise on M ineralo(i)/ and (ieology (1816. 3d ed. 1856), which earned for him the title of 'Father of American Mineralogy.' CLEAVEBS. See Goose-Gra.s.s. CLEBSCH, klepsh, Rudolf Friedrich Al- fred (1S33-72). A German mathematician, born at Konigsberg, Prussia. He studied at Konigs- berg, where he was a pupil of Hesse. Richelot, and F. Neumann. He held the chair of theo- retical mechanics at the polytechnic school in Karlsruhe from 1858 to 1863; was made profes- sor of mathematics at Giessen in 1863. and at Giittingen in 1868. His attention was drawn to algebra and geometry by the study of Salmon's works. In 1868 he founded, with Neumann, the ilathenmtische Annulen. His vast contributions to the theoi^y of invariants: his use of the notion of the deficiency of a curve; his applications of the theory of elliptic and Abeli.an functions to geometry and to the study of rational and elliptic curves, have secured for him a pre- eminent ])lace among those who have advanced the science of geometry. His works >i]ion the general theory of algebr:iic curves and surfaces Ijegan with the determination of those points upon an algebraic surface at which a straight line has four-point contact. Clebsch undertook to render the notion of 'deficiency' fruitful for geometry — a notion found first in Riemann's fheoric der Abelschen Fiinktioncn (1857). By 'deficiency' of a curve is meant the difference be- tween the number of its double points and the