Conversely, if this condition be satisfied, an infinitesimal deformation is possible.
Trend to crustal deformations which in very early geological time gave a beginning to what later came to be the Appalachian mountain system; but this system had its climax of deformation so long ago (probably in Permian time) that it has since then been very generally reduced to moderate or low relief, and owes its present altitude either to renewed elevations along the earlier lines or to the survival of the most resistant rocks as residual mountains.
In any infinitely small deformation of the frame as thus modified, the virtual work of the forces 5, together with that of the original extraneous forces, must ~ranish this determines S.
Imagine the bar CF to be removed, and consider a deformation in which AB is fixed.
(1900) P. 46; Marcel Bertrand, " Deformation tetraedrique de la terre et deplacement du pole," Comptes rendus Acad.
Many instances have been recorded where substitution has effected a deformation in one particular direction, the crystals of homologous compounds often exhibiting the same angles between faces situated in certain zones.
The magnitude of this separation would obviously depend on the magnitude of the substituent group, which may be so large (in this case propyl is sufficient) as to cause unequal horizontal deformation and at the same time a change in the vertical direction.
Attempts have been made to explain magnetic deformation by various theories of magnetic stress,' notably that elaborated by G.
Evi-Jently, therefore, the Appalachians as we now see them are not the still surviving remnants of the mountains of late Palaeozoic deformation; they owe their present height chiefly to the Tertiary upwaroing and uoliftinr.
Triassic SystemThis system has but limited representation in the eastern part of the United States, being known only east of the Appalachian Mountains in an area which was land throughout most of the Palaeozoic era, hut which was deformed when the eastern mountains were developed at the close of the Palaeozoic. In the troughs formed in its surface during this time of deformation, sediments of great thickness accumulated during the Triassic period.
Its deposition seems to have followed a time of deformation which resulted in an increase of altitude in the Appalachian Mountains, and in an accentuation of the contrast between the highlands and the adjacent plains.
This epoch of great deformation and warping marks the transition from the Tertiary to the Quaternary.
It must be incapable of deformation without alteration of length in at least one of its bars.
52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.
465), and in 1854 one on the moon's figure, advocating the mistaken hypothesis of its deformation by a huge elevation directed towards the earth (Ib.
A slight deformation of the earth will thus result; and the axis of figure of the distorted spheroid will no longer be PP, but a line P'P' between PP and RR.
Thomson, who, from the results of Bidwell's observations on the magnetic deformation of cobalt, was led to expect that that metal would exhibit a reversal opposite in character to the effect observed in iron.
In this category may be placed head-deformation, which reached its extreme development among the Indians of North-West America and the ancient Peruvians; foot-constriction as practised by the Chinese; tooth-chipping among many African tribes; and waist-compression common in Europe at the present day.
Many forms of deformation, it may be remarked in passing, emphasize some natural physical characteristic of the people who practise them.
Strains exceeding the "limit of elasticity" result in permanent deformation or (if sufficiently great) in rupture.
The accidental use of a single name, America, for the pair of continents that has a greater extension from north to south than any other continuous land area of the globe, has had some recent justification, since the small body of geological opinion has turned in favour of the theory of the tetrahedral deformation of the earth's crust as affording explanation of the grouping of continents and oceans.
The chains of each pair were connected by bracing so that they formed a stiff inverted arch resisting deformation in its place.
Trend to crustal deformations which in very early geological time gave a beginning to what later came to be the Appalachian mountain system; but this system had Its climax of deformation so long ago (probably in Permian time) that it has since then been very generally reduced to moderate or low relief, and owes its present altitude either to renewed elevations along the earlier lines or to the survival of the most resistant rocks as residual mountains.
The extent of the submergence and the area over which the Palaeozoic strata were deposited are unknown; for in consequence of renewed elevation without deformation, erosion in later periods has stripped off an undetermined amount of the covering strata.
The structure of the region previous to faulting was dependent on long antecedent processes of accumulation and deformation and the surface of the region then was dependent on the amount of erosion suffered in the prefaulting cycle.
Under this head fall the following: - Fasting, or abstention from certain meats and drinks; denial of sexual instinct; subjection of the body to physical discomforts, such as nakedness, vigils, sleeping on the bare ground, tattooing, deformation of skull, teeth, feet, &c., vows of silence to be observed throughout life or during pilgrimages, avoidance of baths, of hair-cutting and of clean raiment, living in a cave; actual self-infliction of pain, by scourging, branding, cutting with knives, wearing of hair shirts, fire-walking, burial alive, hanging up of oneself by hooks plunged into the skin, suspension of weights by such hooks to the tenderer parts of the body, self-mutilation and numerous other, often ingenious, modes of torture.
Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.