(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.
It may be generally concluded that the substitution of alkyl, nitro, hydroxyl, and haloid groups for hydrogen in a molecule occasions a deformation of crystal structure in one definite direction, hence permitting inferences as to the configuration of the atoms composing the crystal; while the nature and degree of the alteration depends (1) upon the crystal structure of the unsubstituted compound; (2) on the nature of the substituting radicle; (3) on the complexity of the substituted molecule; and (4) on the orientation of the substitution derivative.
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.
Attempts have been made to explain magnetic deformation by various theories of magnetic stress,' notably that elaborated by G.
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.
" It has long been known that proglottides of the same species often exhibit sporadic malformation from the normal shape, and the evidence goes to show that the variation was due to arrested growth or some unusual stress or pressure which, acting upon the young strobila, produced a deformation, and that the proglottides so affected could not regain their normal form.
The essential part of many transmission dynamometers is a spring whose deformation indirectly measures the magnitude of the force transmitted through it.
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 chief points of correspondence between these two great land masses, besides the southward tapering, are as follows: - (i) The areas of ancient fundamental rocks of the north-east (Laurentian highlands of North America, uplands of Guiana in South America), which have remained without significant deformation, although suffering various oscillations of level, since ancient geological times; (2) the highlands of the southeast (Appalachians and Brazilian highlands) with a north-east south-west crystalline axis near the ocean, followed by a belt of deformed and metamorphosed early Palaeozoic strata, and adjoined farther inland by a dissected plateau of nearly horizontal later Palaeozoic formations - all greatly denuded since the ancient deformation of the mountain axis, and seeming to owe their present altitude to broad uplifts of comparatively modern geological date; (3) the complex of younger mountains along the western side of the continents (Western highlands, or Cordilleras, of North America; Andean Cordilleras of South America) of geologically modern deformation and upheaval, with enclosed basins and abundant volcanic action, but each a system in itself, disconnected and not standing in alignment; (4) confluent lower lands between the highlands, giving river drainage to the north (Mackenzie, Orinoco), east (St Lawrence, Amazon), and south (Mississippi, La Plata).
The chains of each pair were connected by bracing so that they formed a stiff inverted arch resisting deformation in its place.
Impact.-If a vertical load is imposed suddenly, but without velocity, work is done during deflection, and the deformation and stress are momentarily double those due to the same load at rest on the structure.
The action of pressure is shown also by the fossils which sometimes occur in slates; they have been drawn out and distorted in such a way as to prove that the rock has undergone deformation and has behaved like a plastic mass.
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 deformation of the Appalachianswas accomplished in two chief periods of compressive deformation, one in early Palaeozoic, the other about the close of Palaeozoic time, and both undoubtedly of long duration; the second one extended its effects farther northwest than the first.
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.
In this province, therefore, we find a part of one of those ancient mountain regions, initiated by crustal deformation, but reduced by long continued erosion to a peneplain of modern relief, with occasional surmounting monadnocks of moderate height not completely consumed during the peneplanation of the rest of the surface.
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.
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.
A plane frame of n joints which is just rigid (as regards deformation in its own plane) has 2n3 bars, for if one bar be held fixed the 2(n2) co-ordinates of the remaining fl2 joints must just be determined by the lengths of the remaining bars.
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.
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.
Conversely, if this condition be satisfied, an infinitesimal deformation is possible.
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.
The heights of peaks determined by exact processes of trigonometrical observation are bound to be more or less in error for three reasons: (1) the extraordinary geoidal deformation of the level surface at the observing stations in submontane regions; (2) ignorance of the laws of refraction when rays traverse rarefied air in snow-covered regions; (3) ignorance of the variations in the actual height of peaks due to the increase, or decrease, of snow.
Whatever the deformation of the originally straight boundary of the axial section may be, it can be resolved by Fourier's theorem into deformations of the harmonic type.