Elements of Natural Philosophy, Part 1 |
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Page 3
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
... turning about the tangent to the curve . The rate of torsion , or the tortuosity , is therefore to be measured by the ... turned as we pass from one extremity to the other . The average curvature of any portion is its whole curvature ...
Page 15
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in FS produced , so that YSSU is constant , the locus of U is easily seen to be a circle ...
... turned through a right angle about S in the plane of the orbit . If APB be a parabola , AY is a straight line . But if another point U be taken in FS produced , so that YSSU is constant , the locus of U is easily seen to be a circle ...
Page 16
... turned through by its radius - vector in the same time . 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
... turned through by its radius - vector in the same time . 61. A further instance of this use of the idea of angular velocity may now be given , to solve the problem of finding the hodograph ( § 35 ) for any case of motion in which the ...
Page 17
... turned . Hence ( § 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely ...
... turned . Hence ( § 9 ) the curvature of PQ is constant , or PQ is a circle . This demonstration , reversed , proves that if the hodograph be a circle , and the acceleration be to- wards a fixed point , the acceleration varies inversely ...
Page 18
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
... turned through two right angles . And with regard to G and G ' it is evident that the directions remain the same , while the lengths are altered in a given ratio ; but this is the definition of similar curves . 66. An excellent example ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called Cambridge centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipsoid elongation equal equations equilibrium external finite fixed point flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section Octavo P. G. TAIT P₁ P₂ parallel particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular resultant right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem theory tion torsion uniform unit vertical whole wire
Popular passages
Page 5 - Mathematical and Physical Papers. By Sir W. THOMSON, LL.D., DCL, FRS, Professor of Natural Philosophy, in the University of Glasgow. Collected from different Scientific Periodicals from May, 1841, to the present time.
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Page 9 - The Gospel according to St Matthew in Anglo-Saxon and Northumbrian Versions, synoptically arranged : with Collations of the best Manuscripts. By JM KEMBLE, MA and Archdeacon HARDWICK.
Page 8 - An Analysis of the Exposition of the Creed, written by the Right Rev. Father in God, JOHN PEARSON, DD, late Lord Bishop of Chester. Compiled for the use of the Students of Bishop's College, Calcutta, by WH MILL, DD late Regius Professor of Hebrew in the University of Cambridge.
Page 9 - Morgan's Investigation of the Trinity of Plato, and of Philo Judaeus, and of the effects which an attachment to their writings had upon the principles and reasonings of the Fathers of the Christian Church.
Page 8 - Wheatly on the Common Prayer, edited by GE CORRIE, DD Master of Jesus College, Examining Chaplain to the late Lord Bishop of Ely. Demy Octavo. 7*. dd. The Homilies, with Various Readings, and the Quotations from the Fathers given at length in the Original Languages.
Page 6 - A Catalogue of the Collection of Cambrian and Silurian Fossils contained in the Geological Museum of the University of Cambridge, by JW SALTER, FGS With a Preface by the Rev.
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Page 8 - The Homilies, with Various Readings, and the Quotations from the Fathers given at length in the Original Languages. Edited by GE CORRIE, DD Master of Jesus College. Demy Octavo.
Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.