Treatise on Natural Philosophy, Part 1University Press, 1912 - 527 pages |
Contents
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Common terms and phrases
acceleration action altered angular velocity anticlastic application arbitrary axis centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small initial instant integral kinetic energy Lagrange's length linear momentum moving negative osculating plane P₁ parallel particle path perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface strain suppose tangent plane theorem tion values whole y₁ αξ аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.
Page 219 - We cannot, of course, give a definition of Matter which Matter, will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force.
Page viii - We believe that the mathematical reader will especially profit by a perusal of the large type portion of this Volume, as he will thus be forced to think out for himself what he has been too often accustomed to reach by a mere mechanical application of analysis. Nothing can be more fatal to progress than a too confident reliance upon mathematical symbols ; for the student is only too apt to take the easier course, and consider the formula and not the fact as the physical reality.
Page 230 - The Component of a force in any direction, sometimes called the Effective Component in that direction, is therefore found by multiplying the magnitude of the force by the cosine of the angle between the directions of the force and the component The remaining component in this case is perpendicular to the other. It is very generally convenient to resolve forces into components parallel to three lines at right angles to each other; each such resolution being effected by multiplying by the cosine of...
Page 243 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 241 - The first part merely expresses the convention universally adopted for the measurement of Time. The earth in its rotation about its axis, presents us with a case of motion in which the condition of not being compelled by force to alter its speed, is more nearly fulfilled than in any other which we can easily or accurately observe. And the numerical measurement of time practically rests on defining equal intervals of time, as times during which the earth turns through equal angles. This is, of course,...
Page 443 - ... the residual phenomenon as to be able to detect its cause. It is here, perhaps, that in the present state of science we may most reasonably look for extensions of our knowledge ; at all events we are warranted by the recent history of Natural Philosophy in so doing. Thus, to take only...
Page 222 - In such cases the momentum and change of momentum of the whole body in any direction are, the sums of the momenta, and of the changes of momentum, of its parts, in these directions; while the kinetic energy of the whole, being non-directional, is simply the sum of the kinetic energies of the several parts or particles. 216. Matter has an innate power of resisting external influences, so that every body, as far as it can, remains at rest, or moves uniformly in a straight line.
Page v - The term Natural Philosophy was used by NEWTON, and is still used in British Universities, to denote the investigation of laws in the material world, and the deduction of results not directly observed. Observation, classification, and description of phenomena precede Natural Philosophy in every department of natural science.
Page 240 - Energy (§ 239), if its physical conditions are such that these forces will act equally, and in the same directions, if the motion of the system is reversed. Thus there may be no change of kinetic energy produced, and the work done may be wholly stored up as potential energy. Thus a weight requires work to raise it to a height, a spring requires work to bend it, air requires work to compress it, etc.; but a raised weight, a bent spring, compressed air, etc., are stores of energy which can be made...