Treatise on Natural Philosophy, Volume 1 |
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Page v
... complete account of what is now known of Natural Philosophy , in language adapted to the non - mathematical reader ; and to furnish , to Lose who have the privilege which high mathematical acquire- Lents confer , a connected outline of ...
... complete account of what is now known of Natural Philosophy , in language adapted to the non - mathematical reader ; and to furnish , to Lose who have the privilege which high mathematical acquire- Lents confer , a connected outline of ...
Page vii
... complete the chapter . The third chapter , " Experience , " briefly treats of Observa- tion and Experiment as the basis of Natural Philosophy . The fourth chapter deals with the fundamental Units , and the chief Instruments used for the ...
... complete the chapter . The third chapter , " Experience , " briefly treats of Observa- tion and Experiment as the basis of Natural Philosophy . The fourth chapter deals with the fundamental Units , and the chief Instruments used for the ...
Page 3
... complete , notation , 1 P 2 = ds2 + 2 d2x day ds2 curve . 7. If all points of the curve lie in one plane , it is called a Tortuous plane curve , and in the same way we speak of a plane poly- gon or broken line . If various points of the ...
... complete , notation , 1 P 2 = ds2 + 2 d2x day ds2 curve . 7. If all points of the curve lie in one plane , it is called a Tortuous plane curve , and in the same way we speak of a plane poly- gon or broken line . If various points of the ...
Page 5
... complete , notation , = 1 day P ds2 d2x ds curve . 7. If all points of the curve lie in one plane , it is called a Tortuous plane curve , and in the same way we speak of a plane poly- gon or broken line . If various points of the line ...
... complete , notation , = 1 day P ds2 d2x ds curve . 7. If all points of the curve lie in one plane , it is called a Tortuous plane curve , and in the same way we speak of a plane poly- gon or broken line . If various points of the line ...
Page 7
... complete the explanation , as it depends on the theory of curves on surfaces , which will be treated afterwards . But we shall see that if a plane roll on the sphere , so as always to touch it along the curve in question , and so that ...
... complete the explanation , as it depends on the theory of curves on surfaces , which will be treated afterwards . But we shall see that if a plane roll on the sphere , so as always to touch it along the curve in question , and so that ...
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Common terms and phrases
action amount angular velocity anticlastic attraction axes axis centre of inertia circle circular co-ordinates coefficients components condition cone configuration constant couple curvature curve cylinder denote density differential direction displacement distance distribution ds ds dx dy dz dy dx dy dy edge elements ellipsoid equal equations equilibrium expression external point finite fixed flexural rigidity flexure fluid formulæ function given gravity harmonic Hence homogeneous impulse infinitely small integral isotropic kinetic energy longitudinal mass matter measure moment of inertia motion moving normal section osculating plane parallel particle perpendicular plate portion position potential energy principle prism problem produce quantity radius reckoned rectangular resultant rigid body rotation round shear shell sides simple simple harmonic motion solid angle solution space sphere spherical harmonic spherical surface strain stress substance suppose synclastic tangent plane theorem tion torsion traction twist uniform values whole wire
Popular passages
Page vi - 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 269 - When, in an experiment, all known causes being allowed for, there remain certain unexplained effects (excessively slight it may be), these must be carefully investigated, and every conceivable variation of arrangement of apparatus, etc., tried ; until, if possible, we manage so to exaggerate 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...
Page 269 - In all cases when a particular agent or cause is to be studied, experiments should be arranged in such a way as to lead if possible to results depending on it alone ; or, if this cannot be done, they should be arranged so as to increase the effects due to the cause to be studied till these so far exceed the unavoidable concomitants, that the latter may be considered as only disturbing, not essentially modifying the effects of the principal agent.
Page 172 - Work done on any system of bodies (in Newton's statement, the parts of any machine) has its equivalent in work done against friction, molecular forces, or gravity, if there be no acceleration ; but if there be acceleration, part of the work is expended in overcoming the resistance- to acceleration, and the additional kinetic energy developed is equivalent to the work so spent.
Page 302 - ... surface at the part where the cone is cut by it. A very small cone is said to be cut obliquely, when the section is inclined at any finite angle to an orthogonal section ; and this angle of inclination is called the obliquity of the section. The area of an orthogonal section of a very small cone is equal to the area of an oblique section in the same position, multiplied by the cosine of the obliquity.
Page 22 - Def. When a point Q moves uniformly in a circle, the perpendicular QP drawn from its position at any instant to a fixed diameter AA' of the circle, intersects the diameter in a point P, whose position changes by a simple harmonic -motion. Thus, if a planet or satellite, or one of the constituents of a double star...
Page 145 - We cannot, of course, give a definition of matter which 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 148 - 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 292 - Farther approximn rigid (ie, incapable of changing their form or dimensions), and the infinite series of forces, really acting, may be left out of consideration ; so that the mathematical investigation deals with a finite (and generally small) number of forces instead of a practically infinite number.
Page 269 - In general the actions which we see ever taking place around us are complex, or due to the simultaneous action of many causes. When, as in astronomy, we endeavour to ascertain these causes by simply watching their effects, we observe; when, as in our laboratories, we interfere arbitrarily with the causes or circumstances of a phenomenon, we are said to experiment.