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amount angular velocity anticlastic applied attraction axes axis centre of inertia centrifugal force circle circular co-ordinates coefficients component condition constant corresponding couple course curvature curve degree denote density diagram differential direction displacement distance distribution disturbing earth edge elastic ellipsoid ellipticity equal equations equilibrium equipotential surface expression finite fixed flexural rigidity flexure fluid function given gives gravity Hence homogeneous infinitely small integral kinetic energy liquid mass matter measure moment of inertia motion normal section osculating plane parallel particle perpendicular plate portion position potential pressure principal principal axes problem produce quantity radius ratio reckoned rectangular resultant right angles rigid body rotation round sides simple harmonic motions solid solid angle solid harmonic solution space sphere spherical harmonic spherical surface spheroid square strain stress substance suppose synclastic tangent plane theorem theory tion torsion traction uniform vanish whole wire
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 304 - 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 303 - 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 182 - 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 344 - ... 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 32 - 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 155 - 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 158 - 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 334 - 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 301 - 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.