An Introduction to the Mathematical Theory of Attraction, Volume 2

Longmans, Green, 1913
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Page 77 - The theoretical quantity of material required for a structure is proportional to the sum of the products obtained by multiplying the maximum strain of each member with its length. This sum we shall term "strain-length," and we denote it with
Page 188 - ... the quantities of polarized light in the reflected and refracted pencils are equal, whatever be the incidence. In the case of perpendicular incidence, these formulae are both reduced to the simple expression obtained by Young and Poisson; and when the incidence is 90°, or the ray grazes the surface, the intensity of the reflected light is equal to that of the incident, or the whole of the light is reflected, whatever be the reflecting medium. The latter conclusion has been verified by the observation...
Page 183 - ... case, may be looked on as no inconsiderable evidence of their general truth. It will be observed that the truth of the formulae is here spoken of, not the truth of the hypotheses concerned in obtaining them from theory. Nevertheless, even the complete establishment of the formula for the reflection of light polarized in a plane perpendicular to the plane of incidence would not establish the formula for light polarized in the plane of incidence, although it would no doubt increase the probability...
Page 49 - GO~~v(J obtained by a method similar to that employed in the case of the dimethyl derivative, namely, by treating the product of the action of ^-nitrosodietliylaniline on diphenylcycZopentenone with hydrochloric acid.
Page 182 - ... or a change of sign of the coefficient of vibration. In very highly refracting substances, however, such as diamond, it appears that when the incident light is polarized in a plane perpendicular to the plane of incidence, the reflected light does not wholly vanish at the polarizing angle ; but as the angle of incidence passes through the polarizing angle, the intensity of the reflected light passes through a small minimum value, and the phase changes rapidly through an angle of nearly 180°....
Page xii - ... the second of these equations being merely the analytical expression of the condition that u is a homogeneous function of x, y, z of the degree n, which may be any whole number positive or negative, any fraction, or any imaginary quantity. Let P + vQ be a harmonic of degree e + vf, P, Q, e, f being Differential real. We have reaT" tuents of a vO) 1 ous function ofimiurinary degn-e.
Page 79 - Hence ., 4т« where a denotes the radius of the sphere, and therefore the magnetic action of the sphere at an external point is the same as that of a small magnet at the centre...
Page 187 - ... refractive power — whilst it passes freely through the other, they will then become perfectly distinguishable, the one appearing dark, the other light. This is what seems to take place when such objects as the one in question are illuminated by oblique light ; for a ray of light cannot pass out of a denser into a rarer medium if the angle of incidence exceed a certain limit, and this limit is different in substances of different refractive powers. Thus all rays incident on water, at an angle...
Page 171 - The displacements belonging to common light may bo resolved each into two components, one in the plane of incidence, and the other perpendicular to that plane. The whole of the reflected light is produced by the latter displacements when the angle of incidence is tan-iju.
Page 12 - Hence, if g denote the acceleration due to gravity at any point on the Earth's surface, in the same manner as in Art.

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