Mathematical and Physical Papers, Band 3

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Seite 11 - On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids,
Seite 259 - In the case of other fluids, however, some of them sensitive in a very high degree, the mode in which light is dispersed internally presents some very remarkable peculiarities. One of the most singular examples occurs in the case of an alcoholic solution of the green colouring matter of leaves. This fluid disperses a rich red light. The dispersion commences abruptly about the fixed line B, and continues from thence onwards throughout the visible spectrum and a little beyond. The dispersion is subject...
Seite 261 - The posterior surface marked the distance to which the incident rays were able to penetrate before they were absorbed. This distance was at first considerable, greater than the diameter of the vessel, but it decreased with great rapidity as the refrangibility of the incident rays increased, so that from a little beyond the extreme violet to the end the blue space was reduced to an excessively thin stratum adjacent to the surface by which the incident rays entered. It appears therefore that this fluid,...
Seite 225 - The direction of motion of any particle will represent the direction of the flow of heat in what we may still call the auxiliary solid, from whence the direction of the flow of heat in the given solid will be obtained by merely conceiving the whole figure differently magnified or diminished in three rectangular directions. This rotatory sort of motion of heat, produced by the mere diffusion from the source outwards, certainly seems very strange, and leads us to think...
Seite 361 - ... as to force on the mind the conviction that it arose merely from motes. Indeed, in the former case, the polarization has often appeared perfect, or all but perfect. It is possible that this may, in some measure, have been due to the circumstance, that when a given quantity of light is diminished in a given ratio, the illumination is perceived with more difficulty when the light is diffused uniformly than when it is spread over the same space but collected into specks. Be this as it may, there...
Seite 261 - Startling as such a supposition might appear at first sight, the ease with which it accounted for the whole phenomenon was such as already to produce a strong probability of its truth. Accordingly the author determined to put this hypothesis to the test of experiment. The experiments soon placed the fact of a change of refrangibility beyond all doubt. It would exceed the limits of an abstract like the present to describe the various experiments. It will be sufficient to mention some of the more remarkable...
Seite 211 - I + dt. Of course, if we suppose heat to be material, we cannot help attaching to it the idea of individuality. But if we suppose heat to consist in motion of some sort, which for my own part I regard as by far the more probable hypothesis, we require a definition of sameness of heat, supposing we find it convenient to treat the subject in this way. I am not now going to follow any further the subject which has just been broached ; but I thought it might be worth while to point out in what manner...
Seite 236 - Let the co-ordinates x', y' be measured in the principal planes whose azimuths are a, a + 90°; let /3 be the angle whose tangent is equal to the ratio of the axes of the ellipse described, the numerical value of /3 being supposed not to lie beyond the limits 0 and 90° ; let v be the velocity of propagation, t the time, X the length of a wave, and put for shortness, (1).
Seite 21 - Hence if a solid of revolution of large, or even moderately large, dimensions .be suspended by a fine wire coinciding with the axis of revolution, and made to oscillate by the torsion of the wire, the effect of the fluid may be calculated with a very close degree of approximation by regarding each element of the surface of the solid as an element of an infinite plane oscillating with the same linear velocity*.
Seite 73 - Then 16wVa~* = 1-256, and c : C0 :: 1 : 0'2848, so that the height of the waves, which varies as c, is only about a quarter of what it was. Accordingly, the ripples excited on a small pool by a puff of wind rapidly subside when the exciting cause ceases to act. Now suppose that X is 40 fathoms or 2880 inches, and that t is 86400 seconds or a whole day. In this case...

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