Transactions of the Cambridge Philosophical SocietyUniversity Press, 1842 |
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الصفحة 15
... Hence there results a ß , and e , = = - e , and tan e = α a a = = = tan 0 . b But by ( 11 ) , a , b α = 1 + 2 “ ) } = √ ( 1 1 μ2 sin2 0 ; μ by introducing the index of refraction , and the angle of incidence . Thus , ◊ ( u sin2 0 1 ) ...
... Hence there results a ß , and e , = = - e , and tan e = α a a = = = tan 0 . b But by ( 11 ) , a , b α = 1 + 2 “ ) } = √ ( 1 1 μ2 sin2 0 ; μ by introducing the index of refraction , and the angle of incidence . Thus , ◊ ( u sin2 0 1 ) ...
الصفحة 17
... Hence , the general equations ( 4 ) for the first medium become dy dy dx d dv du - dy d2 u dt d du dv d du dv 2 = + + y2 2 dx dx dy d2 v d du dv 2 2 = dt2 g + +7 dy dx dy dx dx A B where g and y2 = = ρ P dx dy These equations might be ...
... Hence , the general equations ( 4 ) for the first medium become dy dy dx d dv du - dy d2 u dt d du dv d du dv 2 = + + y2 2 dx dx dy d2 v d du dv 2 2 = dt2 g + +7 dy dx dy dx dx A B where g and y2 = = ρ P dx dy These equations might be ...
الصفحة 27
... Hence , we know that Laplace in his Mécanique Céleste , and Poisson after him , have not cared to assume any particular law of force , and even if they had , no means would have been found for its verification , One result of this fact ...
... Hence , we know that Laplace in his Mécanique Céleste , and Poisson after him , have not cared to assume any particular law of force , and even if they had , no means would have been found for its verification , One result of this fact ...
الصفحة 35
... hence V = ΣAP . [ dpe ̄ar { R + p− ( R − p ) } αρ - dpe - ap { p + R- ( p − R ) } R R R + ΣΑΡ . J Ame - adp ( 4πe - al ( 1 + al ) - АП • R e - a R + ΣΑΡ . 5 . = Σ AP . ƒ® [ * = ΣΑΡ . Απ = - a2 2 Ꭱ 4πP The coefficient a2 being the ...
... hence V = ΣAP . [ dpe ̄ar { R + p− ( R − p ) } αρ - dpe - ap { p + R- ( p − R ) } R R R + ΣΑΡ . J Ame - adp ( 4πe - al ( 1 + al ) - АП • R e - a R + ΣΑΡ . 5 . = Σ AP . ƒ® [ * = ΣΑΡ . Απ = - a2 2 Ꭱ 4πP The coefficient a2 being the ...
الصفحة 37
... hence 4π PB Ra2 MP = R π 4T PB a2 = M ' the same value as we obtained by the former process . 17. We have hitherto omitted any consideration of a uniform layer of caloric distributed over space , so as to act equally on every point . It ...
... hence 4π PB Ra2 MP = R π 4T PB a2 = M ' the same value as we obtained by the former process . 17. We have hitherto omitted any consideration of a uniform layer of caloric distributed over space , so as to act equally on every point . It ...
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a² a² action algebra angle apse apsidal distances attraction axis centre co-ordinates coefficients conceive consequently consideration crystals curves density displaced disturbance dv dw dv dx dx dx dx dy dx dy dz dx dz dx² dy dx dy dy dy dz dx e-aa e-al equal equation equilibrium expression former formula function Hence homogeneous function hypothesis inertia inverse Jura lignite luminiferous ether medium molecular forces motion obtain optic axes parallel parametric surface particle of caloric perpendicular phlogiston plane of incidence portion position propagation quantity of matter radius radius of curvature refracted waves repulsive result suppose surface of junction symbols tan-¹ vary velocity Vevey vibrations wave's front weight μ² аф
مقاطع مشهورة
الصفحة 182 - Prove that parallelograms on the same base and between the same parallels are equal in area.
الصفحة 131 - High Plains" of the state1. The surface of the county is a plain which slopes gently toward the east and whose surface is broken by two large valleys, one in the northern and the other in the southern part of the county. The valleys extend almost the entire length of the county.
الصفحة 72 - From the identity of this formula with that for the centre of gravity, it appears that the velocity of the great primary wave of translation of a fluid is that due to gravity acting through a height equal to the depth of the centre of gravity of the transverse section of the channel below the surface of the fluid. 7- The height of a wave may be indefinitely increased by propagation into a channel which becomes narrower in the form of a wedge, the increased height being nearly in the inverse ratio...
الصفحة 95 - SUPPLEMENT TO A MEMOIR ON THE REFLEXION AND REFRACTION OF LIGHT. IN a paper which the Society did me the honour to publish some time ago*, I endeavoured to determine the laws of Reflexion and Refraction of a plane wave at the surface of separation of two elastic media, supposing this surface perfectly plane, and both media to terminate there abruptly : neglecting also all extraneous forces, whether due to the action of the solid particles of transparent bodies on the elastic medium, which ia supposed...
الصفحة 303 - If the antecedence and consequence in question be understood as the interposition of an interval of time, however small, between the action of the cause and the production of the effect, we regard it as inadmissible. In the production of motion by force, for instance, though the effect be cumulative with continued exertion of the cause, yet each elementary or individual action is, to our apprehension, inslantef accompanied with its corresponding increment of momentum in the body moved.
الصفحة 184 - ... in any case or to any extent, as a measure of the quantity of matter. I may remark, that the same conclusion is easily extended to the case in which phlogiston is supposed to have absolute levity; for in that case, a certain mixture of phlogiston and of heavy matter would have no weight, and might be substituted for phlogiston in the preceding reasoning. I may remark, also, that the same conclusion would follow by the same reasoning, if any kind of matter, instead of being void of weight, were...
الصفحة 333 - It is well known that the equation udx + vdy + wdz = 0, is the differential equation of a surface which cuts at right angles the directions of the motions of the particles through which it passes, if the left hand side of the equation be integrable per se.