Transactions of the Cambridge Philosophical SocietyUniversity Press, 1842 |
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الصفحة 5
... dy dz [ dt Su + dav dt δυ + d2w dt2 sw } = fffdx dy dz ( p + dp2 + & c . ) ; the triple integrals extending over the whole volume of the medium under consideration . But by the supposition , when u = 0 , AND REFRACTION OF LIGHT . 5.
... dy dz [ dt Su + dav dt δυ + d2w dt2 sw } = fffdx dy dz ( p + dp2 + & c . ) ; the triple integrals extending over the whole volume of the medium under consideration . But by the supposition , when u = 0 , AND REFRACTION OF LIGHT . 5.
الصفحة 6
... integrals extending over the whole volume under consideration . The formula just found is true for any number of media comprised in this volume , provided the whole system be perfectly free from all extraneous forces , and subject only ...
... integrals extending over the whole volume under consideration . The formula just found is true for any number of media comprised in this volume , provided the whole system be perfectly free from all extraneous forces , and subject only ...
الصفحة 9
... integrals being extended over the whole volume of the fluids to which they respectively belong . It now only remains to substitute for p and p " their values , to effect the integrations by parts , and to equate separately to zero the ...
... integrals being extended over the whole volume of the fluids to which they respectively belong . It now only remains to substitute for p and p " their values , to effect the integrations by parts , and to equate separately to zero the ...
الصفحة 10
... integral ; dz + dx } Su since it is the least value of x which belongs to the surface of junction in the lower medium , and therefore the double integrals belonging to the limiting surface , must have their signs changed . If , now , we ...
... integral ; dz + dx } Su since it is the least value of x which belongs to the surface of junction in the lower medium , and therefore the double integrals belonging to the limiting surface , must have their signs changed . If , now , we ...
الصفحة 14
... integral of the equation will be d2 w dt 2 = yi Id2 w dx2 + d2 w dy ' w1 = € / * B sin y , ( 10 ) ; where by + ct , and a ' is determined by = y , 2 ( b2 — a , 2 ) = c2 = y2 ( b2 + a3 ) , - ( 11 ) . But one of the conditions ( 9 ) will ...
... integral of the equation will be d2 w dt 2 = yi Id2 w dx2 + d2 w dy ' w1 = € / * B sin y , ( 10 ) ; where by + ct , and a ' is determined by = y , 2 ( b2 — a , 2 ) = c2 = y2 ( b2 + a3 ) , - ( 11 ) . But one of the conditions ( 9 ) will ...
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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.