Transactions of the Cambridge Philosophical SocietyUniversity Press, 1838 |
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الصفحة 15
... function of the inde- pendent variables and be made a maximum , we shall manifestly obtain from the corresponding value of that angular direction of the line AB along which the two sets of tensions we are considering have the greatest ...
... function of the inde- pendent variables and be made a maximum , we shall manifestly obtain from the corresponding value of that angular direction of the line AB along which the two sets of tensions we are considering have the greatest ...
الصفحة 24
... function of the angle RPR or EPB , the angle between the line of less re- sistance and the direction AB , ( perpendicular to PR ) in which the B E R K R general tensions tend to form the fissure , the value of the function decreasing as ...
... function of the angle RPR or EPB , the angle between the line of less re- sistance and the direction AB , ( perpendicular to PR ) in which the B E R K R general tensions tend to form the fissure , the value of the function decreasing as ...
الصفحة 29
... function of x . Then the force on the element ds , will be p.8x , and the nor- mal force produced by the tension 7 , will estimated by the effect T = P it would produce , if it acted uniformly on a unit of the line , so that T the ...
... function of x . Then the force on the element ds , will be p.8x , and the nor- mal force produced by the tension 7 , will estimated by the effect T = P it would produce , if it acted uniformly on a unit of the line , so that T the ...
الصفحة 32
... function of a alone , and there- P T T = -.y + C P . ( 1 ) since T = 0 , when y = 0 . force at M4 . PM . 8x , or = The second equation gives T P = y .... This is subject to the condition T " . dx = T = 4. PM . T = const . nearly ...
... function of a alone , and there- P T T = -.y + C P . ( 1 ) since T = 0 , when y = 0 . force at M4 . PM . 8x , or = The second equation gives T P = y .... This is subject to the condition T " . dx = T = 4. PM . T = const . nearly ...
الصفحة 33
... function y ( AE ) . This being the case , it is manifest likewise ( assuming the original system of tensions parallel to AB , to have been uniform ) * that T ( the tension of EF ) will vary very slowly with AE ; and that therefore function ...
... function y ( AE ) . This being the case , it is manifest likewise ( assuming the original system of tensions parallel to AB , to have been uniform ) * that T ( the tension of EF ) will vary very slowly with AE ; and that therefore function ...
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عبارات ومصطلحات مألوفة
a₁ æther Anemometer angles anticlinal appears approximation assume axes axis co-ordinates coefficients Comet consequently considered cos² Crown Glass density determined direction distance dx² elevation elevatory force equal equation expression extrados finite fissure Flint Glass fluid foliis formula function goniatites Hence horizontal hypothesis integral intersection lamina line of resistance Maderæ mass Maxillæ medium mineral veins motion nearly observed obtain parallel particles perpendicular phenomena pinnules plane portion position pressure produced propagated quantity rays refractive refractive index represented respectively shew shewn sin² siphuncle solution Star suppose surface tension theory tion toadstone transmission transverse triangle values velocity vertical vibration wave wave-surface y₁ Λ Λ
مقاطع مشهورة
الصفحة 349 - ... a consequence of the rule that the difference of the squares of the velocities of the ordinary and extraordinary rays within the crystal, is proportional to the product of the sines of the angles which the latter makes with the resultant axes. M. Biot was led to the discovery of this beautiful law by analogyf, and he afterwards observed that it was implicitly contained in the law proposed by Sir David Brewster. The term
الصفحة 9 - I assume this force to act under portions of the earth's crust of considerable extent at any assignable depth, either with uniform intensity at every point, or in some cases, with a somewhat greater intensity at particular points, as, for instance, at points along the line of maximum elevation of an elevated range, or at other points where the actual phenomena seem to indicate a more than ordinary energy of this subterranean action. I suppose this elevatory force, whatever may be its origin, to act...
الصفحة 114 - Their evident analogy to the property of a triangle " that the sines of the angles are proportional to the opposite sides", has suggested another form under which they may be put.
الصفحة 55 - ... to the causes to which we have been assigning such phenomena, could not be produced by successive elevations of different points, by the partial action of an elevatory force.
الصفحة 400 - Very often too, when sound is reflected, these suppositions will lead to sensibly correct results. On this last account, the problem has here been considered generally for all fluids whether elastic or non-elastic in the usual acceptation of these terms; more especially, as thus its solution is not rendered more complicated. One result of our analysis is so simple that I may perhaps be allowed to mention it here. It is this : If A be the ratio of the density of the reflecting medium to the density...
الصفحة 73 - Holme, there is a bed extending for a great wayi surmounted by a parallel series of the secondary strata in contact with it ; but, on a narrow inspection, innumerable veins are seen branching into the strata in every possible direction, illustrating in a very perfect manner the origin of at least one order of veins. In a second case, three beds of trap can be traced in a parallel direction for a considerable space, separated by the regular strata, when suddenly the whole unite into one mass. Had...
الصفحة 461 - ... that joint : if it lie within the cone spoken of, the structure will not slip upon that joint ; if it lie without it, it will. Thus the whole theory of the equilibrium of any structure is involved in the determination with respect to that structure of these two lines — the line of resistance, and the line of pressure. One of these lines, the line of resistance, determining the point of application of the resultant of the pressures upon each of the surfaces of contact of the system ; and the...
الصفحة 126 - Given the sum or difference of two angles, and the ratio of their sines, to find the angles, This...