## Transactions of the Cambridge Philosophical Society |

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النتائج 6-10 من 82

الصفحة 86

Instead of eliminating v at first, we may differentiate (4), considering v as a

equations (a" – vo) (co-wo) no 4-(b"—vo) (co-w") m” + (a" – vo) (bo-v) = 0 ... (1), (x

-ma' — ny)* ...

Instead of eliminating v at first, we may differentiate (4), considering v as a

**function**of m and n determined by equation (3), we shall thus obtain theequations (a" – vo) (co-wo) no 4-(b"—vo) (co-w") m” + (a" – vo) (bo-v) = 0 ... (1), (x

-ma' — ny)* ...

الصفحة 91

The utility of solutions for such equations, occurring, as they do, in the theory of

chances, is more apparent by the proof which they afford of the expansibility of

various kinds of successive

The utility of solutions for such equations, occurring, as they do, in the theory of

chances, is more apparent by the proof which they afford of the expansibility of

various kinds of successive

**functions**on which some doubt has hitherto existed. الصفحة 92

As an illustration, suppose we denote by u, the successive

e e e e being the base of Napier's Logarithms, then, to find its differential

coefficient, we have the equation - ?!, r u... = e", and putting di – “.. u'... = e”. u',:

therefore + ...

As an illustration, suppose we denote by u, the successive

**function**, (r times)e e e e being the base of Napier's Logarithms, then, to find its differential

coefficient, we have the equation - ?!, r u... = e", and putting di – “.. u'... = e”. u',:

therefore + ...

الصفحة 93

which contains an arbitrary multiplier; but it is plain that the expansion of u, being

unknown, Xu, is also unknown, and the successive differential coefficients would

similarly be expressed in forms of unknown

which contains an arbitrary multiplier; but it is plain that the expansion of u, being

unknown, Xu, is also unknown, and the successive differential coefficients would

similarly be expressed in forms of unknown

**functions**; and therefore the ... الصفحة 94

Now similar difficulties opposing the expansion of other kinds of successive

finite differences, by which the law of the formation of the

Now similar difficulties opposing the expansion of other kinds of successive

**functions**, these can only be removed by attending carefully to the equations infinite differences, by which the law of the formation of the

**functions**is expressed.### ما يقوله الناس - كتابة مراجعة

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### مقاطع مشهورة

الصفحة 353 - ... 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 11 - 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 1 - Notwithstanding' the appearances of irregularity and confusion in the formation of the crust of our globe, which are presented to the eye in the contemplation of its external features, Geologists have been able in numerous instances to detect, in the arrangement and position of its stratified masses, distinct approximations to geometrical laws.

الصفحة 116 - 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 57 - ... 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 404 - 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 75 - 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 465 - ... 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 128 - Given the sum or difference of two angles, and the ratio of their sines, to find the angles, This...