## Mathematical Papers of the Late George Green |

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الصفحة viii

... of any material system may act upon each other, if all the internal forces be

multiplied by the elements of their respective directions, the total sum for any

assigned portion of the mass will always be the

.

... of any material system may act upon each other, if all the internal forces be

multiplied by the elements of their respective directions, the total sum for any

assigned portion of the mass will always be the

**exact differential**of some function.

الصفحة 165

YZTn V+J{Xdx + Ydy + Zdz) ; where Xdx + Ydy + Zdz is always an

V will be so likewise, and we may thence deduce (Art. 5) where f is the

characteristic of a ...

YZTn V+J{Xdx + Ydy + Zdz) ; where Xdx + Ydy + Zdz is always an

**exact****differential**. "We thus see that when X, Y, Z are given rational and entire functionsV will be so likewise, and we may thence deduce (Art. 5) where f is the

characteristic of a ...

الصفحة 226

... equations (1) and (2) with the condition (A) applied to each of the exterior

surfaces of the fluid will suffice to determine in every case the small oscillations of

a non-elastic fluid, or at least in those where udx + vdy + wdz is an

... equations (1) and (2) with the condition (A) applied to each of the exterior

surfaces of the fluid will suffice to determine in every case the small oscillations of

a non-elastic fluid, or at least in those where udx + vdy + wdz is an

**exact****differential**. الصفحة 245

... any material system may act upon each other, if all the internal forces exerted

be multiplied by the elements of their respective directions, the total sum for any

assigned portion of the mass will always be the

.

... any material system may act upon each other, if all the internal forces exerted

be multiplied by the elements of their respective directions, the total sum for any

assigned portion of the mass will always be the

**exact differential**of some function.

الصفحة 248

8(p (1) ; Dm and Dv being exceedingly small corresponding elements of the

mas3 and volume of the medium, but which nevertheless contain a very great

number of molecules, and S£ the

due to ...

8(p (1) ; Dm and Dv being exceedingly small corresponding elements of the

mas3 and volume of the medium, but which nevertheless contain a very great

number of molecules, and S£ the

**exact differential**of some function and entirelydue to ...

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angle of incidence applicable axes axis becomes belonging centre coefficients coercive force conceive condition conducting bodies consequently consider constant quantity contained density determine direction distance dx dy dy dx dy dz electric fluid ellipsoid entire function equal to zero equilibrium evidently exact differential expression formula give given Hence homogeneous function immediately deduce induced infinitely small inner sphere integral extending interior light polarized luminiferous ether magnetic medium method Moreover motion obtain parallel partial differential equation particles perfect conductor perpendicular plane plane wave polar co-ordinates positive potential function arising preceding propagation quantity of electricity radius rational and entire rectangular co-ordinates refracted wave remains represent satisfy the equation shell sphere substituted suppose surface of junction term thence theory tion total potential function tricity triple integrals vanish variable velocities of propagation velocity vibrations wave's front whole wire

### مقاطع مشهورة

الصفحة 246 - of the advantages of this method, of great importance, is that we are " necessarily led by the mere process of the calculation, and with little care "on our part, to all the equations and conditions which are requisite and "sufficient for the complete solution of any problem to which it may be "applied.

الصفحة 67 - Since this was written, I have obtained formulae serving to express, generally, the law of the distribution of the electric fluid near the apex 0 of a cone, which forms part of a conducting surface of revolution having the same axis. From these...

الصفحة 245 - If, however, this were not the case, we are so perfectly ignorant of the mode of action of the elements of the luminiferous ether on each other, that it would seem a safer method to take some general physical principle as the basis of our reasoning, rather than assume certain modes of action, which, after all, may be widely different from the mechanism employed by nature ; more especially if this principle include in itself, as a particular case, those before used by M. Cauchy and others, and also...

الصفحة viii - In whatever way the elements of any material system may act upon each other, if all the internal forces exerted be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be the exact differential of some function.

الصفحة 9 - S under consideration, will be expressed by a partial differential of a certain function of the co-ordinates which serve to define the point's position in space. The consideration of this function is of great importance in many inquiries, and probably there are none in which its utility is more marked than in those about to engage our attention. In the sequel we shall often have occasion to speak of this function, and will therefore, for abridgement, call it the potential function arising from the...

الصفحة 283 - Moreover, should the radius of the sphere of sensible action of the molecular forces bear any finite ratio to X, the length of a wave of light, as some philosophers have supposed, in order to explain the phenomena of dispersion, instead of an abrupt termination of our two media we should have a continuous though rapid change of state of the ethereal medium in the immediate vicinity of their surface of separation. And I have here endeavoured to...

الصفحة 3 - CAVENDISH, who having confined himself to such simple methods as may readily be understood by any one possessed of an elementary knowledge of geometry and fluxions, has rendered his paper accessible to a great number of readers; and although, from subsequent remarks, he appears dissatisfied with an hypothesis which enabled him to draw some important conclusions, it will readily be perceived, on an attentive perusal of his paper, that a trifling alteration will suffice to render the whole perfectly...

الصفحة 315 - In the case just alluded to, it is required to determine the circumstances of the motion of an indefinitely extended nonelastic fluid, when agitated by a solid ellipsoidal body, moving parallel to itself, according to any given law, always supposing the body's excursions very small, compared with its dimensions. From what will be shown in the sequel, the general solution of this problem may very easily be obtained.

الصفحة 14 - ... the radius of the spherical conductor to the thickness of the glass in that point. The total quantity of electricity contained in the interior of any number of equal and similar jars, when one of them communicates with the prime conductor and the others are charged by cascade, is precisely equal to that, which one only would receive, if placed in communication with the same conductor, its exterior surface being connected with the common reservoir.

الصفحة 32 - To convince ourselves that there does exist such a function as we have supposed U to be; conceive the surface to be a perfect conductor put in communication with the earth, and a unit of positive electricity to be concentrated in the point p', then the total potential function arising from p' and from the electricity it will induce upon the surface, will be the required value of U.