## Mathematical Papers of the Late George Green |

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النتائج 6-10 من 29

الصفحة 92

But <fy' and dV being perfect differentials, X'

making therefore if = X'

m (1 - frk) f + ty + kV. Although the value of 1c depends wholly on the nat\ire of ...

But <fy' and dV being perfect differentials, X'

**dx**'+ Tdt/' + Z'dg must be so likewise,making therefore if = X'

**dx**'+Y'**dy**+Z'**dz**,, the above, by integration, becomes const,m (1 - frk) f + ty + kV. Although the value of 1c depends wholly on the nat\ire of ...

الصفحة 93

George Green Norman Macleod Ferrers. Moreover / * \dx'd& dy ''

J*r*^rj. (Art. S);. the triple integrals extending over the whole volume of A, and that

relative to da over its surface, of which da is an element ; dl the quantities <f> ...

George Green Norman Macleod Ferrers. Moreover / * \dx'd& dy ''

**dy**"**dz**'"dT/. -4^'-.J*r*^rj. (Art. S);. the triple integrals extending over the whole volume of A, and that

relative to da over its surface, of which da is an element ; dl the quantities <f> ...

الصفحة 165

... in the direction of the co-ordinates x, y, a of a point p, and then make, as in Art.

1,. Jar1'. we shall have, in consequence of the equilibrium, 1 — n ox 1 — ndy 1 —

ndz which, multiplied by

... in the direction of the co-ordinates x, y, a of a point p, and then make, as in Art.

1,. Jar1'. we shall have, in consequence of the equilibrium, 1 — n ox 1 — ndy 1 —

ndz which, multiplied by

**dx**,**dy**and**dz**respectively, and integrated, give. const. الصفحة 211

Then it is well known that the required attractions may always be deduced from

the function •-/, p'dx'

ellipsoid, and a, y, z being the rectangular co-ordinates of p. We may avoid the ...

Then it is well known that the required attractions may always be deduced from

the function •-/, p'dx'

**dy**'**dz**' p being the, density of. the element dx'**dy**'**dz**' of theellipsoid, and a, y, z being the rectangular co-ordinates of p. We may avoid the ...

الصفحة 212

... because for these differentials the degree of F and /is the same. Let us

therefore make 1 dV^ f p'{a~al)dxdydt' = i^7 dx "J fc-sy+^-y'y+^-zy + u'yi1' then this

quantity naturally divides itself into two parts, such that A = xA'+A"t t p'dx'

where ...

... because for these differentials the degree of F and /is the same. Let us

therefore make 1 dV^ f p'{a~al)dxdydt' = i^7 dx "J fc-sy+^-y'y+^-zy + u'yi1' then this

quantity naturally divides itself into two parts, such that A = xA'+A"t t p'dx'

**dy**'**dz**'where ...

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action 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 finite integrals formula give given Hence homogeneous function induced infinitely small inner sphere integral extending interior luminiferous ether magnetic medium method Moreover motion obtain parallel partial differential equation particles perfect conductor perpendicular 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 sensible shell sphere spherical 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 276 - 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 283 - Ebulea (Botydae), -which suflBciently shows that the position which Doubleday would assign to Acentropus is in or near the Hydrocampidae. " It may possibly be remembered that, in a paper which the Society did me the honour to publish in the ' Transactions

الصفحة 246 - ... that relate to the motions of systems composed of an immense number of "particles mutually acting upon each other. One 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 9 - Ifp be a particle of positive electricity under the influence of forces arising from any electrified body, the function in question, as is well known, will be obtained by dividing the quantity of electricity in each element of the body, by its distance from the particle p, and taking the total sum of these quotients for the whole body, the quantities of electricity in those elementa which are negatively electrified, being regarded as negative.

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 283 - Moreover, should the radius of the sphere of sensible action of the molecular forces bear any finite ratio to \, 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.

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...

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. But as the principal object of our paper is to determine the alteration produced in...

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.