## Mathematical Papers of the Late George Green |

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الصفحة 12

infinite when p is exterior to the surface A, and when p is at an infinite distance

from A, V is equal to zero. These two conditions combined with the partial

differential ...

**Moreover**it is clear, that none of the differential coefficients of V = j- — can beinfinite when p is exterior to the surface A, and when p is at an infinite distance

from A, V is equal to zero. These two conditions combined with the partial

differential ...

الصفحة 17

if there were any substances in nature whose magnetic powers, like those of iron

and nickel, admit of considerable developeinent, and in which

coercive force was, as we have here supposed it, the same for all their elements,

the ...

if there were any substances in nature whose magnetic powers, like those of iron

and nickel, admit of considerable developeinent, and in which

**moreover**thecoercive force was, as we have here supposed it, the same for all their elements,

the ...

الصفحة 19

... z, be the rectangular co-ordinates of a particle of this body, p the density of the

electricity in this particle, so that dx'dy'dz being the volume of the particle, p dx'dy'

dz' shall be the quantity of electricity it contains :

... z, be the rectangular co-ordinates of a particle of this body, p the density of the

electricity in this particle, so that dx'dy'dz being the volume of the particle, p dx'dy'

dz' shall be the quantity of electricity it contains :

**moreover**, let r be the distance ... الصفحة 21

... or the total force acting on p in the same direction. In order to show that this will

still hold good, although the point p be within the body; conceive the value of V to

be divided into two parts as before, and

... or the total force acting on p in the same direction. In order to show that this will

still hold good, although the point p be within the body; conceive the value of V to

be divided into two parts as before, and

**moreover**let p be at the surface of the ... الصفحة 22

without the bodies, will be likewise given by - (-j- J ; the function V representing

the sum of all the electric particles in the system divided by their respective ...

**Moreover**, the force tending to increase a line q ending in any point p within orwithout the bodies, will be likewise given by - (-j- J ; the function V representing

the sum of all the electric particles in the system divided by their respective ...

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acting action angle applicable arising axes axis becomes belonging body centre clear co-ordinates coefficients communication compared complete conceive condition conducting consequently consider consideration constant contained corresponding deduce density depend determine differential direction distance easy effect electricity element ellipsoid employed entire equal equation equilibrium evidently expression extending exterior fluid force formula give given Hence immediately incidence independent induced infinite integral interior known light magnetic means medium method Moreover motion nature neglecting observed obtain origin parallel particles particular plane polar positive potential function powers preceding present produced proved quantity radius reduce reflected refracted remains remark represent respectively satisfy shell simple space sphere substituted suppose surface taken term theory tion variable vibrations wave whole zero

### مقاطع مشهورة

الصفحة 274 - 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 281 - 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 244 - ... 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 11 - 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 281 - 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 243 - 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 313 - 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 16 - ... 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 34 - 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.