Mathematical Papers of the Late George Green ...H. Herman., 1903 - 336 من الصفحات |
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الصفحة 50
... , U , etc. functions of the two other polar co - ordinates of p , it is clear , by what has been shown in the admirable work just mentioned , that the potential function V ' , arising 50 APPLICATION OF THE PRECEDING RESULTS.
... , U , etc. functions of the two other polar co - ordinates of p , it is clear , by what has been shown in the admirable work just mentioned , that the potential function V ' , arising 50 APPLICATION OF THE PRECEDING RESULTS.
الصفحة 52
... polar co - ordinates . Then the whole of the electricity will be carried to the surface ( art . 1 ) , and if V be the potential function arising from this electrified surface , for the same point p , we shall have , in virtue of the ...
... polar co - ordinates . Then the whole of the electricity will be carried to the surface ( art . 1 ) , and if V be the potential function arising from this electrified surface , for the same point p , we shall have , in virtue of the ...
الصفحة 55
... polar co - ordinates . Then the whole of the electricity will be carried to the surface ( art . 1 ) , and if V be the potential function arising from this electrified surface , for the same point p , we shall have , in virtue of the ...
... polar co - ordinates . Then the whole of the electricity will be carried to the surface ( art . 1 ) , and if V be the potential function arising from this electrified surface , for the same point p , we shall have , in virtue of the ...
الصفحة 65
... polar co - ordinates and . This expression by changing the direction of the axes , may always be reduced to the form V ' 2a k2 cos 0 = - + - ; a and k being two constant quantities , which we will suppose positive . Then if b be a very ...
... polar co - ordinates and . This expression by changing the direction of the axes , may always be reduced to the form V ' 2a k2 cos 0 = - + - ; a and k being two constant quantities , which we will suppose positive . Then if b be a very ...
الصفحة 67
... polar co - ordinates are r , e , and w , is Q , Qk3 cos hV ' = 2 + = 7 2ar1 From which we may immediately deduce the forces acting on any point p ' exterior to A. to In tracing the surface A , 0 is supposed to extend from 0 = 0 27 : it ...
... polar co - ordinates are r , e , and w , is Q , Qk3 cos hV ' = 2 + = 7 2ar1 From which we may immediately deduce the forces acting on any point p ' exterior to A. to In tracing the surface A , 0 is supposed to extend from 0 = 0 27 : it ...
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angle angle of incidence applicable axes axis B₁ becomes belonging centre coefficients conceive conducting bodies consequently constant quantity corresponding density determine direction distance dv dw dx dx dx dy dz dy dx dy dy dz dx electric fluid element ellipsoid entire function equal to zero equilibrium evidently exact differential expression exterior formula give given Hence homogeneous functions induced integral extending interior luminiferous ether magnetic medium Moreover motion obtain partial differential equation particles perpendicular plane polar co-ordinates potential function arising preceding propagation quantity of electricity radius rational and entire rectangular co-ordinates refracted wave represent shell sphere spherical substituted suppose surface of junction term theory tion total potential function tricity variable velocity vibrations wave's front wire µ² µ³ аф
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 x - 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 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.