Mathematical Papers of the Late George Green ...Macmillan and Company, 1871 - 336 من الصفحات |
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الصفحة 4
... little from a sphere , and on those of ellip- soids , from 1771 , the date of ... infinitely thin canal of this hypothetical fluid , whose per- pendicular ... small compared with that contained in the bodies . An analogous application ...
... little from a sphere , and on those of ellip- soids , from 1771 , the date of ... infinitely thin canal of this hypothetical fluid , whose per- pendicular ... small compared with that contained in the bodies . An analogous application ...
الصفحة 17
... small , compared with the others . The hypothesis of a constant coercive ... infinite number of conducting elements , separated by intervals absolutely ... infinite , its thickness remaining unchanged , and have thence deduced for- mulæ 2 ...
... small , compared with the others . The hypothesis of a constant coercive ... infinite number of conducting elements , separated by intervals absolutely ... infinite , its thickness remaining unchanged , and have thence deduced for- mulæ 2 ...
الصفحة 20
... infinite , it does not therefore necessarily follow that satisfies the ... small quantities . Then , the value of V may be considered as composed of ... small sphere itself , which value is known to be δ ( 2παρ - πιρ ) ; p being equal to ...
... infinite , it does not therefore necessarily follow that satisfies the ... small quantities . Then , the value of V may be considered as composed of ... small sphere itself , which value is known to be δ ( 2παρ - πιρ ) ; p being equal to ...
الصفحة 23
... infinite at any point within a solid body of any form whatever ; then will fdx dz dy U8V + fão U ( dv ) = [ dx dy dz ... infinitely small line per- pendicular to the surface , and measured from this surface towards the interior of the ...
... infinite at any point within a solid body of any form whatever ; then will fdx dz dy U8V + fão U ( dv ) = [ dx dy dz ... infinitely small line per- pendicular to the surface , and measured from this surface towards the interior of the ...
الصفحة 26
... infinitely small sphere whose radius is a to be described round p ' , it is clear that our theorem is applicable to ... small sphere is only an infinitely small quantity of the order a ; there only remains therefore to consider the part ...
... infinitely small sphere whose radius is a to be described round p ' , it is clear that our theorem is applicable to ... small sphere is only an infinitely small quantity of the order a ; there only remains therefore to consider the part ...
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عبارات ومصطلحات مألوفة
angle angle of incidence axes axis becomes belonging centre coefficients consequently constant quantity corresponding density determine direction distance dv dv dv dw dx dx dx dy dz dx dz dx² dy dx dy dy dz dx electric fluid element ellipsoid entire function equal to zero equilibrium evidently exact differential expression exterior finite formula give given Hence induced interior luminiferous ether magnetic medium Moreover motion obtain P₁ partial differential equation particles perpendicular plane plane wave 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 V₁ variable velocity vibrations wave's front wire µ² µ³ аф
مقاطع مشهورة
الصفحة 69 - 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.
الصفحة 247 - 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 278 - 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 248 - 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 elements which arc negatively electrified, being regarded as negative.
الصفحة 316 - ... vibration, it will not be sufficient merely to allow for the loss of weight caused by the fluid medium, but that it will likewise be requisite to conceive the density of the body augmented by a quantity proportional to the density of this fluid.
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 285 - 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 50 - We therefore see, that the total charge of all the phials is precisely the same, as that which one only would receive, if placed in communication with the same conductor, provided its exterior coating were connected with the earth. Hence this mode of charging, although it may save time, will never produce a greater accumulation of fluid, than would take place, if one phial only were employed. 9. Conceive now, a hollow shell of perfectly conducting matter, of any form and thickness whatever, to be...
الصفحة 315 - ... 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 Mr GREEN on the Vibration of Pendulums.