## Mathematical Papers of the Late George Green |

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الصفحة vii

Particular attention should be paid to the mode in which, from the differential

equations of motion, is deduced an explanation of a phenomenon analogous to

that known in Optics as Total internal reflection when the

exceeds ...

Particular attention should be paid to the mode in which, from the differential

equations of motion, is deduced an explanation of a phenomenon analogous to

that known in Optics as Total internal reflection when the

**angle of incidence**exceeds ...

الصفحة 234

It is this : If A be the ratio of the density of the reflecting medium to the density of

the other, and B the ratio of the cotangent of the angle of refraction to the

cotangent of the

vibration ...

It is this : If A be the ratio of the density of the reflecting medium to the density of

the other, and B the ratio of the cotangent of the angle of refraction to the

cotangent of the

**angle of incidence**, then for all fluids the intensity of the reflectedvibration ...

الصفحة 235

lum, as is usual in the Theory of Light, it is proved that on farther increasing the

the phase of the vibration gradually changes. The laws of the change of intensity,

...

lum, as is usual in the Theory of Light, it is proved that on farther increasing the

**angle of incidence**, the intensity of the reflected wave remains unaltered whilstthe phase of the vibration gradually changes. The laws of the change of intensity,

...

الصفحة 237

r Since the disturbance of all the particles, in any front of the incident plane wave,

is the same at the same instant, we shall have for the incident wave <]>=f(ax + by

+ ... This value proves, that the

r Since the disturbance of all the particles, in any front of the incident plane wave,

is the same at the same instant, we shall have for the incident wave <]>=f(ax + by

+ ... This value proves, that the

**angle of incidence**is equal to that of reflexion. الصفحة 238

or if we introduce 6, 0, , the

, m j , ~2U cot0//'' a^ oote, and therefore ^ = r —-y , y a~ cotF' » ' + ' A cot 6 which

exhibits under a very simple form, the ratio between the intensities of the ...

or if we introduce 6, 0, , the

**angle of incidence**and refraction since cot 8 = * , cot 6, m j , ~2U cot0//'' a^ oote, and therefore ^ = r —-y , y a~ cotF' » ' + ' A cot 6 which

exhibits under a very simple form, the ratio between the intensities of the ...

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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.