Mathematical Papers of the Late George GreenMacmillan, 1871 - 336 من الصفحات |
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الصفحة 14
... the same for both . Hence when their distance is very great , the densities are in the inverse ratio of the radii of the spheres . 15 When any hollow conducting shell is charged with elec- 14 INTRODUCTORY OBSERVATIONS .
... the same for both . Hence when their distance is very great , the densities are in the inverse ratio of the radii of the spheres . 15 When any hollow conducting shell is charged with elec- 14 INTRODUCTORY OBSERVATIONS .
الصفحة 15
... Hence , if the diameter of the sphere were twelve inches , and that of the orifice one inch , the density at the point on the inner surface opposite the centre of the orifice , would be less than the hundred and thirty thousandth part ...
... Hence , if the diameter of the sphere were twelve inches , and that of the orifice one inch , the density at the point on the inner surface opposite the centre of the orifice , would be less than the hundred and thirty thousandth part ...
الصفحة 20
... hence the whole integral ( being considered as the sum of all these elements ) will also satisfy it . This reason- ing ceases to hold good when the point p is within the body , for then , the coefficients of some of the elements which ...
... hence the whole integral ( being considered as the sum of all these elements ) will also satisfy it . This reason- ing ceases to hold good when the point p is within the body , for then , the coefficients of some of the elements which ...
الصفحة 22
... tending to increase it . In the same way forces in y and z , and since the fluid forces are equal to zero : hence -- dV dy and — dV dz will be the is in equilibrium all these dV dV 0 = dr da + dy dy + 22 GENERAL PRELIMINARY RESULTS .
... tending to increase it . In the same way forces in y and z , and since the fluid forces are equal to zero : hence -- dV dy and — dV dz will be the is in equilibrium all these dV dV 0 = dr da + dy dy + 22 GENERAL PRELIMINARY RESULTS .
الصفحة 24
... hence by substitution dU " = dx = -fdo " dx dU " dw dx Jdy dzV " -I do " dro In like manner it is seen , that in the part V ' dU ' -Jdy da Vid due to the smaller values of x , we shall have dy dz = + dx dw do ' , and consequently dU ' V ...
... hence by substitution dU " = dx = -fdo " dx dU " dw dx Jdy dzV " -I do " dro In like manner it is seen , that in the part V ' dU ' -Jdy da Vid due to the smaller values of x , we shall have dy dz = + dx dw do ' , and consequently dU ' V ...
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angle angle of incidence ax+by+ct axes axis becomes belonging centre coefficients conducting bodies consequently constant quantity corresponding density determine direction distance 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 integral extending interior luminiferous ether magnetic medium Moreover motion obtain partial differential equation particles perfect conductor perpendicular plane preceding 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