Mathematical Papers of the Late George GreenMacmillan, 1871 - 336 من الصفحات |
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الصفحة 20
... substituted for V in the above equa- tion satisfies it ; 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 ...
... substituted for V in the above equa- tion satisfies it ; 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 ...
الصفحة 21
... substituted for V in - ( 27 ) 9 will give the force arising from this element in the direction tending to increase q , and conse- quently , - ( 24 ) - will give the sum of all the forces due to every element of V , or the total force ...
... substituted for V in - ( 27 ) 9 will give the force arising from this element in the direction tending to increase q , and conse- quently , - ( 24 ) - will give the sum of all the forces due to every element of V , or the total force ...
الصفحة 23
... substituted in the equation ( 1 ) of the preceding number gives p = 0 , and consequently shows , that the density of the electricity at any point in the interior of any body in the system is equal to zero . The same equation ( 1 ) will ...
... substituted in the equation ( 1 ) of the preceding number gives p = 0 , and consequently shows , that the density of the electricity at any point in the interior of any body in the system is equal to zero . The same equation ( 1 ) will ...
الصفحة 24
... 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 ' dx ...
... 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 ' dx ...
الصفحة 34
... substituted in the general value of SU , before given , there arises SU , = 0 , and consequently 0 = SU . The result just ob- tained being general , and applicable to any point p ′′ within the surface , gives immediately 0 = 8 dU dw and ...
... substituted in the general value of SU , before given , there arises SU , = 0 , and consequently 0 = SU . The result just ob- tained being general , and applicable to any point p ′′ within the surface , gives immediately 0 = 8 dU dw and ...
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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