Mathematical Papers of the Late George GreenMacmillan, 1871 - 336 من الصفحات |
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الصفحة viii
... exact differential of some function . " This func- tion , it will be seen , is what is now known under the name of Potential Energy , and the above principle is in fact equivalent to stating that the sum of the Kinetic and Potential ...
... exact differential of some function . " This func- tion , it will be seen , is what is now known under the name of Potential Energy , and the above principle is in fact equivalent to stating that the sum of the Kinetic and Potential ...
الصفحة 165
... exact differential . We thus see that when X , Y , Z are given rational and entire functions V will be so likewise , and we may thence deduce ( Art . 5 ) n - 4 2 − ( 1 − x'2 — y'2 — z'2 ) * . ƒ ( x ' , y ' , z ' ) , = - where f is the ...
... exact differential . We thus see that when X , Y , Z are given rational and entire functions V will be so likewise , and we may thence deduce ( Art . 5 ) n - 4 2 − ( 1 − x'2 — y'2 — z'2 ) * . ƒ ( x ' , y ' , z ' ) , = - where f is the ...
الصفحة 226
... exact differential . udx + vdy + wdz In what follows , however , we shall confine ourselves to the consideration of the motion of a non - elastic fluid , when two of the dimensions , viz . those parallel to y and z , are so small that o ...
... exact differential . udx + vdy + wdz In what follows , however , we shall confine ourselves to the consideration of the motion of a non - elastic fluid , when two of the dimensions , viz . those parallel to y and z , are so small that o ...
الصفحة 245
... exact differential of some function . But , this function being known , we can imme- diately apply the general method given in the Mécanique Analy- tique , and which appears to be more especially applicable to problems that relate to ...
... exact differential of some function . But , this function being known , we can imme- diately apply the general method given in the Mécanique Analy- tique , and which appears to be more especially applicable to problems that relate to ...
الصفحة 248
... exact differential of some function and entirely due to the in- ternal actions of the particles of the medium on each other . Indeed , if dø were not an exact differential , a perpetual motion would be possible , and we have every ...
... exact differential of some function and entirely due to the in- ternal actions of the particles of the medium on each other . Indeed , if dø were not an exact differential , a perpetual motion would be possible , and we have every ...
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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