Mathematical Papers of the Late George GreenMacmillan, 1871 - 336 من الصفحات |
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الصفحة 11
... condition is requisite for the complete determination of V. Now since V = [ pdo = fedo , it is evident that none of its differential coefficients can become infinite when p is situate any where within the surface A , and it is worthy of ...
... condition is requisite for the complete determination of V. Now since V = [ pdo = fedo , it is evident that none of its differential coefficients can become infinite when p is situate any where within the surface A , and it is worthy of ...
الصفحة 12
... conditions combined with the partial differential equa- tion in V ' , are sufficient in conjunction with its known value ' at the surface A for the complete determination of V ' , since it will be proved hereafter , that when they are ...
... conditions combined with the partial differential equa- tion in V ' , are sufficient in conjunction with its known value ' at the surface A for the complete determination of V ' , since it will be proved hereafter , that when they are ...
الصفحة 26
... condition , the necessity of which does not ap- pear explicitly in the demonstration , but , which is understood in the method of integration by parts there employed . : In order to show more clearly the necessity of this condition , we ...
... condition , the necessity of which does not ap- pear explicitly in the demonstration , but , which is understood in the method of integration by parts there employed . : In order to show more clearly the necessity of this condition , we ...
الصفحة 27
... condition originally imposed upon U and V will be expressed by saying , that neither of them has any singular values within the solid body under consideration . ( 4. ) We will now proceed to determine some relations ex- isting between ...
... condition originally imposed upon U and V will be expressed by saying , that neither of them has any singular values within the solid body under consideration . ( 4. ) We will now proceed to determine some relations ex- isting between ...
الصفحة 29
... conditions , it will always be in our power to assign one , and only one value of p , which will produce them for corresponding potential functions . For this we may remark , that the Equation ( 3 ) art . 3 being applied to the space ...
... conditions , it will always be in our power to assign one , and only one value of p , which will produce them for corresponding potential functions . For this we may remark , that the Equation ( 3 ) art . 3 being applied to the space ...
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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