An Introduction to the Mathematical Theory of Attraction
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56 Spherical and Ellipsoidal Harmonics.
164. Analogues of Tesseral Harmonics. When we put t% for in T nl (K), we get and we may write t ns (Z) = (? + Also, we may write ^-(P + lfD-fcK); (55) whence V M (&) = r^i^f?). (56) Another form of u n (Z) is obtained from (37) from which, by means of (56J, we have whence _ (57) 165. Expression for Potentials. If Fand V denote the potentials inside and outside an oblate ellipsoid of revolu- tion, due to a distribution of mass on its surface, we may write ...(58) (59) Surface Distribution corresponding to Potential 57 It is plain from what precedes that Fand V satisfy each Laplace's equation, that Fis finite when = 0, and V is zero when = oo, and that V and V are identical at the surface of the ellipsoid. Hence they satisfy all the conditions required.
166. Surface Distribution corresponding to Potential. Here we may proceed as in Art. 160. If the internal and external potentials V and V be given by the equations (60) and dsi be an element of the normal to the ellipsoid, \d\ **-' but in this case, by Art.
What to read after An Introduction to the Mathematical Theory of Attraction?
You can find similar books in the "Read Also" column, or choose other free books by Francis a Francis Alexander Tarleton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
56 Spherical and Ellipsoidal Harmonics.
164. Analogues of Tesseral Harmonics. When we put t% for in T nl (K), we get and we may write t ns (Z) = (? + Also, we may write ^-(P + lfD-fcK); (55) whence V M (&) = r^i^f?). (56) Another form of u n (Z) is obtained from (37) from which, by means of (56J, we have whence _ (57) 165. Expression for Potentials. If Fand V denote the potentials inside and outside an oblate ellipsoid of revolu- tion, due to a distribution of mass on its surface, we may write ...(58) (59) Surface Distribution corresponding to Potential 57 It is plain from what precedes that Fand V satisfy each Laplace's equation, that Fis finite when = 0, and V is zero when = oo, and that V and V are identical at the surface of the ellipsoid. Hence they satisfy all the conditions required.
166. Surface Distribution corresponding to Potential. Here we may proceed as in Art. 160. If the internal and external potentials V and V be given by the equations (60) and dsi be an element of the normal to the ellipsoid, \d\ **-' but in this case, by Art.
What to read after An Introduction to the Mathematical Theory of Attraction?
You can find similar books in the "Read Also" column, or choose other free books by Francis a Francis Alexander Tarleton to read onlineMoreLess
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