A History of the Mathematical Theories of Attraction And the Figure of the Earth
A History of the Mathematical Theories of Attraction And the Figure of the Earth
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In our eReader you can find the full English version of the book. Read A History of the Mathematical Theories of Attraction And the Figure of the Earth Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A History of the Mathematical Theories of Attraction And the Figure of the Earth
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With respect to Laplace's demonstration of his theorem it must be observed that he expressly supposes the sphere to touch the spheroid. Ivory does not advert to this supposition. It is obvious that if this supposition be made the condition re- quired in Lagrange's investigation will be satisfied ; and so that investigation will furnish an adequate proof of Laplace's theorem : see Art. 1200. And by proper precautions we may also fortify the weak part of Laplace's own investigation.
Laplace's sup...position amounts to the condition, in modern language, that there are to be no singular points on the surface of the spheroid: so that applied to the Earth it would exclude such irregularities as chasms or craters, and ridges or peaks, and mountains or valleys with vertical faces.
No doubt this condition limits to a corresponding degree the range of the theorem about the expansibility of a function in a series of Laplace's functions ; or rather limits Laplace's own de- monstration of it.
1212. We have shewn in Arts.
What to read after A History of the Mathematical Theories of Attraction And the Figure of the Earth?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
With respect to Laplace's demonstration of his theorem it must be observed that he expressly supposes the sphere to touch the spheroid. Ivory does not advert to this supposition. It is obvious that if this supposition be made the condition re- quired in Lagrange's investigation will be satisfied ; and so that investigation will furnish an adequate proof of Laplace's theorem : see Art. 1200. And by proper precautions we may also fortify the weak part of Laplace's own investigation.
Laplace's sup...position amounts to the condition, in modern language, that there are to be no singular points on the surface of the spheroid: so that applied to the Earth it would exclude such irregularities as chasms or craters, and ridges or peaks, and mountains or valleys with vertical faces.
No doubt this condition limits to a corresponding degree the range of the theorem about the expansibility of a function in a series of Laplace's functions ; or rather limits Laplace's own de- monstration of it.
1212. We have shewn in Arts.
What to read after A History of the Mathematical Theories of Attraction And the Figure of the Earth?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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