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Here an important consideration for the verification of the theory presents itself, tf we suppose that the different pentagons which compose the surface of the dodecahedron all uniformly depend on the different edges of the cube as on so many hinges, so that, for example, the two pentagons nils' I', ntOsO', are raised or lowered by the trapeziums I t nYj O i n O', while they will be raised or lowered in a contrary direction by the triangles I s' 1', Os O', we shall have an infinity of different dodecahedrons, the faces of which will be so many equal and similar pentagons. Amofig these dodecahedrons, a part of them will he possible in virtue of some law of decrement, and others cannot be produced by any law, and will be purely geometrical solids. In each dodecahedron, the incidence of the pentagon ntl s' V on the pentagon n t O s O', at the place of the edge n t which determines of itself all the other angles,1 will have a particular measure ; and calculation proves that, in the case of decrement now mentioned, this incidence ought to be 126° 52'8. Now by measuring that which corresponds with it on the dodecahedron of sulphuretted iron, we find it nearly 127°: thus the existence of the law of decrement is confirmed by the agreement of calculation with observation. 'T1T1 1 M 1 1 i . 1______'_____x.
Newspaper Details
Philosophical Magazine
London, Middlesex, GB
Sat, Jul 01, 1809
Page 362
Full Page
Clipped by
Anonymous
USA 15 Jul 2024
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