The Distribution of Brightness in the Penumbra during an Eclipse of the Moon.

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ON the day after the eclipse of October 16, Mr. C. E. P. Brooks mentioned to me that the edge of the umbra had seemed much more sharply defined when the eclipse was nearly total than at an early stage. This observation suggested to me that it might be worth while to work out the theoretical distribution of light over the lunar disc and gain some information about the relation between umbra and penumbra. The diagrams which commonly illustrate the theory of umbra and penumbra in the text-books are shaded in such a way as to suggest that there is a sharp discontinuity in the illumination, the umbra being indicated by one uniform shading, the penumbra by another.

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