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This fourth and final volume of The Collected Papers of Sir William Rowan Hamilton (1805-1865) contains three previously unpublished and important manuscripts, namely, System of Rays and two lengthy letters to de Morgan on definite integrals and Hart on anharmonic coordinates. In addition, the volume contains reprinted papers on geometry, analysis, astronomy, probability, and finite differences, as well as a collection of papers on other topics. A cumulative index for all three volumes is provided, as well as a CD-ROM with all four volumes of the Collected Papers.