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Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. Those readers who are fortunate enough to command the effective aid of mathematical language will find in the appen dices many rigid and easy proofs of important optical theorems which must, in the text, necessarily rest upon more diffuse reasoning. It is hoped that the extraordinary power of the method of analysis presented in Appendix A will recommend it to the student of physics.