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The author desires to record his gratitude to Mr. W. W. Rouse Ball, Fellow of Trinity College, Cambridge, and to Professor W. McF. Orr, F. R. S., of the Royal College of Science for Ireland; these friends have read the proof-sheets, and have made many helpful suggestions and criticisms.
Thanks are also due to the Board of Trinity College, Dublin, for the financial assistance which made possible the publication of the work.
