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I desire to record my respectful acknowledgments for their support and encouragement, without which this book could not have been published, to the Right Hon. The Secretary of State for India in Council, and H.E. The Governor of Madras in Council; as also my cordial thanks to those who have from time to time favoured me with their help and advice. Dr. J. F. Fleet has assisted me from beginning to end in many ways, and I cannot too strongly express my obligation to him: he has not only given me throughout the benefit of his extensive knowledge of the subject, but has taken the trouble to assist me in the often wearisome work of correcting the proofs: while, however, he has supplied me with a few bases for work and some notes, remarks and suggestions, he is not to be held in any way responsible for the methods and teaching in this volume, which are my own. Dr. Robert Schram has devoted many days of hard labour to elaborate calculations for ascertaining the correct value of the śōdhya, an important element for some astronomical processes, at the beginning of the Kaliyuga; and I have also to thank him for his permission to reprint his Table (Table XXIII. of the present Volume) for simplifying the calculation of nakshatras. Mr. A. C. D. Crommelin, of the Greenwich Observatory, was kind enough to advise me in the matter of the late Mr. Sh. B. Dikshit's method of computing the longitudes of Jupiter. My acknowledgments are due to Professor Hermann Jacobi of Bonn for his generous permission to adopt some of the Tables published by him in the Epigraphia Indica, Vols.I., II., and the Indian Antiquary, Vol. XVII., and to reproduce them; but I have not found it necessary to do so for general purposes, and for special purposes have thought that the more proper course for me is simply to refer the reader to the Professor's publications. I have, however, made use of Tables 5 and 6 of his Indian Antiquary article on "Methods and Tables for Verifying Indian Dates" (Vol. XVII., pp. 163, 164), modifying them as explained in §§ 85a to 85c of the Text; and I must tender him my sincere thanks for his permission to do so. Finally, I have to thank Messrs. Thacker, Spink & Co. of Calcutta for permission to reprint, from General Sir Alexander Cunningham's Book of Indian Eras, the Tables here numbered XLI.A. and XLI.B.