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PREFACE. In both these chapters special attention has been paid to the conventions used for the purpose of avoiding ambiguity. It is hoped that a sufficient emphasis has thus been laid on the importance of assigning to every circle a certain direction and a unique pole, a method whose utility has been exemplified also in Chapter X.

Some examples have been added, taken, for the most part, from the papers of the Science and Art Examinations and of the Royal University of Ireland; a few are from collection.

My very grateful acknowledgments are due to Mr., for his help in reading proofs, and for many most valuable suggestions.

J. G. LEATHEM.


 * October 24, 1901.
 * October 24, 1901.