NO extensive changes have been made in this edition. The most important are in 80-82, which I have rewritten in accord
ance with suggestions made by Mr S. Pollard.
The earlier editions contained no satisfactory account of the
genesis of the circular functions. I have made some attempt to
meet this objection in 158 and Appendix III. Appendix IV is also
an addition.

It is curious to note how the character of the criticisms I have
had to meet has changed. I was too meticulous and pedantic for
my pupils of fifteen years ago: I am altogether too popular for the
Trinity scholar of to-day. I need hardly say that I find such
criticisms very gratifying, as the best evidence that the book has
to some extent fulfilled the purpose with which it was written.