The student approaching the subject of summation formulae is constrained to follow the historical order in which it develops in the Journals of the Institute and the Students' Society. Not only is his path made harder by the difficulty of finding a suitable starting point, but the development he must follow is not always the logical one.

The purpose of the present note is primarily to provide the student with a starting point. If a few of the more important conclusions of the subsequent reading are anticipated herein the author feels that the student's appreciation of the original papers by Hardy and Lidstone will be none the less keen for having already navigated some of the wider channels.

It should be added that except in the method of preparation no originality is claimed for this note.