To incorporate in this work the discoveries of the last twenty years would
necessitate the rewriting of at least Chapters XII—XIX; my interest in
Bessel functions, however, has waned since 1922, and I am consequently not
prepared to undertake such a task to the detriment of tny other activities.
In the preparation of this new edition 1 have therefore limited myself to the
correction of minor errors and misprints and to the emendation of a few
assertions (such as those about the unproven character of Bourget's hypo-
hypothesis) which, though they may have been true in 1922, would have been
definitely false had they been, made in 1941.
My thanks are due to many friends for their kindness in informing me of
errors which they had noticed; in.particular, I cannot miss this opportunity
of expressing my gratitude to Professor J. R. Wilton for the vigilance which
he must have exercised in the compilation of his list of corrigenda.