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vi events be positively said that, had want of space not prevented their quotation, examples might have been found to illustrate every rule laid down in the volume.

It was originally intended to have included in the present work chapters on Cadences, and on Harmonising Melodies. The volume has, however, extended to so much larger dimensions than was at first contemplated, that these chapters, which belong rather to practical composition than to harmony in its strict sense, have been reluctantly omitted. It is intended to follow the present work by a treatise on Composition, in which these and similar subjects will be more appropriately dealt with.

The author desires to acknowledge the valuable assistance he has received in the preparation of his work, first and foremost from his son, Louis B. Prout, to whom he is indebted for a very large number of the illustrative examples, and who has also written many of the exercises. Valuable aid has also been received from the late Rev. Sir Frederick Ouseley, with whom, down to the time of his lamented death, the author was in frequent correspondence on the subject of this work. To his friend, Dr. Charles W. Pearce, also, the author must express his thanks for much generous interest and many most useful suggestions, as well as for his kind assistance in revising the proof-sheets of the volume.

It would be unreasonable to expect that the present work will meet with universal approval; but it may at least claim to appeal to teachers and students as an honest attempt to simplify the study of harmony, and to bring it down to date.

, June, 1889.