The present volume contains all that Professor Boole wrote for the purpose of enlarging his Treatise on Differential Equations. Had he lived to publish the second edition he would doubtless have incorporated his more recent investigations with the original work, and it is therefore necessary to explain why another plan has been adopted.<br><br>In some cases Professor Boole had indicated that certain portions of the original work were to he omitted and their places supplied from the manuscripts; but on examination it appeared that in subsequent passages of the work there were references and allusions to the portions thus marked to be omitted which would not apply to the substituted matter. Thus in attempting to carry out the directions it would have been necessary to accept the responsibility of making many alterations, and consequently to incur the risk of failing in the attempt to improve the original form.<br><br>Moreover the Treatise had been for some time out of print, and the long delay which must have been caused by the labour of reconstruction would have produced serious inconvenience to students at Cambridge and elsewhere.