Preface. v 



the Rectification of the Conic Sections, which (with 

 his first Optical Memoir) was communicated to the 

 Royal Irish Academy shortly after he obtained his 

 B. A. degree. This was followed, many years after- 

 wards, by an elaborate memoir, which may, indeed, be 

 fairly called a treatise: " On Surfaces of the Second 

 Order." In this memoir a new definition is given for 

 this class of surfaces analogous to the well-known 

 mode of defining curves of the second order by means 

 of a focus and directrix. 



The articles contained in the third and fourth parts 

 of the present volume were not published during the 

 lifetime of the author. They are records of Courses 

 of Lectures on the subjects of Rotation and Attrac- 

 tion, given by Prof. Mac Cullagh. These records 

 were preserved by Professors Haughton and Allman, 

 and communicated by them to the Royal Irish Aca- 

 demy. 



Two short Papers on Egyptian Chronology, which, 

 like most of Prof. Mac Cullagh' s writings, were origi- 

 nally communicated to the Royal Irish Academy, have 

 been printed at the end of this volume. 



