PREFACE. 



THE present volume contains a complete collection of 

 the scientific works of the late Professor Mac Cullagh. 

 They have been reprinted for the most part from the 

 Proceedings and Transactions of the Royal Irish Aca- 

 demy, in which they originally appeared. Some few 

 have been taken from the Philosophical Magazine. 



Prof. Mac Cullagh' s most important contributions 

 to Science were made in the departments of Physical 

 Optics and Geometry the first class being very much 

 the larger. The discrepancy is not, however, as great 

 as might at first sight appear. A considerable part 

 of his Optical researches, more especially those of 

 earlier date, really belong to the domain of Geometry ; 

 and, if they were so classed, the inequality between 

 the classes would be much reduced. Such a classifica- 

 tion, however, involving the separation of the purely 

 geometrical propositions from their physical applica- 

 tions, would be exceedingly inconvenient, and these 

 propositions have been allowed to remain in the con- 

 nexion in which the author placed them. 



b 



