An Unabridged Printing To Include All Tables: Historical Summary - Preliminary Theorems - The Double Six Configuration; Auxiliary Theorems - The Trihedral Pair Configuration - Analytical Configuration Of The Twenty-Seven Lines And Forty-Five Triple Tangent Planes For The General Equation Of The Cubic Surface - The Construction Of A Model Of A Double Six - The Construction Of The Configurations Of The Straight Lines Upon The Twenty-One Types Of The Cubic Surface - On Some Configurations Associated With The Configurations Of The Lines Upon The Cubic Surface - Bibliography - Intersection Table - Plates