▁of ▁them ▁having ▁a ▁complicated ▁system ▁of ▁pre - period s ▁branch ing ▁into ▁it . ▁Several ▁separate ▁figures ▁of ▁the ▁above ▁type ▁side ▁by ▁side ▁are ▁then ▁necessary ▁to ▁give ▁a ▁graph ic ▁representation ▁of ▁the ▁periodic ities . ▁A ▁lower ▁limit ▁for ▁the ▁lengths ▁of ▁the ▁pure ▁periods ▁was , ▁as ▁far ▁as ▁I ▁remember : ▁ 2 5 2 ▁x ▁ 2 1 ▁x ▁ 2 3 ▁x ▁ 2 5 ▁= ▁ 8 , 1 6 2 , 7 0 0 . ▁ ▁The ▁questions ▁of ▁periodic ities ▁in ▁the ▁case ▁of ▁model ▁c ) ▁was ▁still ▁more ▁involved . ▁It ▁was ▁just ▁not ▁possible ▁to ▁calculate ▁the ▁lengths ▁of ▁the ▁pure ▁periods ▁and ▁pre - period s , ▁let ▁alone ▁give ▁the ▁lower ▁limits ▁which ▁are ▁themselves ▁not ▁incons ider able . ▁ ▁Ci pher ▁Security ▁The ▁principal ▁weak ness es ▁of ▁the ▁En igma ▁were ▁as ▁follows : ▁ ▁W heel ▁I ▁moved ▁uniformly ▁ ▁W heel ▁II ▁and ▁above ▁all , ▁wheel ▁III ▁moved ▁too ▁inf re qu ently . ▁ ▁The ▁period ▁of ▁ ▁was ▁compar atively ▁small , ▁so ▁that ▁when ▁there ▁was ▁a ▁large ▁amount ▁of ▁traffic ▁on ▁one ▁day , ▁on ▁one ▁key , ▁one ▁had ▁to ▁reck on ▁with ▁the ▁conc urrence ▁of ▁critical ▁depth s ▁( this ▁applies ▁at ▁least ▁to ▁the ▁Army ▁En igma ; ▁the ▁naval ▁machine ▁had ▁a ▁fourth ▁wheel , ▁so ▁that ▁a ▁days ▁traffic ▁on ▁one ▁key ▁was ▁spread ▁out ▁over ▁ 2 6 ▁periods