▁compreh ensive ▁outline ▁of ▁the ▁imp lications ▁of ▁their ▁calculations . ▁It ▁included ▁a ▁proposal ▁that ▁the ▁best ▁defence ▁against ▁such ▁a ▁weapon ▁would ▁be ▁to ▁develop ▁one ▁before ▁Germany ▁did ▁so . ▁In ▁a ▁few ▁short ▁pages ▁these ▁two ▁scient ists ▁anticip ated ▁the ▁policies ▁of ▁d eter rence ▁which ▁would ▁shape ▁Cold ▁War ▁ge opol it ics . ▁The ▁second ▁was ▁an ▁explanation ▁of ▁the ▁science ▁supporting ▁their ▁conclus ions . ▁ ▁The ▁memor and um ▁opens ▁with : ▁ ▁Calcul ations ▁ ▁Pe ier ls ' ▁starting ▁point ▁was ▁a ▁paper ▁by ▁Francis ▁Per rin , ▁in ▁which ▁he ▁had ▁derived ▁critical ▁mass ▁calculations ▁in ▁terms ▁of ▁nuclear ▁constants . ▁The ▁phys ic ists ▁considered ▁a ▁sphere , ▁which ▁has ▁the ▁minimum ▁surface ▁area ▁for ▁a ▁given ▁volume . ▁A ▁critical ▁mass ▁occurs ▁when ▁the ▁number ▁of ▁neut rons ▁produced ▁equals ▁the ▁number ▁that ▁escape . ▁Per rin ▁assumed ▁that ▁the ▁mean ▁free ▁path ▁was ▁much ▁larger ▁than ▁the ▁radius ▁of ▁the ▁sphere . ▁Pe ier ls ▁did ▁not ▁agree , ▁and ▁comm enced ▁his ▁own ▁calculations . ▁A ▁key ▁insight ▁came ▁from ▁Fr isch , ▁who ▁wonder ed ▁what ▁would ▁happen ▁if , ▁instead ▁of ▁natural ▁u ran ium , ▁someone ▁gave ▁you ▁a ▁sphere ▁of ▁the ▁u ran ium - 2 3 5 ▁is ot ope , ▁By ▁definition , ▁the ▁mean ▁free ▁path ▁is : ▁ ▁where ▁ ▁is ▁the ▁mean ▁free ▁path , ▁ ▁is ▁the ▁number ▁of ▁target ▁particles ▁per ▁unit ▁volume , ▁and ▁