一句VOA解释That is why most states approved the new Constitution

一句VOA解释
That is why most states approved the new Constitution only on condition that a Bill of Rights would be added.
only on conditin……这里很迷惑,因为它的意思不明白,所以它接着的that从句后面的意思也显得有点模糊,虽然意思很容易看出来.该怎么了解?
我想知道only condition表达的意思，原句我理解成“那就是为什么绝大多数州通过了新宪法XXXXXBill of Rights被加上”，这里面的XXXXX让我想不通怎么解释才会形成通畅的句子，通过新宪法（修正案），后面又说Bill Of Rights被加上，中间就很迷惑了。