Meanings of inconsequent things in English

They might, from their appearance, have been talking of very inconsequent things.

But it is always these seemingly inconsequent things that bear the heaviest reckoning.

Jeb acted very morose and absentminded; instead of giving sensible replies to John's questions about the avalanche, he would mutter and say inconsequent things.

Then there were several witnesses who swore to inconsequent things, such as waiters at the Hotel Central, and the doctor who had examined Cortlandt.