The attorney general said the juror's activity interfered
with the administration of justice
Two jurors have each been jailed for two months for contempt of court after one posted Facebook comments and the other researched a case online.
Kasim Davey, 21, from London, posted an abusive Facebook message during the trial of a man accused of sex offences.
The High Court also heard that Joseph Beard, 29, had told jurors in a fraud trial what he had learned about the case online.
There have been two previous similar prosecutions by the attorney general.
Dominic Grieve brought the cases over "conduct likely to interfere with the administration of justice".
Davey, from Palmers Green, north London, said he had sent the Facebook message last December as a result of "spontaneous surprise at the kind of case I was on".
The judge at Wood Green Crown Court was alerted and Davey was discharged. The defendant, Adam Kephalas, was eventually found guilty of sexual activity with a child.
The High Court heard claims by Beard that he had only wanted to find out how long the proceedings would take as he was worried they would drag on.