Definition of "firmly"

When Timothy and Julia hurried up the staircase to the bedroom floor, where a considerable commotion was taking place, Tim took Barry Leach with him. He had him gripped firmly by the arm, since he felt it was not safe to let him loose, and he had no immediate idea what to do with him.

1963, Margery Allingham, chapter 19, in The China Governess‎

Dotcom mania was slow in coming to higher education, but now it has the venerable industry firmly in its grip. Since the launch early last year of Udacity and Coursera, two Silicon Valley start-ups offering free education through MOOCs, massive open online courses, the ivory towers of academia have been shaken to their foundations.

2013 July 20, “The attack of the MOOCs”, in The Economist, volume 408, number 8845