From The Collaborative International Dictionary of English v.0.48 [gcide]:
Reading \Read"ing\, a.
1. Of or pertaining to the act of reading; used in reading.
[1913 Webster]
2. Addicted to reading; as, a reading community.
[1913 Webster]
Reading book, a book for teaching reading; a reader.
Reading desk, a desk to support a book while reading; esp.,
a desk used while reading the service in a church.
Reading glass, a large lens with more or less magnifying
power, attached to a handle, and used in reading, etc.
Reading man, one who reads much; hence, in the English
universities, a close, industrious student.
Reading room, a room appropriated to reading; a room
provided with papers, periodicals, and the like, to which
persons resort.
[1913 Webster]
From WordNet (r) 3.0 (2006) [wn]:
reading room
n 1: a room set aside for reading