All 8 Uses of

contrary
in
A Room of One's Own

Meetings were held; letters were read out; so-and-so has promised so much; on the contrary, Mr —— won't give a penny.†
Chpt 1 *

on the contrary = an expression used to intensify denial of an idea

Others, on the contrary, maintain that women are half divine and worship them on that account.†
Chpt 2

On the contrary, it is harassed and distracted with hates and grievances.†
Chpt 4

The rooms differ so completely; they are calm or thunderous; open on to the sea, or, on the contrary, give on to a prison yard; are hung with washing; or alive with opals and silks; are hard as horsehair or soft as feathers—one has only to go into any room in any street for the whole of that extremely complex force of femininity to fly in one's face.†
Chpt 5

She made me feel, on the contrary, that instead of being serious and profound and humane, one might be—and the thought was far less seductive—merely lazy minded and conventional into the bargain.†
Chpt 5

Again if one is a woman one is often surprised by a sudden splitting off of consciousness, say in walking down Whitehall, when from being the natural inheritor of that civilization, she becomes, on the contrary, outside of it, alien and critical.†
Chpt 6

For it needs little skill in psychology to be sure that a highly gifted girl who had tried to use her gift for poetry would have been so thwarted and hindered by other people, so tortured and pulled asunder by her own contrary instincts, that she must have lost her health and sanity to a certainty.†
Chpt 3 *

Definitions:

(1) (contrary as in: a contrary idea)
different (perhaps opposite or mutually exclusive)

In formal logic, contrary propositions or contrary arguments describe two things that cannot both be true. They might be described as mutually exclusive. For example, a pet cannot be both a cat and a dog. It doesn't need to be either, but if it is one, it cannot be the other. So the statement that a pet is a cat and the statement that the same pet is a dog, are contrary statements.
(2) (contrary as in: a contrary personality)
disagreeable -- typically in reference to someone's personality
(3) (contrary to as in: contrary to)
in opposition to

You could also think of this as meaning, despite, or in spite of, or in conflict with; but since a common meaning of contrary is opposite, you many find it easiest to think of contrary to as in opposition to.
(4) (on the contrary as in: on the contrary)
an expression used to intensify denial of an idea

More rarely, on the contrary is used to oppose an idea contained in what was just said rather than to oppose what was literally said. Here is an example: "I will not pay you for the work. On the contrary, I may sue you for damages." Suing for damages does not oppose not paying, but it does oppose the idea of paying.
(5) (to the contrary as in: to the contrary)
with an opposite or different effect; or something with an opposite or different effect