Separating Session From Each Browser

scenario:
a user submits a form, create session variables in login.asp and redirect to main.asp

session in login.asp
example: session("uid") = var

experiment:
i tried opening two browsers, and entered two different userid(uid), i also put
response.write(session("uid")) within main.asp to check if different users are displayed.

problem:
the session var from the second browser overwrites the session var of the first browser. so if the first browser "adds" something to a database, it gets the session var of the second browser, and not the first one.

question:
how can i maintain the session var from the first browser? separating each session var from each browser.