select progressive total

From the "I thought this would be trivially easy" dept:

I have a table holding member data for an organisation

CREAT table member (
id SERIAL PRIMARY KEY,
applied date,
...

and i'd like to plot the growth in memberships. I'd prefer to hand off
the data already totaled, if possible.

'2006-02-01', 452
'2006-02-17', 453
...

It semed to me that a self join was the way to go, but that route
produced some flaky results. Here's my latest attempt:

SELECT m1.applied AS date_applied, count(m2.id) AS num_applications
FROM member m1, member m2 WHERE m1.applied <= m2.applied
GROUP BY m1.applied ORDER BY date_applied ASC;

The thing is, some applications fell on the same day, so i'm not even
sure that this approach would work. Can anyone see where i'm going wrong
here? And how can i handle applications that occurred on the same day?
Can this even be done in a SELECT, or should i create a function?

b