Can I add more water when racking from primary to secondary?

So I clearly have no ability to operate in US measurements (cup, pint, gallon, you get the idea). I deal with metric all day at work and so apparently I had much less total volume when I added the wort to the water in the fermenter. Another problem is that my pot was large but relatively shallow so I'm sure more water evaporated than had I used a tall pot. So I added a gallon of distilled water I had lying around (unopened) and about 8 bottles of water prior to pitching the yeast. I still think the level might be low and so since I will be moving to a secondary I could mark the 5 gallon level on the secondary and then just top off with either bottled or boiled (and cooled water). Is this something to do? My only real concern is the introduction of oxygen with the new water addition.

I tend to like heavier stronger beers, but just don't know if it will taste bad say if I have 4 gallons of beer instead of 5?

So far though the yeast are doing their magic. I was shocked to see after 18 hours or so the activity is so vigorous that the whole bottle seems to be churning inside, like I was stirring it constantly. I was always wondering if it would be beneficial to have a stir bar or something inside to make sure the yeast contacted everything in the bottle, but clearly there is no need; the fermenter has its own current!

Thanks everyone for their help so far (I lurked here for a week heavily researching many threads).

justin

You can add it but I would taste it first when you do a gravity reading. If you like big beers then you'll probably want to leave it and try to correct the mistakes next batch.

a very long boil will sanitize and remove most the oxygen from the water if you really want to add more.

I still think I'll play it by ear. I'll mark 3, 4, and 5 gallon levels on the secondary and see where I'm at when I transfer. Quick question though: How much physical liquid from a 5 gallon batch should there be on say bottling day (or transferring to a secondary)? I mean I have a good 1-3" of sediment on the bottom between the yeast cake layer and the grain/extract/hops gunk. I assume this counts as part of the 5 gallons so do you really only have 4 gallons of liquid from a 5 gallon batch at the end of fermentation?