We have recently painted 2 upstairs bedrooms and pulled the carpet. One of the rooms in the older part of the house has a bounce in floor - not bad enough to crack the ceiling downstairs but the light fixture shake a little. The floor has tongue and groove wood flooring that is probably original to the house and no sub-floor.

How do we firm up the floor and make it more stable before replacing the carpet?

A functional steel beam covered in wood to appear as a larger wood beam could also be used in the room below.

Adding flat layers of plywood will have minimal affect, adding 1x lumber perpendicular to the joists is marginally better.

Living with it if it is not a structural issue is the most common solution for older houses built before stringent building codes.

When sistering joists - I think of make-shifting a joist hanger and running the new joist next to the old joist - the entire length. This is connected to the old joist by construction adhesive and screws. Is this the correct way to do this?

16d nails are fine.
Use a nail gun to avoid damage from repeated hammering to drive the new nails.
Very old lumber can be VERY hard.

Construction adhesive has no structural value. There is no reliable data and application methods defined.

Very few screws have any structural ratings either.
Bolts at least have a defined rating, but going over 3/8 inch diameter and using fewer fasteners often exceeds the crush strength of wood (especially the new wood).

Fasteners also need to be correctly distributed to make the pieces of wood behave as a single unit.

Now I'm concerned. How do we make sure that this is correctly distributed?

We will use 16d. Haven't uncovered the tongue and groove yet so really don't know the joist specifics. The room is 11'1" wide. I am guessing the joist is 8".

Each alternate nail in each row is then staggered up about 1 inch to avoid creating to close a line (causes 'zipper' failure along the row of nails).

The separation is about the joist height, with nails then added about the middle of the joist vertically and horizontally between the other nails.

It does take a pretty significant number of nails to make the members act as one, more than a straight loading calculation requires.

The likely lack of any grading on the old wood can be an issue for some AHJs, while others are willing to assume a low grade and go from there.

You are likely to find full dimension wood (often right off the sawmill blade), and possibly larger sections than are commonly used now. You may even find wood that still has round features left from the tree.

That is a new work spec, not a retrofit spec.

The good news . . . the builders that placed the drywall in this portion of the house did put in insulation so we do not have to blow in insulation.

How do you sister joists when there are 6 electric wires running through them? 4 in one hole and about 3 foot away 2 more wires through another hole.

I've been reading your thread with interest, as we've got an under-joisted attic (1x6 on 16", if memory serves). Obviously much worse than yours, to the point that we're afraid to go up there.

So, I forwarded your thread to my husband, and got an interesting response from him:

Yesterday, I finally read the equation for deflection (was related to something at work)
I knew it was some power of the height, but here it is:

deflection = force * span^3 / (width * height^3 * elasticmodulus)

So the difference between 2x8 and 2x6 is a factor of 2.4 wow!

And I didn't realize that the span was cubed, learn something every day.

Actually about 2.3

You have to use the net dimensions of the lumber, not the nominal.

2x8 is 7.25 wide, while a 2x6 is 5.5 wide.

2x lumber is 1.5 in thick, and 1/2 inch under for 6 in or less in width, but 3/4 in under at 8 inches and over.