They make 4' fixtures that are designed to go between 16" OC 2x joints (i.e. the fixture is 14.5" wide. You install some clips to the joist and then the fixture itself has little fingers that engage those clips.

Alternatively, you can use some CF or LED rescessed cans instead.

As Mike says and you suspected, the flying splice is bogus. Either install a junction box or bring the cable into the fixture with a suitable fitting.

Thanks for the tips. Bear with me as I am thinking outloud here a bit looking for some opinions (better than anything I will get from the hardware store).

Im still a little confused on what type of fixture to get and I want to have an idea before heading to the hardware store.

The fluorescent with clips sound interesting but I have never seen them. Something similar to the arms on can lights that attach to the sides of the joists?

concerns:

mounting:
If I were to get a standard fluorescent. would attaching two pieces of 2x4 between the joists, and then attaching the new fixture to them the top of the fixture be OK?

Do I have to be concerned with 2x40 watt bulbs being a fire hazard between the joists (14.5" OC).? The bottom of fixture(bulbs) would be guessing less than 6" from hard plastic tile for the light in the drop ceiling? How much space do I need around the fixture?

Electrical:

Is it OK to leave the flying splice in tact until repair as long as there is no power present at the splice?

Sometimes the current fixture doesnt start right up. I feared it was a wiring issue (loose connection) but there is power at the "flying splice" when the light switch is on regardless if the old fixture starts. No power at splice when switch is off. Probably needs a starter or ballast instead of a loose connection somewhere.

If I get a fluorescent , the BX cable wouild enter the new fixture thru knockout and be secured with one of those conduit fittings that have a screw to hold the cable.

If I get can light (not sure that would be enough light by itself) the can light has box attached to it and BX would enter it the same way as the fluorescent.

A generic lamp (outlet box porcelin type) secured to a box attached to a 2x4 between the joists and then covered in drop ceiling would not be advisable im guessing?

one other question in regards to can light.

I figure I would need about 60-75 watts of light for the small room this is in. Can I mount a can/recessed light in the 14.5" x 9" space between the joists. And just cover it with the same plastic cover in the drop ceiling that covered the flurescent? (instead of having to cut ceiling tile and make the light flush mounted?

A recessed can only needs about 6" width and many can fit in that space, you need to measure them but I've got some in tighter spaces than that.

Thanks. I think instead of fumbling with a 4" fluorescent I will just get a recessed can at Menards. However there are a few choices (5", 6", shallow etc) and I am unclear on which to get

It will not sit flush with ceiling tile. Rather it will be covered by plastic grill on drop ceiling about 5" from bottom of joists. The space is 14.5" between the joists and 9" deep. Its not for accent lighting or spot lighting, just a general ceiling light in a 8x10 room, probably used in conjustion with a table lamp.

If someone would be so kind to point me to which one to buy locally at Menards I would be very grateful.

Thanks

recessed lights at my local hardware store:
http://tinyurl.com/m8x9pgx

Here is a link that might be useful: Recessed lights I can get local:

disregard my last request, picked up a 6" halo new construction can and it was a piece of a cake installing. Hopefully everything is up to snuff no flying splice now (terminated inside the can with their push in connectors and the flex bx secured with a 1/8 fitting)!

Im running it for the time being on a 26 watt/ 100 watt equivilant.... can take a few different kinds including A13?

Is a standard incandescent or CF ok in these types of cans? Is a standard bulb called A13 (something I was not familar with?)