Bicycle Mechanics - swap a 7sp with an 8sp cog set?

If I remove my old 7 speed Shimano DX cog set (from my original DX hub on a 1992 Rocky Mountain Equipe),
will an 8 speed Shimano cog set fit in its place? The width is different, eh?
I think the answer is no and I want to make sure before I try it.

To clarify, the question is: Q) Is the width of a 7 speed and an 8 speed cog set different? If not, can I swap the 7 sp cog with an 8 sp one?

8-speed cassettes are wider than 7-speed cassettes. 8, 9 and 10-speed cassettes are all basically interchangeable (except for Dura-Ace 10-speed aluminum freehubs which have higher splines, but the width is still the same).
If you want to convert your hub to 8-speed, you'll have to buy a new freehub body, which will make the spacing of the hub about 4mm wider (if you keep everything else equal). It's easy to spread a steel frame those 4mm (2mm of flex on either side).
If you go 8-speed, and you've had 7-speed indexed shifting, then you'll need to get 8-speed indexed shifters. Derailers are still compatible.

Other options:
1. stick with 7-speed and just buy a new 7-speed cassette on eBay, or Nashbar and others sell new ones
2. Run 8 cogs of a 9-speed cassette on your 7-speed freehub. This will require using 9-speed shifters.

It will not fit. However you can take a 9 speed cassette and leave off one cog to get 8 speeds on your hub.

It will not fit. However you can take a 9 speed cassette and leave off one cog to get 8 speeds on your hub.

Which also requires a 9 speed chain, raising the cost.
If you were to buy a 9 speed cassette, shifters and chain to have an 8 speed, you may as well spend the extra $30 or so and get the longer Free Hub body and have an actual 9 speed..

Which also requires a 9 speed chain, raising the cost.

And 9-speed shifters which really raises the cost.

That's one of those projects that sounds interesting, and you hear about all the time, but I wonder if anybody ever actually does it. It doesn't sound to me like it would cost out very good.

That's one of those projects that sounds interesting, and you hear about all the time, but I wonder if anybody ever actually does it. It doesn't sound to me like it would cost out very good.
I expect the only ones who have done it are those with older boutique wheels such as disk or time trial wheels that want to continue using them but can't find replacement freehub bodies.

Stick with 7 speed. if you really want a very smooth and efficient ride, replace the cassette with a new set and also get a good 8-speed chain. 8-speed rated chain is generally of better quality than the old 7s chain. Through my experience 7s shimano cassette & KMC chain is a good combination. Funny that you have a 1992 cassette. I ground my set of 7s cassette in two years ( and that is after three sets of chain!!!)

That's one of those projects that sounds interesting, and you hear about all the time, but I wonder if anybody ever actually does it. I ran 8-of-9 awhile, basically while waiting for my purchase list to get long enough to merit placing another mail order.(the store with the best deal on shifters and chain didn't carry bodies.)
Most of it worked like a charm. The 9-spd chain played nice with the, by definition, 7-spd chainwheels and both derailers.
I deliberately ignored the first click (which is supposedly bad as the first click pulls a little more cable to take up some slack) in order to avoid pulling the RD against the limit screw in case I overshot the shifting. Worked fine anyhow, although 9-spd is more sensitive to tuning than the old 7-spd was.
When I finally swapped to a 9-spd body I almost went back to the 7-spd. There's a difference in the dustcap and/or axle seal between 7-spd and 9-spd, so there are a few more bits that needs replacing(apart from the body itself) to get the upgraded wheel fully up to spec.
I eventually got hold of a scrapped 9-spd hub that could donate the axle assembly, so I don't rightly remember exactly which parts I swapped out to get the dustcap/axle seal to match.
Best I remember from reading up on this is that Sheldon Brown says that it's enough to replace the axle seal, and that it's available as a spare.
I have a vague recollection of fiddling around with spacers and washers too, but I really can't tell.