Here's a breakdown of how to approach it:
1. Visual Inspection (under the car):
* Look for Casting Numbers: The most reliable method. The differential housing itself will have casting numbers stamped into it. These numbers (often a series of numbers and letters) will help pinpoint the exact differential type. You'll likely need a flashlight and possibly a mirror to see these clearly. Compare these numbers to a Pontiac parts catalog or a Firebird parts database online.
* Axle Shaft Size: Measure the diameter of the axle shafts. Different differentials used different axle shaft sizes. This is less precise than the casting numbers but can help narrow down possibilities.
* Gear Ratio (Difficult): You *might* be able to visually determine the ring gear and pinion gear teeth count to calculate the gear ratio. This is extremely difficult and not recommended unless you're experienced with differentials. It's better to check the axle code (see below).
* Differential Type (Less Reliable): Look at the overall design. You might be able to see if it's a 8.2-inch, 10-bolt, or 12-bolt differential (common in that era). However, simply looking at the bolt pattern isn't definitive, since there's overlap in bolt patterns across different differentials.
2. Using Vehicle Documentation:
* Original Build Sheet (Most Reliable): If you have the original build sheet for the car, it will specify the differential type and gear ratio.
* Data Plate: The data plate usually located in the glove box or under the hood might give you a clue, though this information isn't always present or complete on the differential. You should look for axle codes (often a letter and number combination) which can be decoded using resources for that model year.
* Previous Owner Records: Talk to the previous owners; they might know the differential specs.
Where to Find Information:
* Online Pontiac Firebird Forums: Enthusiast forums dedicated to 1968 Firebirds are invaluable resources. Post pictures of your differential casting numbers, and experienced members will likely be able to identify it.
* Online Parts Catalogs: Websites specializing in classic car parts often have searchable databases and diagrams.
* Repair Manuals: A factory service manual for a 1968 Pontiac Firebird will include information on the various differentials used that year.
In short: The casting numbers are your best bet for a definitive answer. Don't rely solely on visual inspection of the housing alone. Use a combination of methods, and if you're uncertain, consult with experts in the Pontiac Firebird community.