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Join Date: Jan 2011
Location: Smack in the middle of Illinois
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It's the slide needle jet - it is held in place by the main jet holder or emulsion tube as most people refer to it - notice #2 in the parts breakdown is both the needle and the jet. The pic is not of a 350 carb, but it shows where the part is located. It is the same for all carbs with replaceable needle jets. Other carbs may have the jet as an integral part of the emulsion tube.
Generally it does not just fall out of the carb, it has to be pushed out. If the slide needle was replaced, then the needle jet should be replaced also (they are matched parts in most carbs and are not available for purchase separately, but in other types of carbs they may be sold separately).