The Tasco sounds like a target scope with an adjustable objective. Old rimfire scopes often have short eye relief and typically don’t stand up to recoil. Get a quality rifle scope intended for a centerfire rifle and you’ll be fine.

1” tubes are very common these days and less expensive than 30mm scopes. A photo would help identify the rings/mounts you’re using, but mounts for a 110 Savage are easy to get. I’d recommend a Leupold 2-7X, but even a fixed 4X would be good. Their lifetime service policy is one of the best in the industry.

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