In the end value is determined by what a buyer will pay and what an owner will accept.
You will need to find someone versed in the chairs to get an idea of value but I suspect it is virtually worthless given the rusted condition.
The photo here features the piece upside down - The three prongs would be bolted into the seat of the chair and the "top screw piece" would be facing downward, inserted through the center of the chair legs. I have determined through research that this piece is dated between 1867 (the founding of "The Ford & Johnson CO.") and 1872 (when said company changed to "J.S. Ford Johnson & Co.") and reads "The Ford & Johnson CO. Chicago" around the turn handle seen in the photo. Although I have determined the date and the brand of the chair part, I do not know what the chair part is called or how much it is worth in its current condition. Does anyone know where I can appraise such an item or how much it is possibly worth? Please help me out, I've been researching for days and I am at the end of the trail. Thank you so much in advance!