I have, at last, made my way through most of the seventeen patent documents and have summarised and illustrated them to the best of my ability. They may be found here.
Eight of the patents relate to chair design or chair manufacturing equipment. The others cover a range of inventions including making and repairing highways, mechanical aids for swimming, signalling for railway trains, counting machines, improvements to colliery tubs, etc. The ones relating to chairs are, of course, the ones of greatest interest but I commend you to read the quote from the 1887 patent in which Reilly complains about the fact that so much of the stuffing used in upholstery is infested with moths, grubs and other vermin. It leads him to abandon its use in favour of drum-like seating.