Leaks. Dry and clean the leaking seam on the inside. Remove loose or crumbly caulking. Then squeeze in asphaltic aquarium sealer available from pet stores or the Five and Ten. Let dry for at least two hours.
Glass broken. Break it out and pick out all splinters. Scrape cement completely from the slate and frame. Clean thoroughly and let dry. Have piece of glass cut to size. Mix 100% Portland cement with linseed oil to a thick consistency; roll into a rope and press firmly into the track at bottom and on sides. Slip glass through top of frame and press securely into the cement. Press cement into track at top. Let cement dry one or two days and then trim off excess.