You probably have a piece of reinforcing wood at right angles to the saddle wood grain that is pushing the saddle apart. This should have been "slide fastened" to allow expansion of grains at right angles to each other.
Fix up or install a humidifier to stop this.
SWMBO has a favorite rocking chair. I have recently replaced the rockers for her and I am still her favorite woodworker. We have now noticed that the seat is starting to split. It looks like it along a glue joint going from front to back. The splitting is wider at the rear of the seat and narrower towards the front. At present it is only about 6" long. The split is similar on the top and bottom of the seat. At its widest is about 1/8". I believe the seat is pine. What are your suggestions as to how I can stop the split from continuing and rejoin it where is already apart? Thanks for all your help.