As Darin somewhat suggested wonder if these are Mason Jars with oil tops. A oil top doesn't make a mason jar a true oil bottle.
J B Rhodes was a inventer with two hundred patents, could it be that two of them have come together. Either way they are pretty cool looking.. The vented oil spout was his invention or at least he put a patent on it first.
He was proud of his work and displayed signature logo on many items.You can tell you have a Rhodes wire carrier as its stamped in the cross bar support just below the handle..
Maybe one of his best inventions that has stood the test of time -- The Gibson Guitar.