Satsuma Vases

A friend gave me these vases. From what I found on the internet I think they are Satsuma Vases. The vases each have the same markings on the bottom, a circle with a cross thru it and Japanese Kangi. I have read that the circle with the cross going thru it means they are authentic, not reproductions. I can't find the Japanese Kangi and so can't identify it further. One vase is cracked and looks like it has been glued, the other vase is not. On the insides it looks like there are water lines as if used for flowers. I don't know any history about the vases. Can you tell me what they are and how much they are worth?