Adopting an adult cat

Hi, I could certainly use some good advice in acclimating a new adult cat into the household. Saphie, a two-year old spay, needed a home; my Ophelia, a 10-year old spay, needed a companion having recently lost her life-long friend. Saphie has now been sitting on the window sill for 22 days. She does not get down voluntarily; I carry her spitting and growling to the bathroom a number of times a day to use the litter box after which she immediately returns to her window. Ophelia by the way does nothing more than stare longingly; she wants to make friends with Saphie. I'm at wits end here, people. Any suggestions? Thanks.