Introducing new cat to current cat- question

Question:
 So I recently adopted a 1-2 year old cat (whom I named Leia) from a local humane society as a companion for my 2 1/2 year old cat, Reine. Reine had another companion the same age as her who sadly had to be put down about a week ago. I adopted Leia on Thursday and introduced them the same day, but separated them after a few minutes. On Friday, I kept them in the same room together while I was there to be watching. Since then I have continued to keep them separated only when I am not there to watch. I wanted to get the opinion of people who have gone through this before to let me know how they are doing and when they should be fully acclimated (although I'm sure its hard to tell) So basically, what's been going on since Friday is some hissing which has progressively decreased to just Reine hissing maybe 3-5 times per day. Very little growling anymore. Usually Leia doesn't hiss back although I think when she's caught off guard she does. They have sniffed nose to nose several times now always with Reine pulling back and hissing, then walking away. Reine is always the one who goes up to Leia to sniff her, Leia never comes to Reine. For the rest of the day, they pretty much stay separated but aware of where the other cat is. Often I will find them within a few feet of each other, both sleeping, which I think is a good sign? At night, I leave them out while I sleep and Reine sleeps on my bed, Leia in her new bed on the floor... peacefully. The only interesting/slightly scary thing that happened occurred today. I was playing with Leia and out of nowhere she decided to leap and run towards Reine, who was five feet away just kind of observing. Then she proceeded to chase Reine as Reine tried to run away. There was hissing and growling and I grabbed Leia as quickly as possible. I held her for a minute and both cats continued to growl at each other from a distance of about 8 feet... so I put Leia in a separate adjoining room for a bit while I went downstairs to make dinner. When I came back only a short time later, I let her out again and everything resumed normally... they're back to kind of watching each other but otherwise not trying to hiss or fight... and normally within 2-5 feet of each other. They've been using the same litter box even though I have 2 out and they've been sleeping in each other's beds... So basically, my questions are... what was this episode today-- is it normal?... is it bad?... will it continue / increase?... And overall, how do you think these two are adapting to one another?
Answer:
 OMG it just happened AGAIN... all of a sudden Leia ran towards Reine... and there was swatting and hissing and growling... WHAT is going on... they were doing so well! HELP!!!!!!!!
Answer:
 keep them seperated for a week or so. they will be curious about it each other, sniff the doors, etc. then slowly introduce them. you shouldnt introduce them right away. cant promise they will ever like each other but slow intro should calm them down.