How does Silver overcome Jim's mistrust of him? in chapter 8.

Jim had been apprehensive about Silver's true identity, but his mistrust is overcome after seeing him. Silver did not fit his expectations, so he walked over to introduce himself. Then Jim sees Black Dog......... and Silver sends someone out to chase him for not paying his bill, he pretends not to know of the buccaneers, and makes a scene of the fact he came to his establishment. Silver plays it perfectly, and Jim comes to trust him.

"Now, to tell you the truth, from the very first mention of Long John in Squire Trelawney's letter I had taken a fear in my mind that he might prove to be the very one- legged sailor whom I had watched for so long at the old Benbow. But one look at the man before me was enough. I had seen the captain, and Black Dog, and the blind man, Pew, and I thought I knew what a buccaneer was like--a very different creature, according to me, from this clean and pleasant-tempered landlord."