Full Idea
Though the successive consciousnesses which we have of our own existence are not the same, yet they are consciousnesses of one and the same thing or object; of the same person, self, or living agent.
Gist of Idea
Despite consciousness fluctuating, we are aware that it belongs to one person
Source
Joseph Butler (Analogy of Religion [1736], App.1)
A Reaction
Butler's arguments seems to be that he appears to be the same person, so he is the same person. He is explicitly disagreeing with Locke.
Book Reference
'Personal Identity', ed/tr. Perry,John [University of California 1975], p.102