In the below example, you can see that his use of the word 'your' is meant to show them that there still exists a separation. The independence that the nation is enjoying does not include independence for the slaves. Douglas does not feel a part of the nation, nor a part of the celebration, even though he is giving the speech.
This, for the purpose of this celebration, is the 4th of July. It is the birthday of your National Independence, and of your political freedom. This, to you, is what the Passover was to the emancipated people of God. It carries your minds back to the day, and to the act of your great deliverance; and to the signs, and to the wonders, associated with that act, and that day. This celebration also marks the beginning of another year of your national life; and reminds you that the Republic of America is now 76 years old. I am glad, fellow-citizens, that your nation is so young.