Aristotle's 3 modes of persuasion: Pathos, Logos, Ethos

Pathos; is an appeal to the audiences emotions to gain a response or reaction.
Emotional, Pathos is persuading by appealing to the readers emotion. 
Subjective, Experience that may happen opportunity, in motivational speeches

Logos: is a reasoned discourse, it relates to the speech itself and emotional appeals that have no bearing on the issue.
Logic Factual information academic situations Objective - absence of emotion. Politicians, Medical

Ethos; is persuasion through convincing listeners of one's moral character.
Ethos Relates to expertise and knowledge in a speech.
Speaker, way and power of the speaker, credibility, experience of speaker, Motivational speeches

2. The reason for this speech is that Napoleon wanted his Old Guard to know that he still held them in high regard and that he still loves France and he does the for France. He uses Pathos because he commonly references that he was with them at their battles and their wars when they won or lost.

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Soldiers of my Old Guard: I bid you farewell. For twenty years I have constantly accompanied you on the road to honor and glory. In these latter times, as in the days of our prosperity, you have invariably been models of courage and fidelity. With men such as you our cause could not be lost; but the war would have been interminable; it would have been civil war, and that would have entailed deeper misfortunes on France.
I have sacrificed all of my interests to those of the country.
I go, but you, my friends, will continue to serve France. Her happiness was my only thought. It will still be the object of my wishes. Do not regret my fate; if I have consented to survive, it is to serve your glory. I intend to write the history of the great achievements we have performed together. Adieu, my friends. Would I could press you all to my heart.