Answer: They varied in order for him to gain the support of the people he was speaking to.
Explanation:
In the beginning of Act III, Mark Anthony tells Brutus and Cassius that he supports what they did by killing Caesar. The goal of this was to get on their good side which he did and it allowed him to ask to give Caesar's eulogy which Brutus then acceded to.
When left alone with the body of Caesar, he vows revenge which shows that his support of the conspirators was a farce.
In the eulogy, he gives a rousing speech that enrages the crowd to seek revenge for Caesar by reminding them of the good work that he did. This causes them to go on a rampage and look for those who killed Caesar thereby prompting Cassius and Brutus to escape the city.
Mark Anthony did that to fulfil his promise to Caesar that he would avenge him. This promise was totally fulfilled when he joined forces with Octavian and Lepidus to defeat Brutus and Cassius and kill them and their supporters.
