Answer:
In chapter four, Mills explains how virtue in the end is desired once virtue composes a part that leads to happiness.
Explanation:
Mills is not contradicting the idea of happiness as the ultimate desire, since, in this chapter the author mentions that utilitarianism is valid, because it leads to the fact that something is desirable just because of someone desires it. He says happiness is considered a common good since everyone desires his own happiness. Therefore, happiness is considered a morality criteria.
Mills also explains that happiness is composed by several different parts and that one of those is virtue, that is not commonly desired by itself, but it is desired because it leads to happiness being one of the components. So, as virtue makes part of happiness, utilitarianism considers that virtue must be developed in order to achieve happiness as an end.