Any magistrate in government will have to exercise three different kinds of will: his individual will that pursues his own interests, the corporate will that expresses the will of the government, and the general will that expresses the will of the people as a whole. The fewer magistrates there are, the more the corporate will shall resemble particular wills, and the stronger and more active relative to the people it will be. With a great many magistrates, the corporate will shall resemble the general will, but it will also be relatively weaker and less active. In a large state, where a strong government is needed, fewer magistrates are desirable.
The first two books of The Social Contract deal with the abstract level of political right. In those books, Rousseau explains the principles according to which a republic that upholds freedom and equality might exist. He concerns himself there with the sovereign and with laws, both of which apply generally to all people equally and at all times.
In Book III Rousseau makes the transition from abstract to practical and from legislative to executive, discussing how a republic should be governed rather than the principles on which it should be founded. Instead of discussing a sovereign or laws that are general and apply to all, he discusses a government that is made up of a select group of magistrates and that exercises power in particular cases.
Rousseau's distinction between will and strength is closely linked to the distinction between force and right. In the first two books, he deals with will and right: he discusses simply how things ought to be, how we should will them to be. Now he discusses strength and force: how we can make things be the way we want them to be, how we can put matters into effect. On the whole, Rousseau is very careful to distinguish between force and right. A failure to do so leads to a confusion between government and sovereign, and such confusions lead thinkers like Grotius or ##Hobbes## to assert that there is a social contract binding subjects to a government of one person, who is also the sovereign. A proper distinction between force and right is necessary to grasp the subtleties of legitimate government. The importance Rousseau normally places on this distinction further highlights his own confusion of this distinction when, in Book I, Chapter 7, he insists that people who do not obey the social contract must be "forced to be free."
The discussion of the relative strengths of sovereign, government, and people can be a bit confusing. Rousseau tries to explain himself in terms of mathematical analogies whose clarity can be helpful. But, as he himself acknowledges, we won't find the precision of mathematics in moral calculations, and such precise ratios can be misleading, especially since there is no precise numerical measure for political power.
Rousseau's calculations are based on the assumption that every citizen exercises more than one kind of will. I act first and foremost in my own interests, as a single individual, and exercise a particular will. However, as a member of the sovereign, I also think and act with the general will in mind. If I am a magistrate in government, I also think and act with a corporate will, in concert with my fellow magistrates.