Furthermore, none of these three terms can be altered without the equality being instantly destroyed. If the Sovereign desires to govern, or the magistrate to give laws, or if the subjects refuse to obey, disorder takes the place of regularity, force and will no longer act together, and the State is dissolved and falls into despotism or anarchy. Lastly, as there is only one mean proportional between each relation, there is also only one good government possible for a State. But, as countless events may change the relations of a people, not only may different governments be good for different peoples, but also for the same people at different times.

In attempting to give some idea of the various relations that may hold between these two extreme terms, I shall take as an example the number of a people, which is the most easily expressible.

Suppose the State is composed of ten thousand citizens. The Sovereign can only be considered collectively and as a body; but each member, as being a subject, is regarded as an individual: thus the Sovereign is to the subject as ten thousand to one, i.e. each member of the State has as his share only a ten-thousandth part of the sovereign authority, although he is wholly under its control. If the people numbers a hundred thousand, the condition of the subject undergoes no change, and each equally is under the whole authority of the laws, while his vote, being reduced to one hundred thousandth part, has ten times less influence in drawing them up. The subject therefore remaining always a unit, the relation between him and the Sovereign increases with the number of the citizens. From this it follows that, the larger the State, the less the liberty.

When I say the relation increases, I mean that it grows more unequal. Thus the greater it is in the geometrical sense, the less relation there is in the ordinary sense of the word. In the former sense, the relation, considered according to quantity, is expressed by the quotient; in the latter, considered according to identity, it is reckoned by similarity.

Now, the less relation the particular wills have to the general will, that is, morals and manners to laws, the more should the repressive force be increased. The government, then, to be good, should be proportionately stronger as the people is more numerous.

On the other hand, as the growth of the State gives the depositaries of the public authority more temptations and chances of abusing their power, the greater the force with which the government ought to be endowed for keeping the people in hand, the greater too should be the force at the disposal of the Sovereign for keeping the government in hand. I am speaking, not of absolute force, but of the relative force of the different parts of the State.

It follows from this double relation that the continuous proportion between the Sovereign, the prince and the people, is by no means an arbitrary idea, but a necessary consequence of the nature of the body politic. It follows further that, one of the extreme terms, viz. the people, as subject, being fixed and represented by unity, whenever the duplicate ratio increases or diminishes, the simple ratio does the same, and is changed accordingly. From this we see that there is not a single unique and absolute form of government, but as many governments differing in nature as there are States differing in size.

If, ridiculing this system, any one were to say that, in order to find the mean proportional and give form to the body of the government, it is only necessary, according to me, to find the square root of the number of the people, I should answer that I am here taking this number only as an instance; that the relations of which I am speaking are not measured by the number of men alone, but generally by the amount of action, which is a combination of a multitude of causes; and that, further, if, to save words, I borrow for a moment the terms of geometry, I am none the less well aware that moral quantities do not allow of geometrical accuracy.

The government is on a small scale what the body politic which includes it is on a great one. It is a moral person endowed with certain faculties, active like the Sovereign and passive like the State, and capable of being resolved into other similar relations. This accordingly gives rise to a new proportion, within which there is yet another, according to the arrangement of the magistracies, till an indivisible middle term is reached, i.e. a single ruler or supreme magistrate, who may be represented, in the midst of this progression, as the unity between the fractional and the ordinal series.

Without encumbering ourselves with this multiplication of terms, let us rest content with regarding government as a new body within the State, distinct from the people and the Sovereign, and intermediate between them.