Sec.8.  To illustrate this rule by an example:  Suppose a state to contain 600,000 free persons, and 500,000 slaves.  Adding three-fifths of the number of slaves, (300,000) to the number of free persons, gives 900,000 as the number of the representative population:  and the state would be entitled to three representatives for every two that a state would have which contained 600,000 free inhabitants and no slaves.  So in apportioning taxes according to population, the state in the case we have supposed, would have to raise three dollars for every two that it would raise if no slaves were counted.

Sec.9.  But the advantages of this arrangement are more unequal than may at first sight appear, or than was anticipated by the framers of the constitution.  The benefits are chiefly on the side of the slaveholding states.  In the first place, two-fifths of a large class of property in these states is exempt from taxation, while all the property in the free states is liable to taxation.  Of this the framers were aware.  But they did not foresee the fact, that the laying of direct taxes would be unnecessary, and that the slave states would consequently escape taxation for their slaves.  Only three direct taxes have been laid; and it is not probable that another will become necessary; the treasury being supplied from other sources, chiefly by duties on imports.

Sec.10.  Now, although nothing is gained by the slave states, nor is anything lost by the free states, by the exemption of the two-fifths of the slaves from taxation, since direct taxes are unnecessary; there is a great gain to the slave states, which have between thirty and forty representatives for what their laws hold to be “property to all intents and purposes whatsoever,” for which the free states have nothing in return.

Sec.11.  The constitution does not limit the house to any definite number of representatives; it only declares that the number shall not exceed one for every 30,000 inhabitants.  It requires an enumeration of the inhabitants every ten years; and the next congress thereafter determines the ratio of representation and the number of representatives, and apportions them among the states.  The word ratio signifies rate, or proportion.  It here means the number or portion of the inhabitants entitled to a representative.

Sec.12.  But as a representative for every 30,000 inhabitants, after the population became very numerous, would have made the house too large to transact business with due dispatch, and would have unnecessarily increased the public expense, the ratio of representation has from time to time been increased.  But to whatever number the ratio may be raised, the constitution expressly declares, that “each state shall have at least one representative.”  Neither Delaware nor Florida had, in 1850, a population equal to the present ratio; and without the above constitutional provision, these states would have been deprived of a representation in the house, unless congress had adopted a smaller ratio.