The following is a quote of The Triumph of Injustice by Saez and Zucman.
According to the Constitution, direct taxes had to be apportioned among the states according to the population of each state. For example, if 10% of the US population lived in the state of New York, 10% of tax revenue had to come from there—even if a third of national income was earned in that state (which was roughly the case at the end of the nineteenth century), and even if most taxable individuals (those earning more than $4,000) lived there. Neither the 1894 income tax nor the one of 1862 were apportioned among the states, because apportioning them would have been nonsensical: it would have forced the government to tax the rich very little in the states where they were over-represented (such as New York), defeating the whole purpose of progressive income taxation.
I don't understand how this apportioning would be implemented, if the original tax would be a percentage on the upper tiers of incomes. Maybe I'm just not understanding the English here...