Your are correct that the tariff income in "column 1" is less than the total of Federal receipts in "column 3".
My mistake.
But if you'll do the math, you'll see that tariff income generally amounted to 95% of total receipts, and that every statement made about those total receipts is also true of tariff income.
So your conclusion, "that makes all of your assertions and conclusions invalid," is false.
My point was that over the decades before 1860, tariff rates went up and down, responding to political pressures, that when they went up tariff income fell or grew more slowly than when rates went down -- a lesson with some application to our current political debates.
In 1860 tariff rates of 15% were as low as they had been in 1792, when George Washington was President.
Correction:
Actually, the math is posted right there, in "column 2", and does sometimes reach 95% of total revenues, but in a few years falls to around 50%.
So comparing tariff rates to just tariff revenues does not give us the consistent result of "lower rates produce higher revenues."
But those were the results in 1795 and again throughout the 1850s.
In other years when tariff rates went down significantly (1815, 1835), tariff income fell only slightly.
The big exception is 1840, when both rates and income fell significantly.
No doubt the reasons involve political and economic complexities of that particular age.
Of course, I like "lower rates produce higher revenues" better, and that was one of my points, but obviously a strong and growing economy is also necessary.
One should never read this data to suggest that it's a good idea to raise taxes in the teeth of an economic downturn.
You said: “Your (sic) are correct that the tariff income in column 1 is less than the total of Federal receipts in column 3. My mistake.”
Well, your mistake was in quoting tariff revenue from the wrong source. You then spent time making several mathematical assumptions and calculations on false data that then led you to say:
“So the take-away here is that a lot of political philosophising (sic) over the “injustice” of high tariffs did not correspond to the actual tariffs then in effect.”
So, as you see, based on false data, your assertions and conclusions are invalid, like this that you said:
“My point was that over the decades before 1860, tariff rates went up and down, responding to political pressures, that when they went up tariff income fell or grew more slowly than when rates went down.”
You do not know that to be fact, and I can assure you that if you use the data you quoted, you are in fact wrong.