My list comes from
"Table D.- Exhibit of the number of organizations-volunteers and militia-organized and mustered into the service of the United States during the rebellion-Contintued. O.R.
Lets look at Maryland.
You have 46,638, (I don't know your source)
The U.S. Army says Maryland contributed 18 regiments of infantry, 5 independent companies of Infantry, 1 regiment of Cavalry, 9 independent companies of Cavalry, 5 light companies of Artillery to the United States armed services during the entire war. Lets be conservative and say on this list a regiment is 1000 men, and a company 100. Now we know these numbers were higher or lower according the day of roll call, but over a four year period it averages out to my round numbers. The total would be about 20,900 men.
I said Tennesee contributed 16 regiments of Infantry, 12 regiments of cavalry, 3 independent companies of cavalry, and 1 regiment of light artillery. My rounded off numbering system would put that at about 29,300 men, still higher.
These numbers are probably the most, at any given time during the war, Tennessee and Maryland could ever have in the field, if they ever did. Your numbers, especially Maryland's are higher than my estimation. This is probably due to rotations of troops through these units if your source is correct. Your numbers maybe all the troops ever drafted or enlisted during the war. Except for Vermont, West Virginia, New Hampshire, and Maryland; Tennessee is still higher. The populations of the states is somewhat important, but due to fluxuations from 1860-1870 its very had to make a determination of ratios. I believe about one fourth of Tennesseans considered themselves Unionist (correct me Mr. Turchin). That would be from a total population about 208,520 (using your census data) to pull into the Union army your number of 31,092. Thats 14% of the total Unionist pop. and it may be higher. New Hampshire's 33,937 from a total pop. of 326,073 is about 10.4%. That is remarkable.
But something's wrong with your census and military numbers.
You have Kansas total pop. 107,204 and it contributed 20,149 to military or 18.7% of the total pop. Thats 1 person in five, of every woman, child , and free person of color and old person in that state. The census shows that the total population of white males ages 20-29 was 14,180, ages 30-39 9,241, or about 24,000 men of military age. The numbers show that would have been impossible to field 20,149 men. I have Kansas possibly contributing 17,400 men at its highest and thats 16%. But keep in mind that Kansas grew in ten years from 107,000 to 364,000 or a growth of 239%; Tennessee only grew 13% in its total white population in ten years. So we don't know how much the population was during the war years and your census covers ALL free peoples not free white peoples so your census numbers are off and in some states WAY off. My regimental counts are for whites only. All in all Tennessees numbers are eye opening because its numbers are higher than the majority of the "Union" states and territories.