Any advice on whose this autograph might be?
It is Maj Gen and US Representative Henry Warner Slocum.
He was a major general in the Union Army during the civil war, and later a member of the House of Representatives, representing New York's 3rd District from 1869 - 1873.
He died in 1894.
Well done SD!
Thank you all, but in all honesty, this one wasn't particularly difficult; it took less than a half hour to figure out.
First, looking at the letterhead of the paper told me that it was from the House of Representatives in Washington DC during the 1860s. The date is written Apr 8, 186_.
The date rang a bell with me. Apr 8, 1865 was the day of the Battle of Appomattox Station. The following day, Apr 9, was the day of the Battle of Appomattox Courthouse, and the Confederacy's surrender (General Lee surrendering to General Grant). "The Pen is mightier than the Sword", in that the pen ended the war that the swords could not.
So, from this, I figured that the signature was from a member of the House of Representatives at some point in the late 1860s, or possibly 1870.
Looking at the signature, I picked out the middle initial "W" to focus on. So, I went to wikipedia, and searched the membership listings for each congress during the 1860s, focusing on those members who had a middle initial of "W". That led me to the 41st Congress which met from March 1869 - March 1871, where I found Henry W. Slocum listed. The signature looked like it might be that, so I went to ebay, and found a few documents signed by Slocum, showing his signature on them matched the signature in the OP.
And that's how it's done!