I found a label on the accelerating wheel head and did some research. The wheel-head maker is Benjamin Pierce (1814-1899) and was manufactured in Chesterfield, NH at the Chesterfield Factory (also known as Factory Village and now Spofford Village). Pierce was known for the manufacture of bits and augers. The New Hampshire Historical Society owns a ledger and daybook of Benjamin Pierce and Old Sturbridge Village Research Library owns a Pierce daybook (1859-1866).Another bit and auger manufacturer living in Chesterfield at the time was Richard Henry Hopkins (1831-1877). Hopkins was also a wheel-head maker. It was common for Chesterfield manufacturers to combine the business of creating bits and augers with manufacturing spinning wheel-heads. The forging skills were similar. At one time Hopkins worked for and partnered with Pierce.
Apparently Pierce was selling wheel-heads manufactured by the Hopkins family and others, and eventually made by himself and his son. Around 1868 Frederick Benjamin Pierce, the son of Benjamin, joined as a partner in his father's business. This continued until Benjamin Pierce sold the bit shop to the Currier Brothers in 1882. From what I can tell it appears the elder Pierce may have continued marketing the spinning wheel-heads after he commenced manufacturing them. Pierce also manufactured spinning wheels and flax wheels.
The label reads, "Benjamin Pierce's Wheel Heads /Particular care must be taken to keep them / dry. When used they must be kept well oiled, / and when new bands are required, they must / be smooth and even. Spindles warranted steel. / by BENJAMIN PIERCE, Chesterfield Factory, N.H." I believe it was made sometime between 1853 and 1882.Wheel-heads made in Chesterfield were manufactured according to patents 1803 and 1810 owned by Amos Miner from upstate New York. Miner's 1810 patent gave him exclusive right to manufacture, or license the manufacture of, his wheels until 1824. After the expiration of the patent Chesterfield became the center of manufacturing wheel-heads in New England.
There are maker's marks on the end-grain of the table under the wheel-head. Punched twice are AWheeler and C. W. MUZZY. I found in the census some Wheeler's and a couple of Muzzy's living in Chesterfield but haven't absolutely identified them. If anyone knows for sure the spinning wheel was made at the Chesterfield Factory I would appreciate knowing. Update: After pouring over census records I believe AWheeler is Ashbel Wheeler born about 1817 and C.W. MUZZY is Carlton William Muzzy born about 1837.
The accelerating wheel-head appears to be all original even the braided corn husk bearings. I noticed the spindle is ever so slightly bent and that causes the spindle to wobble. In order to remove the spindle it looks like I would need to remove and replace the corn husks and I hate the thought of doing that if they are original. 
The accelerator head appears to be made of beech wood. 
The table is 45" x 5" x 2".
The wheel diameter is 49". The wheel looks like it is made of Chestnut. At the scarf joint you can faintly see the square headed copper nails. 
The drive cord tracks properly. I will probably remove the knot in the cord and overlap the ends and sew them together then wrap and sew the overlap to prevent fraying. That's how I learned to do it from Norman Kennedy in one of his classes. 
Today I ordered Katy Turner's book "The Legacy of the Great Wheel: Myths, History, and Traditions" from AbeBooks. I also ordered some back issues from The Spinning Wheel Sleuth that contained information about Great wheels.