An inscription on a tombstone shared with her parents in the Maplewood Cemetery in Boscawen, Merrimack, New Hampshire says:
"Emily Maria, daughter of Charles J. and Eliza J. Chadwick, died June 27, 1858, age 2 years, 6 months"
On the other hand, the 1860 US Census lists Emily Chadwick, age 1, living with Charles and Eliza in Boscawen. It is possible that the name was reused for a second child born in 1859 after the first died in 1858.
I have found no other records for Emily Chadwick. However, an Emma Chadwick of the same age appears in the 1870 and 1880 US Censuses as living in the same household as Charles Chadwick.
Several unsourced family trees (including mine) in Ancestry.com show Emily Chadwick, born December 26, 1855, died June 27, 1868. Since the tombstone says that she was two years old when she died in 1858, this is definitely wrong.
My theory is that Charles and Eliza Chadwick named their baby girl, born in 1859, Emily at first, reusing the name of their deceased daughter, but then decided to name her Emma instead. This family was very unfortunate in that at least three of their children died in childhood. Maybe they thought that reusing the name was a bad idea after all.
I have made Emily Chadwick and Emma Chadwick Unmerged Matches. The question is whether there is enough evidence to merge them, or should I leave Emily alone and go with the dates on the tombstone and assume that Emma was the one born in 1859 that shows up in the Censuses?