Answer to the Question; to what half of the 19th century does the year 1850 belong?
The first fifty years being the first half of the 19th century,
it is evident that the year 1850 belongs to that half.
[But the author, A. Darlington, goes on to say the Chinese have a different method of computing time, according to which 1850 would be in the latter half of the 19th century. He concludes, though, that the opening statement is correct.]