it had grown to 413 millions; after that terrible rising it sunk
to 261 millions.

I do not think such definite statements are warranted. The China Year
Book for 1919 (the latest I have seen) says (p. 1):--

The taking of a census by the methods adopted in Western nations
has never yet been attempted in China, and consequently estimates
of the total population have varied to an extraordinary degree.
The nearest approach to a reliable estimate is, probably, the
census taken by the Minchengpu (Ministry of Interior) in 1910,
the results of which are embodied in a report submitted to the
Department of State at Washington by Mr. Raymond P. Tenney, a
Student Interpreter at the U.S. Legation, Peking.... It is
pointed out that even this census can only be regarded as
approximate, as, with few exceptions, households and not
individuals were counted.

The estimated population of the Chinese Empire (exclusive of Tibet) is
given, on the basis of this census, as 329,542,000, while the population
of Tibet is estimated at 1,500,000. Estimates which have been made at
various other dates are given as follows (p. 2):

A.D. A.D.
1381 59,850,000 / 143,125,225
1412 66,377,000 1760--203,916,477
1580 60,692,000 1761 205,293,053
1662 21,068,000 1762 198,214,553
1668 25,386,209 1790 155,249,897
/ 23,312,200 / 307,467,200