John Benjamin Tolkien (b. June 1752 in Gdańsk, d. 1819 in London) was born in the beginning of Summer 1752. I have found this document which tells us about the weather in Gdańsk in the first days of little John's life (his namesake and great-great-grandson was John R.R. Tolkien!). This is part of Wetter-Beobachtungen vom 2 May 1744 bis zum 31 Dezember 1760 by Carl Gottfried Minior (written in the years 1744-1784). Whole text can be found here.
And this is a calendar page with the days of John Benjamin's birth and baptism:
Here John Benjamin's record from the church book of St Salvator in Gdańsk: