Quite apart from the fact that Sir James Young Simpson did not have a son named Pin(c)kney, the dates don't fit.
Pin(c)kney Simpson married Mary Allanson in York, England in 1796, and they had three children: Pin(c)kney Allanson Simpson, born 1797; Thomas Simpson, born 1799; James Pemberton Simpson, born 1801.
Sir James Young Simpson was born in 1811, so he was 14 years **younger** than Pin(c)kney Simpson Jr.
I see that William Adamson and Jessie Simpson had a son William, born in Glasgow in 1855. If you have not already got this birth certificate, I recommend you to get it now. 1855 certificates contain a lot of information that is not collected in any other year, so they are like gold dust fo genealogy. You should be able to get the names of Jessie's parents from her death certificate, assuming that she died in Scotland.