With the aid of a slide rule, abacus, calculator and many pieces of paper
We have the following senario:-
James Sneddon (1788) and David Sneddon (1794) are brothers.
James (1788) marries Rachel Burt and they have a daughter Helen (1811) who marries James Mitchell Snr and they have a son James Mitchell Jnr (1831)
James (1788) and Rachel Burt also have a daughter Ann (1809) who marries Richard Sneddon and they have a daughter Margaret (1837)
David (1794) marries Jane Kyle and they have a daughter Ann (1820)
When Helen (1811) dies James Mitchell Snr marries Ann (1820) his first wife's cousin.
I have uploaded The m.c. of James Mitchell and Ann Sneddon as interestingly it is shown that James is marrying his first wife's cousin! I've not seen that before.
Are you following this so far
Then James Mitchell Jnr (1831) marries Margaret (1837) and they have a son James Mitchell Jnr. Jnr.(1856)
So back to the signature on the d.c. of Jane Kyle. It is James Mitchell Snr shown as son in law (Jane Kyle is his second wife's mother)
When James Mitchell's second wife, Ann dies, the informant is James Mitchell Jnr. Jnr.(1856) shown as grandson.
He is really the first wife Helen's (1811) grandson, but what the heck, I'm sure Ann treated him as her own, after all they were related!!!
PHEW
Best wishes
Jean