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Alan, You sound much more of an expert than me and it may be that the National Army Museum have this wrong, but they describe the 40th as being amalgamated with the 82nd to form the South Lancs. See their webpage on this here:https://www.nam.ac.uk/explore/40th-2nd-somersetshire-regiment-foot#:~:text=This%20infantry%20unit%20was%20formed,Volunteers%20(South%20Lancashire%20Regiment).
According to the National Army Museum, the 13th Foot was a different regiment (designated Light Infantry after the Napoleonic Wars and later titled the Somerset Light Infantry). The 13th wasn't at Waterloo (being in Canada). It wasn't amalgamated under Childers but was amalgamated with the Duke of Cornwall's Light Infantry in 1959, later becoming part of the Light Infantry and then part of the Rifles. See here for the separate webpage:https://www.nam.ac.uk/explore/somerset-light-infantry-prince-alberts.
The twists and turns of individual regimental histories is terribly confusing so I could easily be wrong!
Another source is the Wiki page on the Childers reforms which shows that the 13th and 40th were different regiments and never amalgamated:https://en.wikipedia.org/wiki/Childers_Reforms
Since reading your posts above I have speed read lots and must confess, my memory/recall has been at least in part at fault, but it is interesting that different source material seem to have some information at least confusing erring to incorrect eg Mark Adkin and others refer to 1/40 in the Waterloo companion, you refer to them as 2/40 , other sources ,Somersets 1/13 and second battalion of Somerset's as 2/40. I will when time allows to re read my learning because there is information I have read in the distant past I cannot lay my hands on/remember the source.
I don't blame you Alan and I'm sure I can think of one mistake by me, namely to call them 'South' Somersets - not sure where I got that from!
The main point is that there were two Somerset regiments - the 13th and 40th, one of which had the subsidiary name '1st Somersets' and the other '2nd Somersets'; this could easily confuse the reader into believing that this was a battalion rather than regimental number.
The two regiments has thrown me, because there is a third, not linked to Waterloo or the Napoleonic to my knowledge , my other granddad served in WW1 with...the Somerset yeomanry a territorial cavalry unit. Back to the subject Ian Fletcher in Wellingtons Regiments refers to them as 2/40 ,so we have two respected authors on the subject not agreeing. It is a long time ago I read all I could lay my hands on regarding Waterloo , Wellington ,Napoleon etc, but for my own clarity I am planning another trip to the museum and to ask some questions, assuming they have someone there not using the same source material as us ;-) .
The 40th (2nd Somersets) had a second battalion for a while but it was disbanded. It was the 1st Battalion at Waterloo. You might therefore say they were the 1st/2nd/40th!