If my memory serves me correctly, the Artillery were the first regular Army Unit raised towards the end of the 100 years war as the most Honourable Companie of Artillerie and it still exists as a Territorial Army Unit - The HAC.
I believe the (Royal) Engineers were the second regular Army Unit raised, Royal in brackets because they were not given a Royal charter for a few hundred years.
There is also the rumour that the Royal Artillery lost its blue lanyard to the Royal Engineers as a result of an Artillery unit running from it's guns in the face of the enemy, apparently a Royal Engineer unit rescued the guns, thus resulting in the Artillery being told to wear a yellow lanyard to signify cowardice. The rumour appears to be unfounded, but it is always a good reason for the 2 Corps to have a punch up.
No. The Royal Engineers adopted their lanyard in the 1950's to "brighten up their battledress". The tall tales about them being awarded an Artillery lanyard are just that, tall tales and leg pulling.
The Royal Artillery had 3 group divisions in 1899 : The Royal Horse Artillery with 21 batteries, The Royal Field Artillery with 95 batteries which was one group, The Royal Garrison Artillery which included the coastal defense, the siege, mountain and heavy batteries which was another group. The Royal Artillery was the third group.
Royal Artillery was created in 1722.
Royal Horse Artillery was created in 1793.
Royal Australian Artillery was created in 1901.
Royal Artillery Memorial was created in 1925.
Royal Irish Artillery was created in 1755.
Royal Monmouthshire Royal Engineers was created in 1539.
P Battery Royal Artillery was created in 1805.
Royal Canadian Horse Artillery's motto is 'Ubique'.
K Battery Royal Artillery was created in 1809.
The motto of Royal Canadian Horse Artillery is 'Quo fas et gloria ducunt'.