Some of the symbols used in that time would be tricky to type in Latex, so instead of writing an explanation here, I hope it is okay to just give a reference. There are two books by Florian Cajori, "A History of Mathematical Notations: Vol. I and II", which are a good reference for this specific kind of question. Cayley's and related notations on determinants and n-ary forms can be found in vol II, starting at page 87, particularly look at page 94.