These divisions of the pinnae are called pinnules.
"The Fern Lover's Companion" by George Henry Tilton
Branches simple, 2 to 3 inches long; pinnules about 1/4 inch.
"Narrative Of The Voyage Of H.M.S. Rattlesnake, Commanded By The Late Captain Owen Stanley, R.N., F.R.S. Etc. During The Years 1846-1850. Including Discoveries And Surveys In New Guinea, The Louisiade Archipelago, Etc. To Which Is Added The Account Of Mr. E.B. Kennedy's Expedition For The Exploration Of The Cape York Peninsula. By John Macgillivray, F.R.G.S. Naturalist To The Expedition. In Two Volumes. Volume 1." by John MacGillivray
All the Palaeozoic representatives have non-pinnulate arms, while the Mesozoic and later forms have them pinnulate.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 10" by Various
Its value was much impaired by his preference of the antique "pinnules" to telescopic sights on quadrants.
"Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 4" by Various
Midrib of the pinnules marginal or none.
"The Manual of the Botany of the Northern United States" by Asa Gray