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A diagram in a book I have places Archaic and Proterozoic under "eras".
Is such naming correct? ICS says they are eons, so do most sources I could find, but a 1979 volume of "Treatise on Invertebrate Paleontology" seems to name at least Proterozoic as an era.
Is applying the term "era" here en error? Obsolete usage, once popular, but now generally abandoned? Or perhaps a rare, but correct and accepted, convention?
It is and is not an an error depending on how it is used. They are Eons but in older literature they were also, sort of, eras as the Eons were not subdivided as they are now. Especially in literature dealing with the transitions they might refer to them indirectly as eras, such as "In the previous Proterozoic era", proterozoic being possessive. At the time this was technically sloppy but not a big issue, but now that they are subdivided this would be incorrect to do now.
You also have the issue of plurality in older literature. Spelling can vary from country to country and Paleontology is very much a international discipline. Occasionally in older literature Era can sometimes be used as the plural for Era (like sheep and sheep), so a reference to the Proterozoic era may be referring to the multiple eras in the Proterozoic. Again technically sloppy but in the time before electronic word processing a spelling error that might be ignored.
in a time scale they be grouped with era, as eons were often not included, and again they had no named eras in them. If the diagram included eons however this would be incorrect, but was sometimes done to conserve space since otherwise you would have a large blank section in all the smaller subdivisions to make room for fitting them in the eons, technically wromg but often ignored.
Without knowing the context of usage it is hard to say whether it is an error.
