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The phrase "second usage of" is correct and usable in written English
It is typically used to refer to the second instance of using something. For example, "This is the second usage of the machine since its installation."
Exact(3)
The Court found the second usage of the word to constitute racial abuse.
The current incarnation of M-186 is the second usage of the designation.
A second usage of M-91 was designated from Rogers City towards Cheboygan County along the Lake Huron shore by 1930.
Similar(57)
The O.E.D. gives the first usage of the word "list" as appearing in "Hamlet" — Fortinbras is said to have drawn up a "list of lawelesse resolutes".
The O.E.D. has the first usage, of course, crediting the coiner Frank Mankiewicz cited in this column in 1980 for what I defined as "nouns that have taken an adjective to stay up to date and to fend off newer terms".
It was the first usage of Tunisia's new "anti-terrorist law", widely condemned by rights groups when it was passed in July 2015 in the wake of two terrorist attacks, because of its vagueness.
The third usage of the abstract geometry description is for the automated routing of the harness cables that is presented.
The first usage of the term "computational topology" appears to have occurred in the dissertation of M. Mantyla.
To our knowledge, it is the first demonstrated combination of deep learning and Nexting with general value functions and also the first usage of deep learning for laser welding specifically and production engineering in general.
The first usage of "gastroenteritis" was in 1825.
The episode contains the first usage of the word "meh" in the show.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com