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Discover Ludwig"the second such" is correct and can be used in written English.
It is typically used to refer to a second instance of something already mentioned or implied. Here is an example: "The first time I tried rock climbing, I was terrified. However, the second such experience, I was able to conquer my fear and make it to the top."
Dictionary
the second such
noun
One that is number two in a series.
Exact(54)
It was the second such attack.
The second such "moment" came shortly after.
In the second, such DNA evidence exists and is exculpatory.
The larger Virginia Electric agreement is the second such settlement.
It was the second such attack in six months.
It was the second such reduction in a month.
It was the second such massacre in recent weeks.
It was the second such gathering in as many days.
It was the second such release in two weeks.
It was the second such resolution by the panel.
It was the second such report from CitizenLab.
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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