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The phrase "a second experiment in" is correct and usable in written English.
It can be used when referring to a follow-up or additional trial in a specific area of study or practice.
Example: "The researchers conducted a second experiment in the field of renewable energy to test their new hypothesis."
Alternatives: "a follow-up experiment in" or "an additional experiment in".
Exact(45)
Zuckerman, Hahl, and Kim then set up a second experiment in a similar way to the first.
To start a second experiment, in the hopes of counteracting the first, would be, to put it mildly, rather risky.
To start a second experiment in the hopes of counteracting the first would be risky, to put it mildly.
To figure that one out, we conducted a second experiment, in which investors faced the same choices as in the trust game.
To check that iron really was the culprit, they ran a second experiment, in which they tampered with the wines and retested them.
Much the same effect was seen in a second experiment, in which dosing did not start until the mice were middle-aged, except that cataracts that had already formed could not be reversed.
Similar(15)
We tested this 'desperado hypothesis' in a fourth experiment, in which losers were offered alternative options.
This was replicated in a third experiment, in which pupil size was measured as a physiological marker of alertness.
To verify that the results were specific to video game playing and not due to the use of the eye patch, the researchers conducted a third experiment in which seven participants wore a patch over their good eye for 20 hours during their normal daily activities, such as watching television, reading books and surfing the Internet.
a Third experiment in 1997, b second and third experiments in 2000, c fourth experiment in 2000, d first experiment in 2003, e first experiment in 2004, f first and second experiments in 2006.
In 2009, Pederson and Ko teamed up with radiologist Thomas Vogl at the University Hospital Frankfurt in Germany for what appears to be a first experiment in a single patient.
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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