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The phrase "a third experiment was" is correct and usable in written English.
You can use it when introducing or discussing a specific experiment in a series of experiments or studies.
Example: "In our research, a third experiment was conducted to further investigate the effects of the new drug."
Alternatives: "the third experiment was" or "we conducted a third experiment".
Exact(15)
To probe the kinetics of protein exchange between BTA fibers, a third experiment was done where we prepared separate BTA polymers that were functionalized with either the enzyme or the inhibitor protein (Fig. 4c).
A third experiment was carried out (n=2×20) in which no pre-test was given while, other than that, Experiment III was identical to the first two experiments.
To this end, a third experiment was made to find an optimal system design size.
Two experiments were carried out indoor with artificial light, while a third experiment was carried out outdoor in daylight.
So, a third experiment was devised, the express intention being to show not just a correlation between Need for Uniqueness and Conspiracy Mentality, but also that this in turn varied according to whether a specific conspiracy theory was presented as a minority or majority view.
A third experiment was conducted to investigate the therapeutic capacity of MY-24.
Similar(45)
A first experiment was conducted in August 2013.
A second experiment was aimed at determining whether computer accessibility affects precisely what we remember.
A second experiment was designed to gauge people's memories when they weren't being asked to remember anything.
A second experiment was conducted where noise sensitivity was used as an inclusion criterion.
A second experiment was designed with SOA varied between three groups (23, 58, and 117 ms).
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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