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The phrase "a third experiment in" is correct and usable in written English.
It can be used when referring to a series of experiments, indicating that this is the third one in that series or context.
Example: "In our research, we conducted a third experiment in the series to further investigate the effects of temperature on enzyme activity."
Alternatives: "the third trial in" or "a third study on".
Exact(6)
This was replicated in a third experiment, in which pupil size was measured as a physiological marker of alertness.
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.
Although bees show lateralized visual responsiveness [21], we were able to exclude visual lateralization as a factor contributing to our results by a third experiment, in which droplets on the needles of syringes were presented simultaneously on both sides of the bee, one droplet being distilled water only and one containing the odour.
We also discuss results from a third experiment, in which field crickets (Gryllus alogus) and wolf spiders (Hogna antelucana) were switched from a depleted water source to an enriched water source under several controlled temperatures and humidities, but without controlling the mix of the two sources.
We ran a third experiment in which we used morphing to directly manipulate distance-to-mean while minimizing short-term adaptation effects by equating average distance-to-preceding-stimulus across conditions (Supplemental Experimental Procedures).
We performed a third experiment in which protein was fixed at 30% and the foods differed in their fat carbohydrate ratio (foods X, Y, and Z, Table S3, Supplementary Data).
Similar(54)
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 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.
We then conducted a second experiment in which rhizoboxes were free of beads (data not shown).
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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