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This Japanese novel is centered around isekai, where the main character reincarnates into a noble house and becomes engaged to a fiancée. However, after being deemed useless, he is expelled from his household and seeks refuge under his uncle's care. An invention soon follows; the main character creates a thermometer that can measure magic power and the amount of mana certain spells consume. The main character and his uncle decide to conceal the invention due to its potential for creating a powerful impact and shockwave on the fantasy public. I am pretty sure the thermometer isn't the only invention the mc has created, but alas, I just can't remember.

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    Should have been a "thaumometer".
    – wnoise
    Commented Sep 12, 2023 at 15:25

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You are talking about Shikkaku kara Hajimeru Nariagari Madou Shidou!, translated in English as The Magician Who Rose From Failure.

Several weeks after Arcs Reytheft is disqualified from inheriting the title of viscount, he has a peculiar dream where he had the vicariously experience of the life of another man. The man was living in a world completely different from the one he was living now. He was born in a normal household and had passed due to an accident. Waking up, Arcs decides to make use of those memories to hone his world's magic, all to triumph over his parents who viewed him as useless and regarded him with disdain.

Though he was born as the eldest son of a noble family, he was disinherited due to his lack of magic aptitude. This is the story of his rise in a fantasy world as he makes use of the knowledge of the man who's life he vicariously experienced.

In the official translation for the light novel, the aethometer is created in page 56 of the first chapter of the first volume.

Excerpt from page 57, where aetherometer is first mentioned:

That night, Arcus stayed up researching Sorcerer's Silver and its transformation until dawn. His research confirmed his hypothesis: by exposing Sorcer's Silver to hot aether, it became aetherically reactive. By all accounts, creating a device to measure magic power (which Arcus dubbed an aetherometer) should work.

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