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The Coriolis acceleration is known for ages, much before vectors started to be used. Even at the time when Gustave Coriolis was working, vectors were not well established as they are today. Nowadays, everyone uses vectors to derive the Coriolis acceleration, but how was it derived before, when vectors were still not used as they are now? Was it derived at all or the term was only empirically deduced and used for calculations?

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    $\begingroup$ The derivation is easier in some ways if you don't use cryptic vector calculus notation. It doesn't need anything more advanced than $x = r \cos\theta$, $y = r \sin\theta$. $\endgroup$
    – alephzero
    Jul 30, 2019 at 19:53
  • $\begingroup$ @alephzero Yes, that's basically what was done before vector notation (except Coriolis works in 3D, so he also has a $z$). $\endgroup$
    – Geremia
    Jul 30, 2019 at 20:07

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Coriolis's original paper is:

(cited in: Assis, André K. T. Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force. Montréal: Apeiron, 2014, p. 205 & 521.)

You can see that instead of cross product notation, he writes out all the components; and instead of vector notation, he writes three equations for $x$, $y$, and $z$.

(cf. Crowe's History of Vector Analysis)

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