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I'm trying to understand Maxwell's "Illustrations of dynamical theory of gas" puts forward the argument of equal scattering probability. The area between the spherical zone is not very clear. How does one arrive at that particular derivation?

How did he arrive at $$\frac{1}{2}\sin \phi d \phi$$ $$2\pi \sin \phi d \phi$$ ? Please help.


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    $\begingroup$ Please type out the relevant sections of text. Images can't be accessed for certain people. $\endgroup$ – Aaron Stevens Aug 20 at 20:54
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    $\begingroup$ Is your confusion related to the fact that he's using the mathematician's convention for polar coordinates ($\theta$ for azimuthal angle and $\phi$ for polar angle) rather than the physicist's convention ($\phi$ for azimuth and $\theta$ for polar)? $\endgroup$ – jacob1729 Aug 20 at 21:04