The 9th Mississippi Cavalry was formed by consolidating the 17th Battalion Mississippi Cavalry with the 17th Battalion Tennessee Cavalry, and with Capt. C. A. Jennings' Independent Company of Cavalry.
I could not find a listing for Henry C. Ball in either the 17th Battalion Mississippi Cavalry or the 9th Mississippi Cavalry.
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The gravestone inscription of Henry C. Ball does not say 24th Mississippi Infantry.
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The CMSR of H. C. Ball of the 15th Confederate Cavalry does not list his age, nor his enlistment date. In a previous post George Martin transcribed for you all of the information found in his CMSR.
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The 9th Mississippi Cavalry was not associated with the 15th Confederate Cavalry.
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Have you checked the pension index to see whether or not Henry C. Ball applied for a pension? I would certainly suggest that you check.
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Regards--