Caleb Ball was a millwright who learned his trade in Pennsylvania and moved with is young family to Hardin County in about 1859. He first married Harriet Arnold in Pennsylvania. Harriet died in 1865 and in 1867 Caleb then married Sidney Ann South McDonald who had been widowed during the Civil War. Died before his last son, Caleb was born.
Could possibly be the Caleb W. Ball who served in the 8th Kentucky Cavalry in 1862-3.