A time scale is any nonempty closed subset of \({\mathbb R}\). The time scales calculus unifies and extends the usual differential (\({\mathbb T}={\mathbb R}\)) and difference (\({\mathbb T}={\mathbb Z}\)) calculus. This paper studies the Cauchy function for an \(n\)th order linear dynamic equation on such a time scale. After introducing the basic concepts of the time scales calculus, several important results on the (time scales) exponential function for the first order dynamic equation \(y^\Delta=p(t)y\) are recalled. In particular, the \(rd\)-continuity and regressivity of the coefficient \(p(t)\) imply that the exponential function is real valued and nonzero. The Cauchy function and several other desirable results are then obtained, including the variation of constants formula, Abel's formula for Wronskians of solutions, and the Cauchy function for a factored equation. However, a restrictive assumption that ``every point in our time scale \({\mathbb T}\) is isolated'' brings the problem into a class of the (possibly variable stepsize) difference equations. The reviewer notes that the Abel's formula for a general (time scales) \(n\)th order linear dynamic equation is derived in the paper of \textit{L. H. Erbe, R. M. Mathsen} and \textit{A. Peterson} [Factoring linear differential operators on measure chains, J. Inequal. Appl. 6, No.3, 287-303 (2001; Zbl 1001.34029)], and the Cauchy function with the variation of constants formula for the second order linear dynamic equations appears in the book of \textit{M. Bohner} and \textit{A. Peterson} [Dynamic equations on time scales. An introduction with applications. Birkhäuser, 85-87, 334-335 (2001; Zbl 0978.39001)].