For a spray $S$ on the total space of the tangent bundle we consider a variation of integral curves. The vector field of variation satisfies a kind of Jacobi equation in that appears the curvature of the nonlinear connection induced by $S$. A global form for the Berwald connection associated to a nonlinear connection is given. This is useful in study of the horizontal curves and in variation of such curves. When $S$ is provided by a linear connection $\nabla$ the vector field of variation is just the Jacobi vector field for $\nabla$