Natural transformations of higher order cotangent bundle functors

We determine all natural transformations of the rth order cotangent bundle functor ${\displaystyle T^{r\cdot }}$ into ${\displaystyle T^{s\cdot }}$ in the following cases: r = s, r < s, r > s. We deduce that all natural transformations of ${\displaystyle T^{r\cdot }}$ into itself form an r-parameter family linearly generated by the pth power transformations with p =1,...,r.