Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerian orbital elements. We give here the corresponding time elements in terms of rectangular coordinates. Extensive references are given in the previous paper and will be omitted here. We present additional numerical experiments comparing the use of time elements and time transformations together with the use of time transformations alone. The results indicate a reduction in computational error when time elements are used.