The orbit of P / Encke during the whole of the comet's observed history, 1786-1971, is investigated on a uniform basis. Full perturbations by all nine planets are included, and the nongravitational secular acceleration is allowed for by means of the procedure discussed in Paper V of this series. It is confirmed that the secular acceleration (or, equivalently, the transverse nongravitational parameter A 2) has been decreasing since the early part of the nineteenth century, and it is shown that the decrease seems generally to have been remarkably smooth. An important new result is that the secular acceleration evidently attained a maximum around the year 1820, the curve being strikingly symmetrical on each side of this maximum: the physical implication of this is briefly considered. Dates of perihelion passage (on two assumptions concerning the secular acceleration) are calculated back to the year 1570, and predicted elements are provided for the returns 1974-1984.