The DANCE of VENUS, being the Figure traced by a Line joining the EARTH and VENUS over Eight Years.

Plate XLII.  Drawn to the true Periods.

Fig. 1. periods nearly as 13 : 8

Year 1, day 1

Pass the hand across the plate to turn the years back.

The orbits are here drawn as perfect circles about the Sun, which is a simplification; the periods and distances are the true mean values.

Other Pairs

Each small plate shows its figure finished. Choose one, and it is ruled afresh upon the great plate, with its ratio worked out and the number of loops foretold.

Of the Arithmetic

Take two planets and a ruler. Every few days join them with a straight line, then let them move on. Nothing else is done here. Venus completes her circuit of the Sun in 224.70 days, the Earth in 365.26, and the quotient of those numbers, 1.6256, lies very near to thirteen eighths. So while the Earth goes round eight times Venus goes round thirteen, overtaking us five times on the way, at five places set evenly about the circle. Each line falls close beside the last; where they cross, their envelope shows as a curve, and the curve has five petals.

No influence passes between the two worlds to arrange this. The rose is a fact of division, as plain as a remainder. Change the pair and the fraction changes, and with it the count of loops, which is always the difference of the two terms. Nor is the fit exact: thirteen circuits of Venus fall about a day short of eight years, so each rose lies a hair askew of the last, and none is traced twice. That a sum should prove so handsome is no reason to distrust the sum.

The Elements

PlanetPeriod, in daysDistance, Earth = 1
Mercury87.970.387
Venus224.700.723
Earth365.261.000
Mars686.981.524
Jupiter4,332.65.203
Saturn10,7599.537

Sidereal periods and mean distances from the Sun. Every figure on this sheet is computed from these twelve numbers and no others; the true orbits are ellipses, a little off-centre, and the true figures a little less tidy.