Discovery of the comet and of its periodicity by D'Arrest–Return predicted by M. Yvon Villarceau for 1857 ; verification to within half a day–Importance of the perturbations caused by Jupiter–Research of MM. Yvon Villarceau and Leveau –Return of the comet in September 1870.

Here, again, we have a periodical comet whose periodicity has been determined by calculation, and whose returns have been predicted and observed without the help of any comparison with previous comets. It bears the name of the astronomer who discovered it in 1851, and who recognised the periodicity of its orbit. M. Yvon Villarceau had drawn the same conclusion, and calculated the ephemeris for its next return to perihelion, which he announced for the end of 1857, a prediction verified to within twelve hours. The new comet was seen again at the Cape of Good Hope by Sir Thomas Maclear. On its following return, which took place in 1864, astronomers were less fortunate, and were unable to perceive the comet, whose position in the heavens and distance from the earth were very unfavourable. In 1870 the perihelion passage of the comet took place on September 23; it was observed three weeks before by M. Winnecke, thanks to the ephemeris calculated by MM. Yvon Villarceau and Leveau.

‘Of all the comets which have not failed to return to us,’ says M. Yvon Villarceau, ‘ the comet of D'Arrest is perhaps the most interesting in regard to its perturbations. T do not thinkthat any other comet has been so closely followed by Jupiter.’