Achilles and the Tortoise

Abstract

THE statement of Group-Captain G. S. Roberts, that the first equation in my letter to NATURE to which he refers "is not altogether accurate", would appear to mean that it does not cover the general case of a tortoise with any possible start. It was made clear in my letter, however, that this equation applies only to the case of a tortoise with a specified start, namely, 10 units of distance. In this particular case I showed how it was possible, by a special adjustment of the ratio p/λ, to secure the result that Achilles would overtake this particular tortoise only in an infinite time. Given this particular (adjusted) value of p/λ, it follows that, for tortoises travelling according to the same law of speed, those with a start of less than 10 will be overtaken in a finite time, whereas those with a start of greater than 10 would not be overtaken by Achilles even in an infinite time.