One of the principal functions of air traffic control is to ensure that aircraft do not conflict, that is, do not approach each other sufficiently close to give rise to the possibility of collision. (Another function of air traffic control is to ensure that aircraft do not conflict with terrestrial objects, but this is outside the scope of this paper except in so far as such objects can be treated as aircraft with zero velocity.) The ‘possibility of collision’ is, of course, a matter for definition. It is often treated as an approach within 5 miles in plan and 500 or 1000 ft. in height (Fig. 1). The definition must depend upon the form of the aircraft track information available to the air traffic service—essentially flight plans updated by pilot reports—or the radar observations with which this paper is primarily concerned.