Baron 58/58TC
Air Traffic Control Fully Certified
ATC Issue All Types; Conflict NMAC
General None Reported / Taken
Human Factors
A Baron [was] inbound for Runway 12R on a right downwind. A Diamond departed the crossing Runway 23 for a right turn out and a northbound flight along the river. When I anticipated the Baron would be past the departure end of Runway 23; I cleared the Diamond for takeoff. The Diamond turned right early instead of continuing runway heading for a half mile this put him directly in the Baron's flight path instead of behind him. I did not notice the Diamond's early turn because I was dealing with opposite direction traffic over the river both north and southbound there were 3 northbound and 2 southbound on visual sight seeing tours going opposite direction. I was pointing out traffic to the sight seeing tours that were passing on the river; looked to see that the separation existed with the Diamond and cleared him for take off looked back to the arch to point out traffic for the sight seeing tours and the Baron called NMAC as the Diamond turned early in his face. Instead of anticipating the Diamond would continue 1/2 mile before turning as is standard; I should have clarified that he needed to continue straight out for 1/2 mile before starting his westerly turn.
Tower Controller described a NMAC between a departing aircraft and another near by aircraft. The reporter noted that more specific instructions should have been issued to the departure.