THERE WERE 3 SMA ACFT IN A NIGHT TOUCH-AND-GO PATTERN. 2 HAD AN NMAC.

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AT ABOUT H10 PM MY STUDENT AND I DEPARTED NEWTON RWY 17 FOR MULTIPLE LNDGS. AFTER OUR SECOND TOUCH-AND-GO; WE HEARD NY RPT ENTERING L DOWNWIND FOR 17 AT NEWTON. BOTH PLANES COMPLETED 1 TRIP AROUND THE PATTERN WITH Y IN THE FRONT. WE WERE DEPARTING THE PATTERN TO THE W. MY STUDENT RPTED THAT WE WERE 4 MI TO THE W OF THE ARPT AND INBOUND FOR LNDG ON RWY 17. AT THIS TIME ANOTHER PLANE; Z; RPTED 8 MI N. Z RPTED A 'LONG FINAL' FOR RWY 17. I SAW Y JUST TAKING OFF RWY 17. AT THIS TIME Z RPTED THAT HE WAS ON A 3 MI FINAL AND DID NOT HAVE US IN SIGHT. I KNEW THAT Y WAS BEHIND US AT THIS TIME BECAUSE I SAW THEM TURN L XWIND AS WE TURNED L DOWNWIND. MY STUDENT HAD RPTED WHEN WE TURNED L BASE WHEN I NOTICED THAT MY STUDENT HAD NOT ALLOWED FOR ENOUGH SPACING BTWN US AND Z WHO WAS NOW ON ABOUT A 1 MI FINAL. AT THIS TIME I TOOK CTL OF THE PLANE AND EXTENDED 20 DEGS OF FLAPS AND DID SOME SHALLOW S- TURNS TO PROVIDE THE NECESSARY SPACING. WHEN WE WERE AT ABOUT 500 FT AGL AND ON ABOUT A 1/2 MI FINAL; Y OVERTOOK US AND PASSED ABOVE AND TO OUR L. I ESTIMATE THAT Y WAS CLOSER THAN 200 FT AWAY; AND WE ENCOUNTERED A SHORT PERIOD OF TURB FROM THE PROPWASH AND WINGTIP VORTICES. I IMMEDIATELY RPTED THAT WE WERE ON A 1/2 MI FINAL AND Y ALSO RPTED A 1/2 MI FINAL. I DECIDED THAT WE SHOULD ABANDON THE LNDG AND PERFORM A GAR. I ANNOUNCED OUR INTENTIONS. Z ANNOUNCED THAT HE HAD CLRED RWY 17. Y CONTINUED WITH THE APCH AND DID A TOUCH-AND-GO. I ANNOUNCED THAT WE WERE DOING A CLBING R 270 DEG TURN TO RE-CROSS MIDFIELD AND ENTER THE L DOWNWIND FOR RWY 17. TODAY; I DISCUSSED THIS EVENT WITH THE CHIEF INSTRUCTOR AS TO WHAT SHOULD BE DONE ABOUT THIS INCIDENT. I REALIZE THAT THE FARS DO NOT MANDATE THAT PLTS RPT THEIR POS AND INTENTIONS IN THE TFC PATTERN AT A NON-TWRED ARPT; HOWEVER; THE BASIC RESPONSIBILITY OF 'SEE AND AVOID' APPLIES AT ALL TIMES; IN ADDITION; FAR 91.111 (G) APPLIES TO THIS SITUATION.