C172 PLT AND A PA28 HAD A NMAC IN PAO CLASS D AIRSPACE.

Narrative

WE APCHED PAO FROM THE SALT PONDS. WE ENTERED THE PATTERN (NORMAL R FOR RWY 31). EVENTUALLY; ON DOWNWIND; APPROX ABEAM THE RWY 31 NUMBERS; WE WERE TOLD BY TWR THAT WE WERE #3 TO LAND. THE VISIBILITY WAS VERY POOR; SO MOST OF MY CONCENTRATION WAS ON LOOKING FOR OTHER ACFT. ONE ACFT ON SHORT FINAL STATED HE WAS GOING AROUND. I CONTINUED DOWNWIND BECAUSE I HAD NOT SEEN ANOTHER ACFT PASS YET. SOON ONE DID (THE ONE I THOUGHT TO BE #2) AND I DID MY TURN TO BASE. 1/2 WAY ON MY TURN TO FINAL; THERE WAS A CHEROKEE VERY CLOSE JUST BEHIND US. WE CONTINUED STRAIGHT AHEAD AND THE CHEROKEE DID A R 360 DEG TURN (WE NOTICED EACH OTHER AT THE SAME TIME). THE CHEROKEE NOTED ON THE RADIO THAT HE GOT CUT OFF AND I NOTED I WAS #3. I BELIEVE THERE WERE 2 EVENTS THAT CAUSED THE CONFUSION: 1) I WAS COUNTING #1; #2; #3; ETC OF THE ACFT IN THE AIR AND WHERE THEY WERE IN THE PATTERN. IN DISCUSSING IT WITH A PLT WHO WAS ON BOARD IN MY ACFT; THE CTLR PROBABLY WASN'T COUNTING THE GUY ON SHORT FINAL THAT EVENTUALLY WENT AROUND. IT WOULD HELP IF THERE WAS A UNIFORM WAY TO COUNT THESE. 2) I SHOULD BE MORE VIGILANT AS TO WHAT TYPE OF ACFT IS #1; #2; ETC. THE DISTR FOR ME WAS POOR VISIBILITY (HAZE).