I Purchased A New Condenser Fan. The Old Fan Had Three Wires One To The Contactor(black) Then Yellow Wire To The Capacitor And Brown Wire To Capacitor. The New Motor Has Four Wires Brown , Brown With White Strip, Black And Purple. The Fan Diagram Shows You Can Connect With Only Three Wires. It Shoews Brown To Capacitor And Brown And White To Capacitor One Says L1, Then Purple To The Insulator. I Assume The Purple Goes To The Contactor And You Do Not Connect The Black From The New Motor. Should I Connect The Brown Wire To The Same Point As The Original Brown Wire And The Brown With White Stripe To The Location Of The Original Yellow Wire??

You said that you have two brown wires, one solid and one with a white stripe. You should have bought a new capacitor with the motor, if you did connect the two brown wires to the new capacitor. The other two wires go directly to the contactor. One on each hot leg after it goes through the contactor... If you did not buy a new capacitor then I do not know if you have a dual capacitor or just a single that runs the motor.
If you have a dual ( a capacitor that both the fan motor and the compressor use) you can connect the solid brown wire to the dual capacitor to the post that is marked 'fan' connect the purple to the center post of the dual capcitor. Connect the black the screwon the capacitor that does not have a wire going from the contactor to the capacitor. You can tape up the brown wire with the white stripes. The brown wire and the purple wire actually connect inside the motor.I will try to make this a little easier if I can.

Brown connects to one post on a single capacitor or to (fan) of a dual capacitor.

Brown with white stripe connects to other post on single capacitor, Tape if it is a dual capacitor.

Black goes to Contactor

Purple goes to Contactor if you have a capacitor with just two post.

If you use the dual capacitor the purple goes to the center post of the capacitor... that post will also have another wire on it possible yellow that comes from the contactor...

I hope you can understand this... If not re-post and someone witll help.

Just wanted to thank you guys for posting this information. It helped me to fix my own similar problem. My fan stopped spinning on my condenser last week. I replaced the motor and capacitor and fan blades too. The old fan blades were permanently rusted on to the old motor shaft. I could not figure out how to wire the new motor to the dual run capacitor environment that my condenser runs off. The new motor came with its own capacitor and had 5 wires instead of the 3 wires that were on the old motor. The new motor had green (ground), purple, black, brown, & brown/white. I hooked the brown & brown/white to the new run capacitor that came with the new motor, purple to L1, & black to L2, and green to the chassis(as is indicated on the replacement motor). The top of the old dual run capacitor was bulging out indicating a failure, so I replaced it as well. The only wires going to the replacement dual run capacitor were the power lead from C to contactor & HERM to the condenser motor. Everything works in this configuration, but the fan will never turn off. From what you folks indicated, I do not need the run capacitor that came with the new fan motor. What I need to do is plug the brown to "FAN" on the dual run capacitor, and the purple to "C" on the dual run capacitor, and tape off the brown/white. This should keep the fan motor from being always on. I am going to try this in an hour. Thank you everyone!