GD (please set up your signature),
Thanks. I'll add you and your machine to the machine database.
Your lathe from what I can see in the three photos looks pretty good. FYI, it is a 10x24, not 10x36. The "42" in the TH42 model number and in the 942 bed casting and part number means 42" bed length. The headstock takes up about 12" and the tailstock about 6" so on an Atlas 9", 10" or 12" lathe, bed length minus 18 is the approximate distance between centers. In the rest of the model number, "T" means Timken bearings on the spindle (blank or no letter would mean Babbit bearings). "H" means Horizontal countershaft ("V" would mean Vertical). The only thing that I see wrong is the link belt on the spindle. The correct V-belt Industry standard number is 4L410.
If your motor is slow to start but does eventually, the culprit is probably the Start capacitor. If it won't start at all without manually pulling or twisting, it could be the capacitor and it could be the centrifugal switch.
In DOWNLOADS (read instructions for use in the Sticky area at the top of this Forum), you will find the latest version of the Parts Manual, the Atlas Technical Bulletin on the 10" Timken headstock, and some other useful information.
You should also acquire a copy of the Atlas "Manual of Lathe Operation and Machinists Tables". Published from 1937 through today (but the last Edition number was , there were 33 editions, the first 15 of which aren't numbered, but say just say "Copyright 1937" on the copyright page. The one that you want will have plastic binding. Chapter 7 will be bound in (not a loose supplement) and cover the Atlas F-Series 10". There will be no price on the Copyright page. And the lubrication photograph on page 6 (un-numbered, it follows page 5) shows a 10F with horizontal countershaft and rectangular switch plate. Unless someone here has an extra, best source will be eBay. But most eBay sellers don't know anything about what they are selling and seldom show photos of the important pages. You will have to write them and ask.