I have a JD 310g backhoe that leaks oil out the breather on the top left hand side of the rear axle. Am looking for a cause
Welcome to HEF bill1 ! Serial number? Many hours on this machine? Is the hydraulic oil level going down or the transmission oil level going down. This will help narrow down where it is leaking in the axle. Transmission pressure supplies the PB and Diff lock oil pressure, hydraulic oil is the supply for the brake pistons. Most likely cause will be the park brake piston seals if the transmission level is going down.
The serial number is T0310GX959817 and the hours are 3753.2 hrs. Is there no return line from axle? It seems to occur more so on major temperature--- change -outside -10 F to shop 50 F. I will have to monitor oil levels now that I know what to look for and maybe drain some oil from rear end.
That is what I would suggest. Get all oil levels correct and monitor closely. When the axle is going up something else has to be going down. Nope. When brakes, park brake or diff lock is released the oil for activation returns through whatever valve is actuating them. With good seals there is no oil leakage so a return line is not needed.