Your description of the engine purring in waves sounds as if it may be hunting slightly - that is, the engine speed varies cyclically, with probably about 2 or 3 seconds length of cycle. If it is doing that, the carburetor mixture adjustment screw probably needs to be turned anticlockwise about an eighth to a quarter of a turn, but if you are not familiar with these engines it might be best to get the problem a bit clearer first. Find the mixture screw anyway - and note which is the mixture screw and which is the idle speed screw. The idle speed screw is on a lever and it holds the throttle butterfly slightly open when the speed control is at minimum setting. The mixture screw sticks out from the carburettor body. Both of these screws have springs under their heads to keep them from moving due to engine vibration. You routinely adjust the mixture by running the engine at normal grass-cutting speed and finding the rich limit (turn screw anticlockwise) and the lean limit (turn screw clockwise) until it runs slightly poorly in each case, then putting it halfway between those two limits. If this procedure doesn't work, always put the screw back where it was in the first place while you figure out what has gone wrong: don't adjust various things in succession and leave every one of them messed up.
