Though there are others out there who know their Petters much better than I, this is my understanding of the subject:-
When Petters decided to introduce a small 1 1/2 HP engine (the Little Pet) to fill out the bottom end of the 'M' range, a drastic cost cutting exercise was required - the engine would need to sell a good deal more cheaply than its bigger counterparts, whereas in reality of course manufacturing cost for engines of similar design but various sizes are not that different. Out went the reed type air valve, replaced by conventional cylinder wall inlet ports, also the skew gears for the magneto drive were deleted in favour of straight cut spurs which neccesitated mounting the magneto on the front of the crank case and pushing the fuel pump round the back (to the space vacated by the air inlet). Perhaps the most drastic change was to make the cylinder, hitherto cast in unit with the crank case, a separate item, this enabled a headless design to be used which likely worked out cheaper to make than a separate head with gasket etc. This cylinder was cooled by a elegant acorn / rugby ball / pear, call it what you will, shaped hopper. This hopper was suitable for most purposes where it could be topped up occasionally by the man in charge of the engine, but, where especially long runs with no attention were required, a simple closing plate enabled the engine to be tank cooled.
As is well known, this series one engine was not a success, blow back from the inlet ports tended to cover the engine and everything round it with oil and the magneto drive gears were said to be noisy (not sure I believe that on to be honest) but, for whatever reason the engine was soon redesigned. Back came the inlet valve on the back of the crank case, the fuel pump moved to the front and there was really no option but to mount the magneto at right angles to the crank shaft, driven but the same system of skew gears as the rest of the range. All this must have eroded to cost benefits somewhat, but the headless cylinder with it's attractive hopper was retained.
This is how the engine stayed until the whole 'M' range was redesigned to become the 'New Model Universal' incorporating ball and roller main bearings and the 'Calibrator' lubrication system. At this point the 1/2 gained a conventionally water jacketed cylinder (still separate from the crank case) with detachable head this being of the ball / apple top shape if hopper cooling was required.
Apologies for the lack of dates in the above (can't be bothered to look for the relevant books), but I hope it goes some way towards answering your questions about the smallest member of the Peter 'M' family.