The periscope slides into a hollow rectangular bracket, which you can see in Karl’s photo. It’s held in place by a knob that goes in the slot you can see on the face of that bracket in the photo: the knob is turned tight, and there’s often a small latch on the bracket that goes underneath the knob so the periscope can’t actually fall out if the knob works its way loose.
This is why you usually see the turret turned to the right, over the co-driver’s hatch, when the vehicle is on the move outside of combat:
View attachment 402083
Since we’re striving for accuracy here, I need to address this
The official American name for the vehicle is
3-inch Gun Motor Carriage M10 — this is what it says on the front cover of the vehicle’s technical manual, TM 9-752 of 25 November 1943, which I have on my shelf.
Technically, the British name for this vehicle was
Achilles, but nobody ever seems to have used that. British troops, reports and so on all simply called it an “M10”, to the best of my knowledge. Achilles Mk. I was apparently the version with triangular counterweights, the Mk. II with the elongated “duckbill” ones, say most sources. However, I suspect this to be an error by 1960s/’70s AFV authors (who are not exactly unknown to have made ones like these that still haunt us today), and my theory is that the Achilles Mk. I was actually the M10, while the Mk. II was the M10A1.
Officially, the British variants armed with the 17-pounder gun were the Achilles Mk. IC and Mk. IIC (the letter C, not the Roman numeral C). However, in practice these vehicles were called “17-pr M10” by British troops. I suspect that if you were to take a time machine to 1944 and asked about “that Achilles over there”, nobody would understand which vehicle you were talking about.
Again largely due to those 1960s/’70s AFV authors, people nowadays are under the impression that the 17-pounder versions
only were called Achilles. The Wikipedia article does nothing to dispel this myth, and I suspect that rewriting it will just get people annoyed with you and revert the changes …
The US Army deployed early M10s to North Africa, indeed. Note that these are the type in which the upper rear wall of the turret slopes inwards, like you can see in the photo you posted. Most model kits, though, have the vertical rear wall that was introduced a bit later to give a little more room inside.
I’m not sure of British use of M10s in Africa, though.