sur toute son étendue

17:58 Aug 6, 2017 

Thank you so much for your clear explanation, I completely get it now! I really misconstrued this description!

17:18 Aug 6, 2017 

In the sentence you are asking about, the author is not talking about the change in thickness of the disk as you move out from the center to the rim (cross-section of the bulge). “partour” tells us that it refers to a variation in thickness as you move around the rim (along its circumference). It is not “bumpy” or irregular – it will vary simply as a result of the geometry of the thing. This isn't the place for a rather complex mathematical proof, but basically the thickness at the rim is defined by the locus of intersection of the ellipse (outer form of the disk as seen from front or back) and the circular depression (probably spherical in this case) formed within it (the bulge).

In an ideal case, that circumferential thickness variation would be absolutely smooth (no bumps) – and the thickness would be greatest at two opposing poles. Of course, the shape of an ancient Egyptian mirror will be somewhat less than ideal, but it will still have this smooth variation.

17:03 Aug 6, 2017 

Thanks everyone. I think my author is contrasting the bulge (convex) with the rest of the disk (edge of bulge to rim, maybe the "body" of the disk?) whose thickness is bumpy instead of gradually thinning or thickening to the edge/rim. Is this interpretation impossible based on the French? My author always uses bordure, bord but never pourtour for the rim/edge of a mirror. He always is very consistent and very specific, thank goodness, with his use of épaisseur, never varying, thickness makes sense every time.

19:47 Aug 5, 2017 

Not really an idiom; try considering it thus:

le pourtour n'a pas une épaisseur uniforme sur toute son étendue"

... is not the same thickness over the whole of its length

I wouldn't really say 'perimeter', perhaps 'periphery' or just 'circumference' — to me 'perimeter' conveys a tad more of the abstract notion of 'that which surrounds', rather than the geometrical aspect. "A perimeter fence" / "Rub your finger round the periphery..."

Logically, it's hard to speak of the 'length' of something circular, which is why they speak of its 'extent'; but I think that sounds contrived in EN. Or you could just say "not the same thickness everywhere".

However, from the way it is being used, I suspect perhaps "'pourtour' here means not the geometrical notion so much as the physical component — the 'surround' or 'edging strip' or 'rim' or somesuch.

19:28 Aug 5, 2017 

Apologies, it didn't at first sight seem to need more, but perhaps this is significant:
Ce détail est rendu d'autant plus sensible que c'est précisément dans le voisinage immédiat de cette plus forte épaisseur, que se manifeste la moindre épaisseur.