thanks - yes, I seem to recall the expression "no such thing as black glass". Ordinarily, black was achieved by the inclusion of shed loads of manganese, plus the fact that presumably as glass becomes thicker translucence decreases until at some point all transmitted light ceases - have to say this bowl, like it's owner, is fairly thick. I think there is some mention of iron filings being used to achieve 'black', but how successful this was on larger pieces I've no idea. I will try peering through the glass, again, and see if a stronger light source will do the trick.
Looking at your 'page 7' it's possible than I'm missing only the frog, as I can't see No. 34 sitting on one of those circular plinths - though seem to think I have a spare somewhere which might do temporarily.
If you feel confident that the bowl here is Davidson that's fine, and I'll request Anne (Mod.) to change my subject heading, and again thanks for the correction. Just for interest, and comparison, I'll post a couple of pieces of Davidson's matt black bowl 'sets' later today.