This has been a long time mystery for me. My lucky stone, well that's what one of my sons said it was. Not that it's brought any my way I found it about twenty years ago on Hornsea south beach.
3 cm long
These are concretions. Each orb will have begun 'growing' on a nucleus of some sort, and eventually some intersected each other.
Similar concretions can be found as distinct masses (intersected concretions on their own, with no matrix, though less regular than yours, and flatter), and some of those have gained the name 'faery stones', or 'fairy stones'
Maybe your son knew something...
Algonquin indians "often carried them as lucky charms when they went on fishing or hunting expeditions. Lovers offered the most beautiful Fairy Stones to their loved ones. The biggest specimens occupied a place of honor in their homes, or according to the legend, these special stones assured a protection against bad spirits. They also were said to bring good health and prosperity to the occupants of the home."
Yours, in terms of connected concretions, is also a bit like the gogotte concretions of France.
Google image search - http://www.google.co.uk/search?q=Gogotte&hl=en&source=lnms&tbm=isch
Yes - I think the concretions are composed of micro/crypto-crystalline silica, such as flint, judging by surface texture (smoothness + percussion micro-fracturing).
What appears unusual to me is that the orbs seem to be relatively spherical and relatively independent. That is, despite bumping into each other, sutures remain between them; if it were normal flint in chalk, I would expect the lumps to have coalesced without such sutures producing just one irregular lump (like the one in this discussion - http://www.thefossilforum.com/index.php?/topic/22505-fossil-found-in-uk/). You know what I mean?
I wonder if the orbs have a radial microcrystalline structure - which could make them chalcedony. Chalcedony orbs do tend to remain orbicular and distinct as they grow, as one can perceive from this polished cross-section -
Do you know of any orbicular chalcedony from the area?
I am not suggesting you do so, but breaking one of the orbs could be instructive.
If you or your son find another one, try breaking that.
And let us know, please!
Thanks for the further photo.
I can see various things but nothing definitive, unfortunately.
So I can make no closer suggestion at the moment.
Unless somebody else comes forward with another suggestion and/or you find another one (to break/saw open), we may have to leave it not properly identified.
Oh gee (I take it that is the original specimen) - I hope the break was clean - so you can glue it back together and avoid the wrath of your son!
The absence of conchoidal fracture and a very slightly rough surface suggests is is microsrystalline not cryptocrystalline - hence not flint/chert. But I can see no sign of radial crystal structure (nor concentric banding), so it is probably not chalcedony (cutting and polishing could reveal such structure, perhaps on a very fine scale).
Quartz casts of sea urchins (perhaps internal so relatively featureless) are ruled out by some of the orbs' intersecting each other. Such good orbicular shape also points away from that notion.
There is no obvious core, despite the broken surface seeming vaguely to be passing close to the centre. So the orbs are not the result of slight concretionary growth over a spherical fossil of some sort. There could, however, be a small nucleus not intersected by the break, but the shape of such a small nucleus is unlikely to influence the shape of the concretion.
I am forced to conclude the lumps are concretions, though why so distinctly orbicular, I don't know. I can only guess that the host rock and chemical and physical gradients might have been sufficiently uniform that, as the concretions grew, there was no reason for them to grow faster in any one direction than another.
The substance is probably silica, probably in the form of quartz. Rather than make that supposition of quartz, one should test in case they are a different mineral. The main tests would be acid (could show carbonate), and scratch hardness. I state 'should'. However, you may feel you have subjected your lucky stone to enough indignation already!