What you could be looking at are not black eggs but a "Black Scale" insect infestation. Can you post a picture of this? Also, do you see this on the twigs?

My friend has exactly the same problem and rightly or wrongly has taken every leaf off !
A close up photograph would be much appreciated.

Hank, do I read you correctly? Your friend has taken every leaf off of his tree? If so, forget about a picture of the tiny black eggs, lets get a picture of your friend so we can find a way to visually identify the Henricus amice defoliator and control this person! LOL!!!

Have asked him to take the photo, and when it arrves I'll let you have it.

Thanks Hank.

Sorry Loosestrife, I thought you wanted a photo of his tree so that was what I asked him for. But I'm still waiting for it , and as for a photo of himself I don't that will be forthcoming.
To tell you the truth I hadn't a clue he'd done wrong taking the leaves off - shows how much I know about it !