I have read several posts regarding these cases. I have found enough difference in the Arm & Hammer hallmark to, at least for my own purposes, make a distinction between them.

First picture is of the higher quality Philadelphia Perfection 14K gold plated case.

This pic is of a cheap, very thinly plated case in which I have seen many Time Ball Specials as well as other swiss fakes. Note the hallmark has more striations than the Philly case and oddly, is a more realistic image. The hand is actually gripping the handle where on the Philly case the hand looks to be above of the handle.

An ad for the Philadelphia case.

A previous post on this topic.

Arm & Hammer Hallmark

Another thinly plated case with a Tornado hallmark in which I have seen many Time Ball Specials and assorted swiss fakes.

That arm & hammer is a cool Trade-Mark Lorne, too bad it denotes such a humble case.