The "Fyne Poynt" pencil section begins on page 30.
The closest pattern I see to yours is the Rosette Pattern. It went for $22.50 back in the day (solid 14k gold).
The description of the Fyne Poynt says, in part, "Turning the section at the top of the pencil feeds the lead in the central magazine forward as in other pencils of this type, but instead of having to take the pencil all apart in order to refill it, the simple action of unscrewing the point exposes the magazine carrying the refill leads. In this magazine are carried six leads, two inches long, each in a separate compartment so that they cannot break or jam. As the lead feeds forward, the detachable nozzle holds it firm and rigid at all times. Immediate access to the eraser is had by *simply removing the cap at the end of the pencil*.
Pocket clips are attached to all long-length pencils. The short-length pencils, convenient for carrying in a lady's purse or for attachment to the end of a gentleman's watch chain, are made with bale and ring."
There's no mention of unscrewing so I'd simply pull while imparting a slight twist. Which makes sense because if the cap was screwed on there'd be no need for the bail and it could be a more traditional ring top.
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