Esterbrook's first attempts at fountain pens were like most manufacturers of the time and were eyedropper filled.  Esterbrook, however, did not make their own pens during this period, and had them made by other manufacturers including Wirt, De La Rue, and Conway Stewart.  These eyedropper pens are quite rare and highly prized by collectors.

This is a 314 Relief eyedropper filler in a taper slip cap.  The barrel end is marked clearly with a number 3.  This pen was made by Wirt ca. 1903.  Notice the end of the barrel has marking clearly indicating Made in U.S.A.

Here's the barrel imprint.

Here is the pen uncapped.  The nib simply states R. Esterbrook Relief and is a fine flexible nib.  This is one of Wirt's vented feeds with a ventless nib.

Here's a view of the vented feed on the number 3 eyedropper.

This is a model 6 Eyedropper made also by Wirt. Nib and feed are identical as above model, as are imprints.