Here's the
Geneva Stop parts that install on the bottom of the barrel. The mechanism stops the spring just short of a full wind, and just short of being fully wound down so as to make the best use of the mid-section of the spring where the power is most consistent.
As a practical matter this is really not something that would make a notable difference on a watch like this, especially today. Other factors will impact the rate over its runtime to a greater degree than the slight variations in the mainspring strength.
As with everything in a watch, the key to installing the mechanism correctly is to understand how it works. The easiest way to do that is to carefully study it before it's disassembled.
For these, all of the leaves of the Geneva wheel are concave, except one. The cam can not pass the convex leaf. So with the mainspring at rest (unwound) the convex leaf goes just behind the cam that that the Geneva wheel will turn, as the watch winds, until the convex leaf comes around.
The install position also requires a small amount of tension on the spring to fit the cam. Thus fully run down, where the watch stops, is actually just short of the spring being fully relaxed.
Elgin serial number 6457374 is a grade 150, 18 size, 21 jewels, made about 1896.
