My Eureka goes fast when the battery gets low and the arc declines. I know they should be reasonably 'isochronous', but there's a pretty good chance that over the 100 years since it was made the weights may have been tampered with - or the spring (which doesn't exactly look pristine) distorted.
I suspect that to reset it to be isochronous with an (expensive) new spring might be the work of a lifetime(!), so I'm leaving well alone. I'm really not sure if there is a known 'method' to do this? I'm also not sure how much (if any) temperature compensation is built in?
With a fresh battery it keeps time to about half a minute a week, and this goes on for several months before it gradually begins to gain as the battery weakens. When running correctly, the arc should be near 360 degrees. I have seen clocks run with much less.
Its worth saying that Eurekas have a dubious reputation for timekeeping, but a stabilised supply would certainly improve mine based on what I have seen. Someone (Brian Mumford?) used to do a stabilised supply I believe.
I use a single 'D' size Duracell which lasts over a year and for most of that time gives acceptable timekeeping in my eyes.