The railroad going up Mt. Tamalpais employed Shay locomotives as well as Heisler. I used to think they were all Shay but learned that the No. 9 that is being restored is a Heisler.

"The most significant design difference between Shays and Heislers was the arrangement of the driving cylinders. The Shays had either two or three driving cylinders mounted on the right hand side of the locomotive. Since the weight of the driving cylinders sat only on one side, the boiler was mounted offset to the left to provide a counterbalance. In the Heislers, the driving cylinders were located in the middle of the locomotive."[1][2]

[1] https://www.friendsofno9.org/post/mechanic-s-corner-geared-l...

[2] https://en.wikipedia.org/wiki/Heisler_locomotive

You can still ride a Shay-powered train at https://en.wikipedia.org/wiki/Cass_Scenic_Railroad_State_Par.... It's an old-time logging railroad that goes up into the mountains from a former https://en.wikipedia.org/wiki/Company_town founded in 1901.

These were used in Australia on the Newnes railway line. Newnes was a shale oil mining town; its history is particularly colourful because its remoteness made it difficult to import sufficient food for the town's population.

https://en.wikipedia.org/wiki/Newnes_railway_line

https://en.wikipedia.org/wiki/Newnes,_New_South_Wales

Not an expert, but...

As Wikipedia partly mentions, Shay designs were very well suited to low-speed operation on dirt-cheap (often temporary) tracks. That generally meant narrow-gauge, light rail & iffy roadbed, tight curves, and steep grades. Low-speed-only was the only sort of operation you'd want to attempt - tracks suitable for higher speeds would have cost far more, but provided minimal benefit for logging, mining, and other Shay use cases.

A bit fuzzier, but I also recall Shays being considerably more easily maintained (vs. conventional steam locomotives) in situations with minimal facilities, equipment, and trained staff. Not sure how much that was locomotives being designed to the customers' needs, vs. being intrinsic to the Shay mechanical layout.

And a bit of context - a century or so ago, modern heavy road construction equipment and heavy trucks mostly didn't exist. Vs. railroad tech did. So for logging, mining, and many situations where we'd say "d'oh, just build a road and use trucks" - they just laid some RR track and used that.

I was wondering where the 116 surviving machines are. These are not the type you see in Utah (American made 4-4-0). Instead they were built for rough (sometimes temporary) track and steep inclines. Often used in mining and logging.

Edit: They have a link to their known locations.

I think my dad had a copy of the book that had this data.

That site is borderline unreadable. You'd think there would be some basic info on the landing page.

https://en.wikipedia.org/wiki/Shay_locomotive