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Wow--it really is 100% mechanical. Looks electrical from the front.
Actual article title is:

> The 'Librascope' Mechanical Weight and Balance Computer

The modified title uses the term "whippletrees" that is not used or described in the article, which I had to look up:

https://en.wikipedia.org/wiki/Whippletree_(mechanism)

Thanks. I was going to edit my post to include that article.

I also found this 1983 video from the librascope company, which mentions the weight and balance computer in the first minute:

https://youtu.be/nYeERxT1g38

Trying to understand exactly the function that is being computed - is it a weighted sum of the inputs?
Pretty much, it is computing a centre of gravity for the plane.

The CG needs to be in certain limits otherwise the stability of the plane is compromised.

You take the moment-arms of weights and sum them together and come up with mostly front-aft balance. You could have left-right imbalance as well obviously but this is mostly a function of fuel imbalance.

Yes CG calculation is a weighted sum (of weights, but lets call those mass to avoid confusion) with the weight for each dial being fixed. The result of the sum is divided by the total mass to get the CG.

This thing displays total mass on the left (that's just an ordinary non-weighted sum of all dials), and on the right is shows the result of dividing the weighted sum by the total mass.

Aniston has a long history of loving mechanical computers, from this device to the far more popular nomograms and slide-rule-esque Flight Computers. My dad was a pilot from the 70s to the late 90s and always said that the one advantage they definitely had over the electronic equivalents (which were in t he background pretty much that whole time) was that they'd be guaranteed to never fail in an electrical failure and were incredibly robust, both physically and to the design limits of the plane.
Did you see the flyer at the bottom? They didn't misspell “computor”, like everyone else does by now. Apparently the author knew Latin.
Is the title misleading? I am on the fence. The computor very much uses whippeltrees, as evidenced by looking at the backside of the UI, but does a page dedicated to a mechanical computer need to provide a introduction to basic concepts of mechanical computers? Where does it end? An introduction to arrays or linked lists every time a computer oriented page mentions anything to do with storing some data objects? How far down the stack of turtles do we go before we reach a point where Hermione is chiding us for "It's Reducto Abs-URD-ah. Not Reducto Absurd-arrh!"?