Doesn't work either.

Well, of all the ways for something in runecasting to fail to work, "nothing happens" is better than a lot of things that could have happened. How about the unused one she hand-drew and then made a photocopy of, can she get anything out of that or did putting it in the photocopier ruin it somehow? Same pot of water, same incantation. 

The photocopier did not ruin it.

Eeee magic!

The next step is to vary an incantation and see if that varies the effect. The diagram says nothing in particular about boiling, just water and heat. Over the course of a few days she assembles and practices a French version of "Heat the water in the cup in front of me; bring it to sixty Celsius" and repeats her diagram copy/wait/check procedure. Then she tries the new incantation, this time with a thermometer in the water.

It reaches... eighty-five Celsius.

Weird. Does that happen every time? She spends the entire next week's worth of free time just doing that experiment over and over, recording the temperature each time.

It varies slightly depending on how much water there is.

Yeah, she's not trying to draw her own diagrams until she understands what's going on here. Does more water produce a lower final temperature? Does water that starts out hotter produce a higher final temperature? 

More water with an incantation specifying sixty degrees gets a lower final temperature. Water that starts out hotter produces a higher final temperature.

And is the final temperature always higher than sixty C, or is it sometimes lower?

Always higher.

What if she starts with ice in the pot but the incantation still says "water"? (She debates with herself for a while before doing this one, and has the "if you're reading this I died doing magic" letter out on the table again.)

Absolutely nothing happens.

Phew. If she swaps out the ice for water and tries again, is the diagram still good or did the failure use it up?

The failure used it up.

How bothersome.

She's going through a lot of diagrams and diagramming time with all this science, and even with the "wait 48 hours and double-check your copying" rule she's going to mess one up eventually. It's worth investing some more time in finding a way to mass-produce them.

Photocopying didn't work, but something more manual might. What if she gets some air-dry modeling clay and an exacto knife and makes some really careful models of all the runes in reverse, arranged mirror-style on a sheet, then paints it with ink and stamps it onto a page? This might take a lot of tries to get first a stencil, and then a painting-and-stamping attempt, perfect enough that she deems it worthy of incanting at.

Once she tries a stamped diagram, that works fine.

Sure, but can she then paint and stamp again with the same stamp until she gets another good one and use that?

Yes, subsequent stamps also work!

Woohoo! No more copying that one anymore, not that it isn't already burned into her brain. More to the point, any future diagrams only need to be done perfectly once. 

Next step: swap out the number in the incantation from "sixty" to "eighty". Holding all else constant, does this produce consistently or intermittently hotter water?

It never goes below eighty and the variance is less, but it varies a bit along the same dimensions.

This magic system demands a lot of precision going in for a relatively noisy result coming out. Maybe controlling for environmental circumstances really carefully will be instructive. Does playing back a recording of an incantation work like reciting it?

Nope. Does nothing and doesn't use up the inscription.

How about reciting the incantation loudly vs quietly? (This was such a good pick for first spell; it has a really easily measurable effect size!)

Volume makes no difference alone, but if she actually whispers, unvoicing all the voiced sounds, then it doesn't work (whether this uses up the inscription depends on whether she started any properly pronounced words before switching to whispering: if she whispers it all, the inscription is still usable, and if she whispers only some, the inscription is used up but nothing happens).