I had this explained I think, by some publisher's representative being guest of honour at a Con 25 years ago.
A pace is not and should never be accurately defined. Ars Magica is a narrative game, not a tactical game, and paces give the level of accuracy appropriate for the narrative. If yards (let alone metres) were used, the game would get a more tactical feel, and encourage players to think like engineers.
To get the right narrative feel, I interpret a foot also, not as an American or Imperial foot (maybe they are the same, I don't know), but as the length of my foot, or your foot, or which foot does not matter at all.
This is a smart choice and IMO one that fits Ars Magica well.
It does however pose some problems. when trying to answer specific question like "how big a tower can i conjure"? which is question that is not just reasonable to ask but that the core book tries to give a consistent answer to.
I would say yes. The base spell does not include a Perdo requisite for recessing the foundation into the ground so I see no reason why the rest of the tower would need to. I might however require that you reinvent the spell from scratch with a description that read something like:
You create a foundation 20 ft deep and 30 feet in diameter and a tower 30 feet in diameter and 80 feet tall of which e.g. 40 feet protrude above the ground and 40 remain underground.
My home island covenant performed a PeTe circle spell to dig a pit before conjuring the mystic towers, letting us have a tower with as much above as beneath the earth. We hadn't actually thought about the fact that the default tower adds a foundation.
I disagree with your first sentence there. As I showed by quoting the base individual for each Form, size is defined by a volume, not mass. It is the size of the object that matters -- a cubic pace is the same size no matter if the object is solid or hollow.
ArM5 p.113 only uses mass when speaking about added magnitudes, to make the math easier by using a x10 multiplier for each magnitude.
Note that spells like Conjuring the Mystic Tower do not create a substance, it create an object made of that substance.
Creo spells can only use T:Ind or T:Group (see ArM p.113 also, top insert).
If you use T:Ind, you are creating a discrete object up to the maximum base individual size. Adding a magnitudes allows you to create a bigger object with 10x the size (volume).
If you use T:Group, then you are creating a number of discrete individual such that their total mass is 10 times that of a base individual. An added magnitude multiplies that by 10 again.
This means that a T:Ind Herbam spell can create a base individual. If you are creating a plant, that plant can be up to 1 pace in each dimension. Adding a magnitude to increase size means your plant can be roughly 2 paces in each dimension, meaning a small tree. Not a tree that has the mass of 10 cubic paces of solid wood.
A T:Group Herbam spell can create a number of individuals plants whose total mass is equal to that of 10 base individuals. That means 10 plants 1 pace in each dimension, or many more smaller plants.
Also the thing people forget about building underground is dealing with the water that inevitably creeps in. How deep is the water table in your area? Conjure the Mystic Tower is a solid piece of stone (therefore no cracks for water to seep in, but water can still leach through some stones. Most caves have lots of water in them and were formed by water and flood regularly. Certainly hermetic magic can waterproof stuff, but wardings cause warping, so you're probably better off with magical sump pumps (Perdo or Rego Aquam spells to get rid of it).
I think the guidelines on page 113 of the core rulebook are pretty clear that when you add extra magnitudes each added magnitude multiplies the available mass by 10 (I would cite it here but I am afraid that Atlas games would consider it copyright infringement). I agree that its weird to have the base individual be determined in volume and the extra individual available for added magnitudes added in mass, but the conversion is as mentioned above straightforward.
Regarding conjuring towers the primary limiting factor on the size of the tower is how many extra magnitudes you add to make more stone and thus how much extra mass you have to play around with. I think the fact that the spell has 3 extra magnitudes(!) added for its complexity does justify that the tower should be designed by the volume of stone conjured rather than by the smallest box/cylinder that the entire tower fits inside.
Generally its always a good trade in terms of vis to increase the target/magnitude of creo spells that create things, because you get a 10 fold increase in the amount of stuff you create for every 1 pawn extra you pay.
It can be, but only if what you want to create is a substance rather than objects. You want gold? A bigger chunk through an added magnitude is the way to go. You want gold jewelry? Not so much, because a bigger bracelet isn't so useful after all. Then, using T:Group (and adding magnitudes to the group's size) is much more interesting.
Yes, the text mentions mass, but only as a way to specify that one does not multiply each dimension by 10, but rather the whole mass of the target is multiplied by 10.
Ask yourself what the target is. In the case of Creo spells, the target is either a discrete object or a group of discrete objects. Not an amount of stuff arranged whichever way I want it to be.
For example, Conjuring the Mystic Tower create a tower of stone. A tower contains empty space. A base individual tower would be very small, amounting to a pace in each direction. When you add a magnitude to increase the size of that small tower has its size (mass) increased by 10. The mass of a small tower is not the same as the mass of a solid chunk of stone. So the mass of your larger tower is not the mass of a solid chunk of stone multiplied by 10, but that of a small tower multiplied by 10.
It is a bit unfortunate that p.113 has used the wording of mass as an indication of increased size. It would have been clearer (though a bit more mathematically challenging for some) to just say that each dimension increases by 2 (thus volume increases by 8). I guess the authors wanted to keep things mathematically simple by using x10.
The reason for this is simple enough. The x10 factor is universal. Whether the target is an 3D object or a 2D boundary, or even, in some cases, one dimensional, like a rope.
But they could have written volume rather than mass.
