Materia is known as extrinsic magic. It involves the creation of magical workings whose effect is meant to be immediate and occurs outside of the mage, presumably out of their aura of effect. Please note that there is a further distinction between the aura of effect and area of effect. The former is closer to the mage while the latter is pertinent to the spell construct’s immediate environment and may arise as a consequence or as the intended effect of the spell. Herein, we find the magic that mages are best known for by the non-mageborn such as [Fire Bolt], [Ice Lance] or [Wind Shield]. It encompasses all the known schools of magic, both material and immaterial From: Introduction to Arcane Workings, Curricula of Magecraft, The Xzerion Institute and Arcanum.

Getting a semblance of order in the workshop took the whole of two days. Most of it involved shoving things into empty crates and putting it somewhere that was not the working space.

By the end of the second day, his hands were throbbing with ache from mana burn. Using spell matrices to work materia effects was well and good where efficiency was required. However, the improvised dusting required him to flex his magical muscle in ways that required ingenuity. Hence the soreness.

“ If only I could measure my mana expenditure,” Arthur groaned as he levered himself off his bed. It was day three. Mana burn still smarted something fierce like syringe needles pulling against his skin. Brainfog sapped his will to get things done and therefore Arthur felt that he’d rather remain in bed for less extraneous tasks. A memory twinged in his consciousness, of having received a jab and being out of sorts for a weekend.

“ Guess there’s no practicals to be done today eh?” He said looking towards the notes and blueprints on the bedside dresser. Feeling that he might as well skip breakfast, he pushed up his pillows and reviewed his notes. He was hoping that he'd be good to go by noon.

With a grimace, he browsed through the calculations he’d worked backwards from the slew of information gleaned from the dwarven reference materials . What had hounded him for a while were the units of the metronic system that consisted of metra and centa and vella. 10 vella made a centum which he thought was apt since it was derived from the thickness of vellum parchment.

He was quick to draw parallel between the measurements from the scale on the blueprints even though some were smudged from running ink.

One thing he realized was that the average handspan of a dwarf was larger than a humans. It was 15 centa wide from the pinky finger to the thumb/

Thankfully, that meant he didn’t have to use his shoes to make a standard metre rule. The lengths were close enough that the deviation could be ignored. While he used the metric system, dwarves used the metronic system; even the etymology was close enough.

For masses, he’d incorporated his knowledge of physics―it had stayed with him despite his wonky memory. Some things were hard to get rid of, more especially those that had stayed with him from highschool to technical college.

The first thing he’d done was to derive how much energy a thaum could yield before planning out the overall design of an arcane engine.

The notes on thaums specifically mention that 1 Thaum is the Power required to melt two spoonfuls worth of Gold. References purport that Power, capital P is anything but an abstract concept or that the value is just an acceptable rule of thumb. Delving into it will have me go into Alchemy—chemistry was never my thing. Nonetheless, I can also translate it to usable units. Power is the rate of energy transfer; which means energy per second…or in this case casion; a matter of nuance. So—

In the formula for calculating the energy in a thaum; we assume that 1 Thaum is the cumulative amount of mana required to melt two spoonfuls worth of gold using a [Heat] rune ( a Runesmith’s Heater Plate is used for this).

A spoonful of gold contains 12.5 gran’aums, therefore, two will contain 25 gran’aums. ( Note: an alchemist’s spoon, not a dinner spoon is to be used here. A normal table spoon will give you an error of 0.5g).

Therefore, assuming the heat of fusion of gold is ΔHf= 67kJ and we have 25g at hand;

q = m·ΔHf

ΔHf= 67kJ Heat of fusion.

m= 25g (gran’aums)

q= 0.025 x 67000= 1675 joules

25g= 1675 joules

It then follows that,

1 thaum= 1675 joules

As for 1 aum of gold i.e 1kg;

1 thaum= 1675 joules

1 thaum= 25g =1675 joules

( ? )thaums = 1000g= 67,000 joules

( ? )thaums= 67,000 joules

67000 joules/1675 joules x 1 thaum= 40

= 40 Thaums

Assuming no heat loss and mana bleed, to melt 1kg of gold using a [Heat] rune, one would need 40 thaums of mana, equivalent to 67000 Joules.

Melting 1 gran’ aum of gold requires 0.04 Thaums of mana.

‘ That was a lot of work,’ Arthur thought wryly. He had been completely immersed in it two days ago and though tedious, his [Eidetic Memory] has allowed him to perform some much needed calculations with crystal clarity.

It was also a marvel to discover the sophistication of the dwarves in the use of gems as focus, mana sources and catalysts for and how they’d arrived at the mana holding capacity of diamonds and other similar minerals. Contrary to what he thought mana crystals were generally reserved for catalysts or converters and could not have their surfaces etched directly.

Nonetheless, looking for derivation of a gem’s mana capacity had almost run him bald until he discovered that diamonds were used as the index of mana storage. He’d almost glazed over the relationship between Erythean coal and diamonds which culminated in a eureka moment and some facepalming.

While the theory had been roundabout with some inclusion of fluff and posturing, soon enough he’d worked out the equation. Even that was not without cursing the waste of parchment from the amount of arithmetic he had to do―

Coal, form of carbon puts out 8kWh of energy per 1kg (1 aum)

In essence, that translates to 28,800,000 joules of energy over one hour assuming a constant rate of and complete combustion.

1 kg= 28,800,000 joules

1000g= 28,800,000 joules

1g= 28,800 joules

1 gran’aum of diamond, the equivalent of a 5 carat diamond, therefore stores as much as 28,800 joules;

enough to melt 25 gran’aums of gold 17 times or fire a bullet 23∼14 times. For comparison, a bullet would have 1250 ∼ 2000 joules of kinetic energy or 0.74 ∼ 1.2 units of thaum comparable to a tier 2 [Stone Dart] spell from the Ter affinity. An average person punches at 135-150 joules, experts can reach 400 joules. A bolt or an arrow, shot without augmenting using skills such as [Piercing Shot] would have ∼ 300 joules of kinetic energy. A [Shatter Bolt] which is a hallmark of pure transference of kinetic energy is almost at par with the most powerful handgun, the .500 S&W, (at 3350 joules against 3,900 joules) which translates to ∼ 2 thaums of mana. It is a favored spell for self-defense of some personages as it offers the most lethality on a 1 carat diamond ring. Depending on the person’s mana regeneration, two casts are available before one has to fully recharge the spell focus. ( The true value ∼2 thaums is in actuality rounded off for ease of use but scholars will use 1.719 thaums in their calculations)

5 carats= 28,800 joules

1 thaum= 1675 joules

5 carats = 17.1940 thaums of mana

Therefore, a 1 carat diamond can store 5760 joules of energy which translates to 3.4388 thaums.

Ps:

The thaumic unit seems to be indivisible into smaller units. So everything below is measured as a decimal—introduce subdivision? There is no way to determine if I can measure my mana capacity. I have to assume there may be or there might not be a formula for determining one's capacity from the number of spells cast. Filling up a diamond seems to be a plausible cause of action but with no way of ascertaining the draw rate i.e thaum per second my best guess is to use a tier 2 shatter bolt as the baseline for how many spells I can cast. Is the power variable? Still remains to be seen— Also diamonds do not give a round number i.e 3.44 . Does it have a meaning like π? Will have to ask somewhere. However, Lonsdaleite diamonds which have a higher density than diamond, i.e 58 percent harder than pure diamond, have a theoretical capacity that is 45 percent more than that of pure diamond which gives the round number of 5 thaums for one carat. This is what is used to measure thaumic input, output and throughput for artifices. Is there one used to measure the mana depth of a mage?

Unfortunately, Arthur’s calculations weren’t the end of it. There was more material he’d crossed out for lack of prevailing theories and calculations that petered out in the middle. Some of them outlined the value of torque of a theoretical arcane engine as well as derivations for the values of the aer and pyr mana that would serve as fuel for thaumic reactions.

Whatever happened when pure mana underwent attunement to a certain affinity was mind-bogglingly another rabbit hole of its own. For example, aer and pyr fusions tended to have values almost five times those of ordinary mana. That meant he had to find to start factoring conversion constants in his thaumic equations. With his brain being a let-down however, he skipped that part and moved on to the actual meat of the thing.

Arthur reviewed how the hulls of typical dwarven vessels were made up of layers such that they were their own system. The hull was composed of the outer hull, intermediate null-steel insulation, the honeycomb structure of the aerostat floats and then the interior hull which also contained a double layer.

The honeycomb structure of the aerostat float was such that with a given number of cells was a gem that served as a focus and mana source in one. The density of the cells, that is the number of cells per given measure, had a direct correlation to the amount of lift the ship would be capable of.

The honeycomb design was mostly for structural integrity as the aer saturation within the float increased or decreased. As for the aertherite crystals, they functioned as convertors, catalyzing inbound mana from the mana sails into the required affinity.

Mana sails did not have a complete conversion efficiency per se, but they did cut down on the time required to collect aer mana alongside any unaspected mana that was available. Only after conversion was the mana shunted to the aerostat floats, to be distributed through the malachite or any other gem that formed the point of interaction with the space inside the aerostat float.

For efficiency, aertherite crystals would be bundled up in a canister with leads connecting the mana conduits from the sails and those from the floats. The entire assembly had the appearance of an electrostatic capacitor blown up to the size of a water dispenser bottle and was aptly named the aertherator. Insulating every aerostat cell was null-steel to prevent the mana from seeping outside or being affected by external mana.

Following that kind of design, aerships had hulls thicker than their seafaring counterparts. Additionally, the fore and aft sections had entire compartments dedicated to the aerostat floats as well as selected areas of the portside and starboard sides for even distribution of lift and balance.

A majority of aerostat floats would use malachite as the cheapest mineral that could readily conduct aer mana; it was common enough within copper deposits and therefore cheap. There was some kind of relation between the color of the gem being used and the affinity .At the top of the heap were emeralds which went into the more expensive ships.

Since they were situated closer to the outer hull, aerostat floats had allowances to venting of excess air mana. Venting could also be used to sustain flight to smaller escort or away boats called glide skiffs whose aerostat floats and mana sails are smaller.

While aerostat floats provided lift, steering and forward propulsion depended on wind. If it came to it, Air magic could be called upon to expedite the ship’s speed.

Arthur’s theoretical engine was supposed to change that by using compressed thaumic reactions of aer and pyr. From the computations, aer alone would have enough power at par with hydrogen without the constraints of storage. Ambient mana had a negligible mass and was readily available in the air; the only mass he had to worry about was the crystals.

And if Arthur’s supposition was correct, the amount of power would scale. Thus far, he’d been working on the assumption of the energy put out by pure unaspected mana. The exact value of an aer and pyr fusion was still an abstract because he had no instruments with which to ascertain the true magnitude. He would put that aside and concern himself with crafting an aer only engine to gauge the feasibility of thaumic reactions for thrust.

The Arcane engine would have a collector, condenser and nozzle; more straight forward than a turbofan engine and as simple as a water jet engine. It could even be seen as a true air jet engine.

Nonetheless, actual combustion would not occur, but saturating a small space with aer and providing an exit nozzle had the same effect just without the heat. He would however, be able to see the afterglow of the thaumic reaction. The only heat he’d have to worry about was friction in the fan shaft.

By the time Arthur had gotten to the part about required actual exertion, there was a crick at the nape of his neck. He took one glimpse at his watch, then remembering that it was out of sync, shrugged and finally pulled himself off the bed.

There was no window in at eye-level through which he could gaze from but the room was lit by ambient lighting. The actual cathedral motif windows were head heights above him, almost bordering the cornices of the vaulted ceiling and the chandelier.

After freshening up, mostly a brief splash of water to shake off the fugue and the morning ritual he’d forgone earlier he gathered up his notes. Ensconced in some dwarven reference material were his drawings of potential aership designs that would be feasible. They weren’t complete, save for the most important thing that was the propulsion mechanism he was going to build his ship around.

The keep was eerily quiet, not even Aeskyre was around. Normally he’d find her in the kitchen during the mornings.

‘Maybe she’s gone on one of her excursions again,’ Arthur thought as he fixed something from the leftovers which he carried with him to the Keep’s workshop. As soon as the food quelled the protestations of his stomach, he put down his written materials. He unfurled his blueprint parchments and gave the notations a once over before he embarked on actual work.

The first thing he did was start carving out the ironwood board from the weather-beaten hull of what used to be a dwarven ship. Most of the wood was decades old and he'd been lucky to even get three whole planks.

Already accustomed to it, he got a leather apron cleaned of its grease and dust and donned a pair of dwarven made goggles. His gloves were cleaned and aired to get rid of the smell of wet leather, went to his hands and were secured with knots at the back of his hand—a lucky find otherwise he'd have to contend with dwarven gloves which were a size too large.

Arthur picked a particularly sturdy piece of timber with the least damage, placing it on the worktable to be secured by bench dogs he'd hammered in himself. They were spare chisels he'd found in a tool chest somewhere. Then he started planing of the unwanted parts, shaping the wood for main body of his first craft—