Excerpt from the Discussions with a Master series, 5th Edition, 1999. Editor notes from Hermione redacted nee Granger included.

To my lord and ladies, Masters of the Arcane Lore of the Hidden Light, Seekers of the Lost; to Sir Fredrick-Umblekirk, Lady Aichen and her coterie, to the great Patron of Uz, Lord Coomb and Majister Sinister, and to the most enlightened explorers of the great realm we call our home: greetings.

The query sent to the Foundation has vexed our best mind not for its simplicity, but for the scope in which your request spans. A simple answer is oft wrong, yet brilliant in truth; the hand once burned is cautious evermore. Definitions limited to a few pages are inadequate to convey the true majesty of what you have asked. But the greatest challenges are not so simple that any hedge-mage could succeed. Whereupon we have brought the best of resources to this task, seeking out the wisdom of sages and texts from ages before memory.

Hereupon we shall begin: What is power?

Two words must be further clarified before continuing. There is a difference between power and potency. Uninformed minds could confuse these terms as synonyms, misappropriated through a dullard's mind.

Power is the output of magic from a wizard, frequently measured in unit variants of thaum. Three thaums will transfigure a mol of iron to copper (nearly two troy ounces, or 14 dram), for precisely one minute. Thirty thaum will extend that transfiguration to ten minutes. (Editor's Note: A thaum is roughly equivalent to 22.5 kilocalories, the measurement of energy in heat and sustenance. H.G.)

Driving the force of any spell, ritual or enchantment is this concept of power. Active magics may be altered through the subtle interaction of the caster and the subject of casting. Any art of potioneering depends on this to a small extent, in that what is concocted must be melded in the control of a being carrying power inherent in its veins. Golems and muggles are incapable of more than preparatory work in a myriad of disciplines from engraving some ritual markings (excluding Mage Grade and above) to maintaining inert ingredient storage for high level potion laboratories.

Potency is the ability to bring the power inherent within the wizard to a single point. The immaculate potential, or purity (see: Sacrifice, by Aichen Bacan, 2012) shall not be addressed, nor does it apply to potency.

Power and potency are two aspects inherent to any wielder of magic. Without power, the greatest wizard would be incapable of the most basic of spellwork. Without potency, every wizard and witch in history would struggle to perform spells in any efficacy; only those having a strength on the level of Merlin or Morgana would be capable of performing magic at all.

We may improve this understanding to a greater point. For this, we must accept that there are many studies beyond the comprehension of some, but mastered by a few.

Transfiguration utilizes power in the most visible manner. A charm may be incanted and forgotten in fractions of a second, and wards may be created through application of natural environmental influences. But the transfiguration of one object into another may be observed; we may record durations of the change, how complete that change becomes, and the accuracy inherent within the shift. Depending on the creativeness of the caster, an efficient change will alter skin into fabric and transform the internal properties to the desired qualities.

How is this done?

First, the power required changes the existence of a transfiguration focus on a scale too small to be seen. Through diligent research, we understand that muggles have developed what may be considered as a crude facsimile of Alchemy, expending vast quantities of time and energy to shift masses of coal into diamonds. While necessitating enough financial investment to purchase a medium-size Manor, the end result is a perfect sample of a diamond. (Editor's note: Graphite, not coal, but made of the same substance. H.G.)

The factor of greatest import is how the transformation takes place. In the simplest of terms, heat and pressure are applied to the coal, adding energy to its existence. In time, the coal absorbs sufficient quantities of energy, and adds the essence to itself, rendering the final product: a diamond. Incomplete transformations result in dark glass-like shards, filled with black chunks of coal.

There is an advantage, and disadvantage to the muggle method. A great advantage is that this transformation is permanent, and therefore closer to Alchemy than true Transfiguration. The disadvantage is in the limited nature of change; only diamonds are able to be made, and it is creating an object that can be considered to be further along the natural process than actual change.

Transfiguration applies the same principle by adding energy to a substance, and forcing it to change its nature to the next nearest substance. Bronze may be transfigured into copper and tin, while steel may be changed into iron quite easily. Adding power skips entire groups of minerals, and potency ensures minimal waste of power, further promoting escalation of transfiguration (for further study, take advantage of the Avalon Equations Explained, by Majister Patron-de-us).

But what of inorganic Transfigurations?

All readers would do well to understand that this difference is the true core of mystery. How does magic change what we see to what we desire?

That is not the purpose of our explanation.

Wood is a living thing, and our observations indicate a certain connection between it and coal. There is already a link between coal and diamond; yet wood is living while diamonds are dead.

The correlation is plain: adding magic to a substance will change the very nature of that substance. Directing how much magic is added, and controlling the manner of application, could be considered the very soul of Transfiguration.

Consider the hedgehog to pincushion exercise: a good student will alter the creature into an object of single consistency. An adept will create multiple layers, of outer cloth and inner cushion. A Master will ensure pins are created within the object at the same time. This is a demonstration of mental agility, concentrating the mind on multiple aspects of the transfiguration subject at once. It is no coincidence that the greatest Transfiguration Master's in recorded history have evinced a high intelligence, or possessed the gift of a savant.

Most will perform such creations through visualization. Familiarity with the materials being transfigured eases the transition difficulty; the greater the familiarity, the faster the transfiguration.

Each material being transfigured takes a certain quantity of power. As an example, we may observe a simple yet powerful object of history like a staff. Six to nine feet of solid oak is the traditional length in Britain, and it once proved the weapon of choice for the great battles of antiquity.

Oak is one of the most durable living substances to exist, stronger than bone per cubic inch. But metal armor is stronger still, and a shield charm deflects both with ease.

A Transfiguration Master of average power and potency will begin the change by altering at least a portion of the stave's length to steel; assume an approximate fourteen inches (or an est. 141 mol, 282 troy ounces, or 94 dram) in the tradition of the Norse svardstav. Without going into exquisite calculations, we may estimate a thaum investment of 1,269 thaum (or 1 flamel) for this change. To counter the weight shift, the oak shaft may be elongated to a sufficient degree as to counterbalance the metal cap; as equal weight is equal in expenditure, an additional flamel is applied.

Further additions will require additional investment. Adding a metal shell of steel will increase the cost by 0.5 flamel per foot (given enclosure rather than full transfiguration), and smaller details such as grooves, reinforcing structures and enhanced materials will add even greater costs.

If the wizard is of greater potency, the cost will be of lower investiture, as the lost power will be of equally lower value. A wizard of greater power may perform the transfiguration at a more rapid pace, with his greater output capacity.

Despite all these calculations and estimations, unless a truly massive quantity of power is involved, or Alchemy, the weapon will always return to its pure oak state. There may be a greater association with the transfiguration after the change, lowering future investment costs, but even with the most acclimated of substances, the change is inevitable.

Why?

Let us consider the relatively simple prospect of a river. If mass and velocity were added to its course, such as a flood, the river would alter its original course. Once the excess water is exhausted, the river will return to its original form. Likewise any transfiguration will return to its original substance. Any power added to the material is just that: added power. No river may stay heightened, and no object may retain an enhanced state of power. This is the irresistible, ancient power of kaos, first theorized by Salbei Fürst Uwe-Uffe der Zwietracht in the 3rd century AD. Through time, the term has adopted the Greek terminology for change, becoming entropy. All transforming magics fall under the regulation of this force – all power will be reduced (see: Disjunction: Burning Fates by Lord Gray, 1233).

Alchemy is the sole exception to entropy. The power generated by an Alchemist renders the change permanent, albeit in ways only a handful understand in all recorded history. The closest any of the Foundation have reached to solving this dichotomy is the realization that an Alchemist's power and potency may be equal to another, but the purity of his magic retains properties no one else understands (Editor's Note: Honestly, hasn't anyone read Neutron Inclusion for Transfiguration Permanence by Nick Fallem?).

We humbly conclude that without speaking in person and demonstrating various models and charts, this is the closest we may come to explaining the Power of Magic. We remain your humble colleagues,

Charles Levinhand, Arch-Chancellor of Miscellanea, Chrono Studies Division and Grand Poobah of Derisivity.

And

Majister Flowing-Over-Waters, Visiting Transfiguration Master, Wandering Adept, and Calvin-Hobbsian Specialist