Presently a matrix somewhat similar to that derived from Twisk appeared on a second plate.

"Next, let us try Sir Jaucinet!" said King Throbius. "Soon we shall see who is father to whom!"

Osfer drew blood from Sir Jaucinet's nerveless arm and constructed the matrix peculiar to the lord of Castle Cloud.

King Throbius turned to Madouc. "There you see three matrices, representing the innate fabric of yourself, your mother, Twisk, and this noble knight. By the most subtle means, Osfer will now subtract the influence of Twisk from your matrix, to create a new matrix. If your father is Sir Jaucinet, the new matrix will be identical to his, and you will know the truth of your paternity. Osfer, you may proceed."

"Sire, I have completed the operation. Behold the two matrices!"

"I assume they are identical?" said King Throbius.

"Not at all, and in no particular!"

"Aha!" said King Throbius. "So much for Sir Jaucinet; he may be excused. Liberate him from your thrall, Madouc; bid him be on his way."

Madouc obeyed the instruction. Sir Jaucinet gave instant vent to peevish complaints, and demanded reasons for the many inconveniences to which he had been put.

"I can give you no easy response," said Madouc. "It is a long and detailed story."

"What of the frogs in my mustache?" demanded Sir Jaucinet. "Is their presence such a complicated affair?"

"Not altogether," Madouc admitted. "Still, King Throbius has ordered your departure, and you had best hurry, since the afternoon is waning and the way is long."

Sir Jaucinet, his expression one of deep chagrin, turned on his heel. "Wait!" called King Throbius. "Osfer, apply the ‘Four-fold Spell' to speed good Sir Jaucinet on his journey."

"Indeed, Sire, while he conferred with Madouc, I applied the ‘Six-fold Spell'," said Osfer.

"Good work, Osfer!" King Throbius spoke to Sir Jaucinet:

"As you march home, each of your strides will carry you six yards, and you will arrive at Castle Cloud well before you expected."

Sir Jaucinet bowed stiffly; first to King Throbius and then to Osfer. For Madouc he spared only a glance of moist-eyed reproach; then he was gone, bounding across Madling Meadow on six-fold strides, and was soon lost to sight.

King Throbius turned to Osfer. "Now then: let us deal with the peasant Nisby."

"Sire, you will note on this dish the matrix of Nisby, which I have already taken the liberty of constructing."

Madouc went to look. To her dismay, Nisby's matrix resembled her not at all, and everyone agreed that her paternity surely resided elsewhere than with Nisby. Glumly Madouc liberated him from his nerveless apathy; Osfer applied the ‘Six-fold Spell' and Nisby was sent on his way.

King Throbius addressed Madouc in a somber voice: "My dear, I have taken your interest to heart, and I cannot say that I am pleased with our findings. You have been sired neither by Sir Jaucinet nor by Nisby; hence, we are left with this shadowy weirdling with vacancy for a face. The Third Statute of Logic, sometimes known as the ‘Law of Exclusion', forces me to declare him your father. You may liberate him and hold your reunion at whatever time and place suits your best convenience; no doubt you will have much to tell each other."

Madouc cried out in a troubled voice: "Your logic is naturally superb, but should we not also test this creature's matrix?"

King Throbius spoke to Osfer: "What is your opinion?"

"I suggest a third matrix, if only to create a philosophical symmetry."

King Throbius said: "I am not opposed, though the test will be redundant. However, you may approach Madouc's father, draw three minims of blood and erect a matrix for all to see."

Osfer gingerly approached the black-cloaked figure, then halted in bafflement.

King Throbius called out: "Why do you delay? We are anxious to demonstrate Madouc's paternity!"

"I am in a quandary," said Osfer. "He wears cloak, boots and gloves; he lacks neck, face and scalp. In order to draw his blood, I must remove the cloak, and expose his person. Shall I proceed?"

"Proceed, by all means!" commanded King Throbius.

"Ordinarily we would respect his modesty, but delicacy must be put aside, along with the cloak. Madouc, you may avert your eyes if you wish."

"I will see what needs to be seen," said Madouc. She ignored Sir Pom-Pom's disparaging snort. "Continue with the work."

Osfer, with little fingers extended, in the manner of a fastidious tailor, unclasped the buckle at the neck of the cloak, which then fell somewhat apart. Osfer looked into the gap and gave a startled exclamation. With a single sweep he drew the cloak aside, to reveal a squat gray-faced troll with a bottle nose, pendulous cheeks and eyes like small balls of black glass. His arms were long and knotted; his splayed legs were thrust into tall boots. Osfer cried out: "It is Mangeon the troll!"

Twisk gave a thin wailing shriek of distress. "Now I understand all! With what ignoble cunning he took his lewd revenge!"

Madouc quavered: "Despite all logic, can this truly be my father?"

"We shall see!" said King Throbius. "Osfer, build the matrix!"

"Sire, I have preceded your command! The matrix is already formed! You may examine it as you see fit, and compare it with that provided by Madouc."

King Throbius peered down at the two matrices. He spoke in perplexity. "How can it be? Does madness rule the world? Does the sun rise in the west? Is water wet and fire hot, or is it all in reverse? Logic has played us all false! This matrix is more at discord than both of the others together! I am baffled!"

Madouc could not restrain a yelp of happy relief. "Sir Jaucinet is not my father. Nisby is not my father. This repulsive halfling is not my father. Who then is my father?"

King Throbius examined Twisk with a speculative eye. "Can you clarify this puzzle?"

The dispirited Twisk could only shake her head. "The time is long past. I cannot remember every trifle."

"Still, one of these trifles produced Madouc."

"So much is conceded," said Twisk, "but memories blend; faces merge. When I shut my eyes, I hear whispers-beguilements, adoration, sighs of love requited-but I find no name for these voices."

King Throbius noticed Madouc's disconsolate face. He said: "Do not despair! There remains yet another arrow in the quiver! But first I must deal with this odious troll."

Twisk spoke with fervor. "He deserves no mercy; he caused me great unease."

King Throbius pulled at his beard. "It is a complex situation, since I cannot decide which of our laws he has violated. His trickery was instigated in part by Twisk herself, but his response seems inordinately rude. Flirts through the ages have notoriously enjoyed immunity." King Throbius paced back and forth, and the implets who carried his train were hard-put to carry out their duties. Osfer meanwhile took Mangeon somewhat aside, along with several of his thaumaturgical instruments.

King Throbius came to a halt. He raised his hand in a majestic gesture. "I have arrived at a judgment. Mangeon's conduct has been sordid and disreputable. Further, he has affronted the dignity of Thripsey Shee. The penalty must be consonant with the offense; still we must take note of contributory circumstances. We will therefore allow Mangeon tranquillity and scope for remorse; we will urge him, whether he is so inclined or not, along the narrow path of restraint. Osfer, do you understand the nature of my indication, or must I spell it out in full detail?"

"Sire, I have understood you fully, and indeed I have already implemented your sentence, in full and final scope."

"Osfer, you are a marvel of efficiency!" King Throbius turned to Madouc. "You may now release Mangeon from his paralysis"

Madouc touched Mangeon with the pebble. Instantly he gave vent to furious roaring complaint. "I deplore the outrages committed upon my person! They represent an irresponsible philosophy!"