While the false Point C Vertex is excavated and lined with pitch-a blot in the desert, a stain on the endeavor, a rat that gnaws at Miss Keaton's s.h.i.+vering heart-the project nears completion and the Red Planet rises in the Egyptian sky, on its way toward opposition, just as Earth ascends in the violet, hour-long evening dusk of Mars. Further accidents are reported and additional work stoppages have to be curbed, and rumors of more insidious unrest percolates among the overseers, yet the Equilateral moves, like the silently gliding planets themselves, toward its appointment with maximum elongation. The last section of the petroleum line arrayed around the triangle is laid. Each of its three hundred and nine taps have been installed.

As antic.i.p.ation of the Equilateral's completion seizes the fellahin, who continue to maintain an imperfect understanding of its purpose, Point A is jolted by news that the settlement will be inspected by the Khedive himself, said to be a monarch of cunning, culture, and enlightenment. He will be accompanied by no less a dignitary than Sir Harry.

The excitement's enough to rouse Thayer from his sickbed. Bint gives him a haircut. He steps from the tent wan and unsteady, but he's fully heartened, not only by the coming visit, but also by the Red Planet's increasing proximity. Every day it's another half million miles closer to Earth.

Ballard is forced to take men off the Equilateral to prepare suitable accommodations and tidy up Point A, which after two years of hard service has fallen into a disorder barely remarked by its inhabitants. Latrines that have caved in have been incompletely filled. Chickens peck between tents, many of which are slack and roughly patched. A costly puddle of water leaks from the hammam. Broken machinery has been left where it failed. Unsightly structures have gone up adjacent to the Nag Hammadi track, in Point A's outlying districts and suburbs. Ballard orders them rebuilt. The engineer is furious at the delays entailed by these preparations, especially as the improvements will be abandoned in weeks, immediately after maximum elongation, when the project is concluded.

Thayer is surprised that Sir Harry himself is coming to Point A. The astronomer shared rostrums and headlines with him as the Concession's capital was raised, yet since ground was broken he has become a reclusive figure, in communication with Thayer only intermittently, and usually only on the subject of expenses. This is his first journey to the Western Desert. It's unclear whether he still comprehends the project, and whether he still believes in it.

When the chairman of the Board of Governors is lifted from his carriage, the fellahin who are aware that he's a Knight of the British Empire wonder from which untimely, ill-favored Crusade he's returned. The pale and disheveled Englishman seems debilitated from the desert's rigors. The men set him on his feet. He takes a few steps forward and vomits onto the sands.

The astronomer announces, "Sir Harry, we welcome you to Point A, the Vertex of Angle BAC, the southernmost and westernmost point on the Equilateral! We hope to make your stay here as comfortable as possible."

Sir Harry replies, "It's certainly cost me enough."

The military orchestra a.s.sembles around the Khedive's carriage. The entire camp turns toward the vehicle. The royal fanfare begins and is aborted several times before the Khedive finally appears, his uniform neatly pressed, his cap perfectly set. A large man, with a barrel chest that bulges against his tunic, he waves as if vast armed legions stand behind the orchestra. He bows to Miss Keaton and clasps the hands of the astronomer and the engineer.

Due to the governor's indisposition, and also because of the intense heat, the welcoming pleasantries are curtailed to a brief rededication of the settlement, which is to be called Point Khedive Abbas Hilmi II in perpetuity. That evening a supper under the fixed stars and wandering planets is prepared by royal chefs with provisions brought from Cairo. Thayer delivers a stirring address that reminds his audience of the Equilateral's high purposes. Ballard reads the text written for Sir Harry, who is still ill and looks on balefully. The Khedive's remarks are reiterated in six languages. The company retires early, in preparation for the following morning's balloon ascent.

The machine has been s.h.i.+pped from London and inflated overnight in the scrub a few steps from the former site of the scaffold, whose remnants have been scrupulously removed. Beneath the swaying gas envelope an observation car is stamped with the words: MARS CONCESSION. The Khedive is delighted; he's said to take a keen interest in modern technology, examples of which, including telephones and flush toilets, are installed throughout his palace, according to amused visitors from the English colony. He briskly questions the pilot, a dark, taciturn junior officer in the Royal Navy who has served aboard the Khedive's Suez yacht, the Mahroussa. The Khedive poses a singularly original question. Did not Amenhotep III's Eighteenth Dynasty employ similar vehicles for flight? He recalls an inscription to that effect on the Third Pylon, in the Temple of Amun. The sailor replies in vague affirmation, a.s.suring him that he's perfectly familiar with the balloon's cla.s.sic Egyptian provenance, as well as with its modern operation. Ballard notes the s.h.i.+fty response.

Sir Harry hardly seems to have benefited from having pa.s.sed the night in the guest house that was constructed for his use and furnished with a featherbed and bra.s.s lavatory fittings. Through fatigue-rimmed eyes he looks at the ascension balloon with disgust, as if it's yet another device designed primarily for his discomfort. Ballard asks if he would prefer to remain in camp.

"No, I'll do it," he says through gritted teeth.

The balloon's shadow dances among the dunes. Some inexplicably idle fellahin observe the party from a distance, their expressions pa.s.sive, as if Montgolfiers are common desert flora.

The pilot welcomes the Khedive, Sir Harry, Ballard, Thayer, and Miss Keaton onto the gondola, which hovers inches off the ground, its ballast bags loaded with sand-imported from Britain with the gondola. The vehicle rocks as it takes on the pa.s.sengers' weight. Ballard briefly reflects, before an ascent hardly as dependable as a lift's, that it carries the four men essential to the Equilateral and the millions of pounds sterling that have been invested in it. Gripping the gondola's railing, the aeronauts wave to the onlookers, a small party of Europeans and the Khedive's entire entourage, including the military band, which performs "G.o.d Save the Queen" and the Egyptian national anthem, composed by Verdi.

The land they've been excavating suddenly drops away, accompanied by applause and hurrahs. Point A is far below at once.

As the sun-bleached tents and mud-brick structures of the settlement recede, Thayer murmurs surprise. In his carriage with Bint a few weeks ago, he thought he was circ.u.mnavigating a burgeoning metropolis. But very quickly now Point A is seen to be a modest desert outpost, a few hundred yards square, a cl.u.s.ter of tents and buildings, of which only the hammam and the pitch factory may be recognized.

Then the two sides of the triangle radiating from Point A come into view, diverging toward points beyond the horizon three hundred miles apart, two black, throbbing lines laid into the sand, just as foreseen in Thayer's letter to Philosophical Transactions in 1883, just as Ballard surveyed them in 1891 and '92. They cut through whatever dunes or hillocks they encounter. Their blackness imprints itself on Thayer's retinas. No one can doubt from this height or from any other that these are the artifacts of a sensitive, calculating intelligence. The balloon rises and the Equilateral continues to reveal itself.

The music from the Khedive's military band reaches them, with some of the instruments muted in the breeze and others amplified, producing exactly the sort of heavenly cry we may expect in the atmosphere's upper strata.

Exhilaration courses through Thayer's veins. He's impressed with even more force than he was at the pitch factory, when he saw little more than Vertex BAC, or when he stood on the ridge above Side AC. His eyes are wide, his mouth half open. All these years of hard labor are laid out below him on the alabaster plain as if on his own drafting table.

Without saying a word, Thayer takes Miss Keaton's warm right hand and squeezes it hard. For the next several minutes the secretary is unable to see the Equilateral, or the desert at all, or to hear the winds whistling through the lines that attach the gondola to the balloon. He releases his grip. When her vision clears and she can inspect the Equilateral below, she doesn't think of looking for the foreshortening of the triangle's upper portions in the far distance.

"My Lord Jesus."

At first Thayer believes it's Ballard who's whispered this gentle oath, but no, it's Sir Harry.

The few minutes aloft have wrought a transformation. Color has returned to his face. His mouth's twisted into an unguarded grin that's nearly boyish.

"My Lord Jesus," he repeats. "Look what we've brought off! This is the greatest mark of man's hand upon the Earth. Ballard, you've earned your place in history. Professor Thayer-" he begins, and then simply embraces him, almost overcome.

The Khedive is visibly moved as well, making lip-smacking noises and inward sighs. He lightly claps his hands.

"Bravo," he says. He releases a childish giggle.

Having taken out his pocket telescope, Thayer surveys the excavations. He follows each line below him, AC and AB, to its vanis.h.i.+ng point. He removes his face from the gla.s.s to a.s.sure himself that the lines are actually there. They are! Thayer gazes at the figure for several minutes as their vessel sails farther into the thinning air, then, beaming, he turns to the unmarked, unmapped desert to the south. He antic.i.p.ates additional, more complicated geometric figures beyond the ones planned for this decade. In the next century, they will dig a line that intersects two parallel lines, producing congruent angles; also, a circle with an inscribed angle half the size of a central angle subtending the same arc. Meanwhile, his companions continue to marvel at what their labor, their capital, and their viceregal writ have accomplished so far.

They marvel, yet Ballard intuits that something's amiss. He's stirred into an unfocused wariness that will, in short course, save the expedition from disaster.

With his gla.s.s raised again, Thayer examines the low line of hills on the southern horizon. Something arrests the instrument's drift. He peers at the hills with the intensity that he normally reserves for celestial observation. His mouth opens slightly. He closes down his other senses, even the internal commentaries and distractions that normally accompany thought, and bears down on the field of view.

"What do you see?" the Khedive asks.

Ballard and Miss Keaton follow the line of the gla.s.s to the horizon, they don't see anything, and they turn back to the astronomer.

Thayer is straining now, his eyes narrow, his jaw set hard as he studies the distant hills. But Ballard is the one who observes something definite-a deadly, silvery flash-right on board the gondola.

The engineer lunges at it, but the weapon strikes the Khedive first.

In a moment Ballard is wrestling on the narrow deck with the pilot, his hands gripping the wrist that holds the knife, whose cruel arc ends in a black ivory handle. There are cries and shouts and Thayer drops his gla.s.s against the rail, shattering the lens. Then the Khedive, uncowed by the attack, falls on the would-be a.s.sa.s.sin, pins him, and puts his knee hard against his windpipe. The man loses the knife and Miss Keaton kicks it away. Thayer and Sir Harry, who have stood back from the scuffle, cut lengths of mooring rope with the relinquished blade. They truss the man like a game fowl, even as he issues a series of imprecations.

But the Khedive is hardly finished.

He questions him severely in Arabic, apparently demanding to know his cause and his patron. The pilot responds with taunts that, Thayer gathers, impugns the honor of the Egyptian royal family, including by name the late Khedive Tewfik. This abuse enrages the son, who puts the knife to his throat. The bound man writhes in rebellion.

When the Khedive jerks him from the deck, the gondola s.h.i.+fts precipitously. As Thayer falls forward and grabs a guy wire supporting the basket, there's nothing between him and the Equilateral, which is laid out in front of him, quite close it seems, like his destiny. The Khedive inclines the pilot over the rail.

"Your Highness!" Sir Harry cries.

But the Khedive knows no inhibition. With a strength infused by his righteous anger at the insult to Mehmet Ali's royal line, which has governed Egypt for ninety years, he hauls the man over the railing, holding him by the ropes. The prisoner has been cut by his own knife. Blood freely runs down his face and uniform, but of more immediate concern to the dangling wretch is the obduracy of the African continent, thousands of feet below.

This threat proves remedial. Fear is lit in the villain's eyes as he apprehends his situation, which is made even more intolerable by the immobility of his hands, arms, and feet. When the Khedive poses the question again, the man responds-if not with complete civility, for terror has gained command over his composure, then at least usefully. The Khedive is sobered by the information imparted. A spasm of concern roils his forehead. He asks the man another question with evident urgency.

The Khedive is sufficiently satisfied by the man's response to return him to the gondola, so that he can be further interviewed by the police. But he proves to be an unwieldy package. As the Khedive pulls him in, the prisoner slips from his grasp.

Suddenly lightened, the balloon rockets heavenward. Sir Harry falls to the floor of the gondola, but the others grab the rail and watch the man drop, turning over and over, still bound. The vessel is now soaring above the southwest interior of the excavations. As the traitor silently plummets, and more seconds seem to pa.s.s than is possible, he shrinks in apparent size until, the Equilateral rus.h.i.+ng to meet him, he becomes no more than that which is without parts, a single-dimensional element, a position but no magnitude-in other words, a point. Given that Egyptian methods of extracting information would blanch a Turk, his fall is a certain mercy.

"Professor Thayer," the khedive says, once the balloon stabilizes at its new alt.i.tude, about seven thousand feet. "I trust that your expertise in the arts and sciences encompa.s.ses the piloting of ascension balloons."

Thayer is in no position to confess that this is his first aeronautical expedition, as either operator or pa.s.senger. He consults with Ballard quietly on the use of the gas valve above the gondola, and together they make the adjustments necessary to descend comfortably. Employing the distinct, gentle breezes that prevail at each alt.i.tude, they reach the ground not far from Point A.

A military detachment rides out at a hard gallop. The Khedive's bodyguards saw from below that something sinister was transpiring on board the gondola and when they witnessed the body plunge into the desert wastes, they expected the worst. They cheer when they're met by the beaming Khedive, refreshed by his tussle with the treacherous pilot.

Not until then does anyone remark that the Khedive's tunic is sliced open across his chest, probably by the villain's initial parry. While his commanders voice consternation, the Khedive, who has already shown his royal mettle, coolly proceeds to unb.u.t.ton his uniform.

The knife has gone clear through his tunic and undergarments, but when these are removed his corpulence shows itself unpunctured. The skin's marked only by a pale pink scratch that runs the full length of the blade's course, from nipple to umbilicus. It's as straight a line as anything conceived by Euclid.

Thayer is puzzled by the attack on the Khedive. Once they've returned to Point A, he asks Ballard if he believes the Mahdists are responsible.

"They're adamantly opposed to Egypt's rule in the Sudan," Ballard notes. "They despise the Khedive-as a tool of the British, for his Albanian blood, for his palaces, for his yachts, and for his harem girls. Fair enough, I suppose. He's bold to come this far south, and d.a.m.n foolish. But the a.s.sa.s.sin was not sent by the Mahdists at all."

"Then ... ?"

"The Sublime Porte has never reconciled itself to the Equilateral."

"But I went to Constantinople! I met with the Sultan. I gave him sketches of Mars, showing the ca.n.a.ls definitively. He expressed enormous enthusiasm."

"The Turks are masters of dissimulation," Ballard says. "Rather than play a losing hand, they switch the deck."

Unable to overtly resist the Concession, the Ottoman Sultan fears the Equilateral as yet another European scheme to wrest Egypt from his increasingly feeble grip. The Khedive's elimination would have jeopardized the project and sent Egypt into more than its usual turmoil. Yet the Mahdists would have been the ones to profit, so, Ballard concedes, perhaps Thayer's original supposition is correct.

The engineer asks Thayer what he observed through his pocket telescope.

"Nothing, really."

"Reticence doesn't become you, Thayer. Before that bit of unpleasantness with the pilot, you were looking at a definite position on the ground."

Thayer turns to gaze across the desert. He finds the approximate place, staring at it for a while, but without the advantage of elevation.

"There was motion of some kind," he says at last. "I think that's what it was, motion, not a distinguishable object. Motion in the desert always catches the eye. This was on the horizon, a disturbance, a boiling, or something like the seething of a hive. I don't know. I saw it for only a moment and then I was jostled and I lost my gla.s.s." He adds, "Now, thank you, I have to send to London for its replacement."

Twenty-Five.

They never learn the particulars of the turncoat's confession, but his concluding statement is enough to bring about a series of arrests. Men are taken away. A Nubian corporal surrenders unprompted. Two bodyguards suddenly turn on a third, putting him in irons. Complementary actions are taken within the Khedive's palace in Cairo. The seizures seem entirely at random, or according to occult principles. The a.s.sault on the viceroy's life may have involved the Sublime Porte, and it may have involved the Mahdists, and it must be part of a larger scheme, but whatever it is, the conspiracy operates below the plane of the Equilateral. It recalls to the Europeans that they sojourn in Byzantine lands.

Because the lands are Byzantine, the evening's royal banquet unfolds as scheduled, with the scheduled extravagance: slaughtered goats, martyred lambs, mountains of rice, towers of figs and dates, a panoply of jellies and sauces, and rolling blue c.u.muli of has.h.i.+sh smoke. The bagnio girls have joined their sisters from the Khedive's harem for the night. Decked out in new raiments, hennaed, rouged, and bangled, they've been imparted with fresh glamour. They're pillowed at the table with the Khedive and his European companions, and they encourage and amplify the party's ribald humor. The Cairo haremites seem less worldly, but perhaps even more enticing for their pretensions to l.u.s.trous innocence. A wizened musician picks at a qa-noon. Miss Keaton has of course absented herself.

Thayer is considerably more troubled by the attack than the Khedive appears to be, and even Sir Harry seems to have recovered his composure. The astronomer ignores the girls and eats little. No one speaks of the arrests. The two visitors to Point A lean across their plates to share a private observation. Sir Harry snorts in amused contempt. Thayer recognizes that he doesn't know every arrangement that has been made between the Khedive and the Concession. Not every appendix and codicil has been made public. The machinery of world politics turns invisibly. The ties of blood, clan, sect, and military obedience that maintain the Khedive's rule, and parallel ligatures bound in opposition to it, lie beyond Thayer's comprehension.

His early departure is hardly remarked. The day has taken much from him. When he arrives at his quarters, Bint has already left. He performs his own toilet and puts himself to bed, winning no more than an uneasy slumber that's roiled by visions of flas.h.i.+ng knives and men plummeting into geometric figures.

Waking fevered in a darkened tent, Thayer calls for Bint. Another attendant appears. She comes at once, deferential and comely.

"Where's Bint?" he asks, the question a parched croak.

She smiles modestly and says, "Bint."

The girl looks very much like Bint, with the olive skin and almond eyes characteristic of the Near East's women. As a rule, males and females of the Eastern races do not display the variety of physical characteristics that distinguish individuals among the Europeans. Compare, say, Miss Sarah Bernhardt with Miss Eleonora Duse; both lovely and talented, yet as different in appearance from each other as the ocean and the sky (with the tempestuous Divine Sarah being the ocean, of course). Thayer can't be blamed for confusing the ident.i.ties of two ordinary Arab serving girls.

"Yes, I need Bint," he says. "Please send her to me."

"Bint," she repeats. She pours water from an earthenware pitcher and offers him the cup.

Knowing that he's ill and that fever can cloud his perceptions, and also because he's a man of open mind, Thayer wonders if he's mistaken, and if this is indeed the girl who has been taking care of his domestic needs for more than a year. Especially after the turmoil of the previous day, he can be mistaken. He considers the familiarity of her features and mannerisms: the prow-like nose, the wide-eyed stare; she leans forward when she speaks, raising an arm as if in defense.

"You're not Bint," he declares. "Bint! Are you here?"

He struggles to stand and, still in his nightgown, he pulls open the entrance to the tent.

The shock of light and heat, accompanied by waves of nausea and vertigo, drives him back at once. Aware of his frailty, the girl gently takes him by the shoulders and brings him to his chair. He can't have expected more tenderness from anyone, not even from Bint.

Despite the girl's protestations, which are in the same key as Bint's and similarly unintelligible, Thayer dresses himself and goes out to Miss Keaton's bureau. She's behind her typewriter.

"What happened to Bint?"

"Good morning, are you all right?" She gets up from her desk. "You look ghastly."

"Bint's not in my tent. Some other girl is there. She calls herself Bint but she's not."

"That's odd," she agrees briskly. She studies him, worried. He's flushed now and his eyes are red. "How late did you remain at the banquet? Dr. McKinnon told you not to overindulge. Do you have a fever?"

"You didn't send her away?"

He stares at her intently, as if her most minute features, some so minute they border on the invisible, may betray the most vitally important truths.

"No, I wouldn't do that. I would ask you before I did, but I'm sufficiently occupied with the Equilateral! We still have men excavating Side AB. I'm calling for the doctor. If the fever has returned-"

"You didn't send her away?" he repeats.

She stops to consider the question. She can ask him why he thinks she would send her away, but his only possible response will humiliate her. All this, over an Arab serving girl ... To think he believes that she would ... She's dismayed, and then angry. He stands before her, waiting for her to confirm his suspicions. Her anger is dulled when she recalls the shortened sides. Before she can speak, before she can formulate the single correct series of words that will make him see, he rushes from the bureau.

Thayer soon loses his way to the women's dormitory, encountering unexpected lanes and alleys, before finding himself at the door to the tea room. This is where the jingle of female laughter was heard several months earlier.

Gazing off into s.p.a.ce with a melancholic aspect redolent of the East, the Turk is in his accustomed place behind the counter. He's surprised to see anyone at this hour, especially the astronomer.

Thayer says, "I'm looking for Bint."