“Make that two adherents, then, Doctor.”
Leibniz actually stopped in his tracks and turned to examine Daniel’s face, to see if he was jesting. “I am honored, sir,” he said, “but I would prefer to think of you not as an adherent but as a friend.”
“Then the honor is all mine.”
They linked arms and walked in silence for a while.
“Paris!” Leibniz said, as if it were the only thing that could get him through the next few days. “When I get back to the Bibliothèque du Roi, I will turn all of my efforts to mathematics.”
“You don’t want to complete the Arithmetickal Engine?”
It was the first time Daniel had ever seen the Doctor show annoyance. “I am a philosopher, not a watchmaker. The philosophickal problems associated with the Arithmetickal Engine have already been solved…I have found my way out of that labyrinth.”
“That reminds me of something you said on your first day in London, Doctor. You mentioned that the question of free will versus predestination is one of the two great labyrinths into which the mind is drawn. What, pray tell, is the other?”
“The other is the composition of the continuum, or: what is space? Euclid assures us that we can divide any distance in half, and then subdivide each of them into smaller halves, and so on, ad infinitum. Easy to say, but difficult to understand…”
“It is more difficult for metaphysicians than for mathematicians, I think,” Daniel said. “As in so many other fields, modern mathematics has given us tools to work with things that are infinitely small, or infinitely large.”
“Perhaps I am too much of a metaphysician, then,” Leibniz said. “I take it, sir, that you are referring to the techniques of infinite sequences and series?”
“Just so, Doctor. But as usual, you are overly modest. You have already demonstrated, before the Royal Society, that you know as much of those techniques as any man alive.”
“But to me, they do not resolve our confusion, so much as give us a way to think about how confused we are. For example—”
Leibniz gravitated toward a sputtering lamp dangling from the overhanging corner of a building. The City of London’s new program to light the streets at night had suffered from the fact that the country was out of money. But in this riotous part of town, where (in the view of Sir Roger L’Estrange, anyway) any shadow might hide a conspiracy of Dissidents, it had been judged worthwhile to spend a bit of whale-oil on street-lamps.
Leibniz fetched a stick from a pile of debris that had been a goldsmith’s shop a week earlier, and stepped into the circle of brown light cast on the dirt by the lamp, and scratched out the first few terms of a series:
“If you sum this series, it will slowly converge on pi. So we have a way to approach the value of pi—to reach toward it, but never to grasp it…much as the human mind can approach divine things, and gain an imperfect knowledge of them, but never look God in the face.”
“It is not necessarily true that infinite series must be some sort of concession to the unknowable, Doctor…they can clarify, too! My friend Isaac Newton has done wizardly things with them. He has learned to approximate any curve as an infinite series.”
Daniel took the stick from Leibniz, then swept out a curve in the dirt. “Far from detracting from his knowledge, this has extended his grasp, by giving him a way to calculate the tangent to a curve at any point.” He carved a straight line above the curve, grazing it at one point.
A black coach rattled up the street, its four horses driven onwards by the coachman’s whip, but veering nervously around piles of debris. Daniel and Leibniz backed into a doorway to let it pass; its wheels exploded a puddle and turned Leibniz’s glyphs and Daniel’s curves into a system of strange canals, and eventually washed them away.
“Would that some of our work last longer than that,” Daniel said ruefully. Leibniz laughed—for a moment—then walked silently for a hundred yards or so.
“I thought Newton only did Alchemy,” Leibniz said.
“From time to time, Oldenburg or Comstock or I cajole him into writing out some of his mathematical work.”
“Perhaps I need more cajoling,” Leibniz said.
“Huygens can cajole you, when you get back.”
Leibniz shrugged violently, as if Huygens were sitting astride his neck, and needed to be got rid of. “He has tutored me well, to this point. But if all he can do is give me problems that have already been solved by some Englishman, it must mean that he knows no more mathematics than I do.”
“And Oldenburg is cajoling you—but to do the wrong thing.”
“I shall endeavour to have an Arithmetickal Engine built in Paris, to satisfy Oldenburg,” Leibniz sighed. “It is a worthy project, but for now it is a project for a mechanic.”
They came into the light of another street-lamp. Daniel took advantage of it to look at his companion’s face, and gauge his mood. Leibniz looked a good deal more resolute than he had beneath the previous street-lamp. “It is childish of me to expect older men to tell me what to do,” the Doctor said. “No one told me to think about free will versus predestination. I plunged into the middle of the labyrinth, and became thoroughly lost, and then had no choice but to think my way out of it.”
“The second labyrinth awaits you,” Daniel reminded him.
“Yes…it is time for me to plunge into it. Henceforth, that is my only purpose. The next time you see me, Daniel, I will be a mathematician second to none.”
From any other Continental lawyer these words would have been laughably arrogant; but they had come from the mouth of the monster.
I laid the reins upon the neck of my lusts.
—JOHN BUNYAN, The Pilgrim’s Progress
DANIEL WAS AWAKENED one morning by a stifled boom, and supposed it was a piece being tested in the Artillery Yard outside of town. Just as he was about to fall back to sleep he heard it again: thump, like the period at the end of a book.
Dawn-light had flooded the turret of Bedlam and was picking its way down through struts and lashings, plank-decks and scaffolds, dangling ropes and angling braces, to the ground floor where Daniel lay on a sack of straw. He could hear movements above: not blunderings of thieves or vermin, but the well-conceived, precisely executed maneuvers of birds, and of Robert Hooke.
Daniel rose and, leaving his wig behind, so that the cool air bathed his stubbled scalp, climbed up toward the light, ascending the masons’ ladders and ropes. Above his head, the gaps between planks were radiant, salmon-colored lines, tight and parallel as harpsichord-strings. He hoisted himself up through a hatch, rousting a couple of swallows, and found himself within the dome of the turret, sharing a hemispherical room with Robert Hooke. Dust made the air gently luminous. Hooke had spread out large drawings of wings and airscrews. Before the windows he had hung panes of glass, neatly scored with black Cartesian grids, plotted with foreshortened parabolae—the trajectories of actual cannonballs. Hooke liked to watch cannonballs fly from a stand-point next to the cannon, standing inside a contraption he had built, peering through these sheets of glass and tracing the balls’ courses on them with a grease-pencil.
“Weigh out five grains of powder for me,” Hooke said. He was paying attention to part of a rarefying engine: one of many such piston-and-cylinder devices he and Boyle used to study the expansion of gases.
Daniel went over to a tiny scale set up on a plank between two sawhorses. On the floor next to it was a keg branded with the coat of arms of the Silver Comstocks. Its bung was loose, and peppered with grains of coarse powder. Next to it rested a small cylindrical bag of linen, about the diameter of a fist, plump and round as a full sack of flour. This had once been sewn shut, but Hooke had snipped through the uneven stitches and teased it open. Looking in among the petals of frayed fabric, Daniel saw that it, too, was filled with black powder.
“Would you prefer I take it from the keg, or the little bag?” Daniel asked.
“As I value my eyes, and my Rarefying Engine, take it from the keg
.”
“Why do you say so?” Daniel drew the loose bung out and found that the keg was nearly full. Taking up a copper spoon that Hooke had left near the scale (copper did not make sparks), he scooped up a small amount of powder from the bung-hole and began sprinkling it onto one of the scale’s frail golden pans. But his gaze strayed towards the linen bag. In part this was because Hooke, who feared so little, seemed to think it was a hazard. Too, there was something about this bag that was familiar to him, though he could not place it in his memory.
“Rub a pinch between your fingers,” Hooke suggested. “Come, there is no danger.”
Daniel probed into the linen bag and got a smudge of the stuff on his fingertips. The answer was obvious. “This is much finer than that in the keg.” And that was the clew that reminded him where he had seen such a bag before. The night that Roger Comstock had blown himself up in the laboratory, he had been grinding gunpowder very fine, and pouring it into a bag just like this one. “Where did this come from? A theatre?”
For once Hooke was flummoxed. “What a very odd question for you to ask. Why do you phant’sy such a thing should come from a theatre, of all places?”
“The nature of the powder,” Daniel said. “Ground so exceedingly fine.” He nodded at the bag, for his hands were busy. Having weighed out five grains of powder from the keg, he poured them from the scale-pan into a cupped scrap of paper and carried it over to Hooke. “Such powder burns much faster than this coarse stuff.” He shook the paper for emphasis and it made a sandy rasp. He handed it to Hooke, who poured it into the cylinder of the Rarefying Engine. Some of these engines were wrought of glass, but this was a heavy brass tube about the size of a tobacco-canister: a very small siege-mortar, in effect. Its piston fit into it like a cannonball.
“I am aware of it,” Hooke said. “That is why I do not wish to put five grains of it into the Rarefying Engine. Five grains of Comstock’s powder burns slow and steady, and drives the piston up in a way that is useful to me. The same weight of that fine stuff from yonder bag would burn in an instant, and explode my apparatus, and me.”
“That is why I supposed the bag might have come from a theatre,” Daniel said. “Such powder may be unsuitable for the Rarefying Engine, but on the stage it makes a pretty flash and bang.”
“That bag,” said Hooke, “came from the magazine of one of His Majesty’s Ships of War. The practice used to be, and still is on some ships, that powder is introduced into the bore of a cannon by scooping it up out of a keg and pouring it in. Similar to how a musketeer charges the barrel of his weapon. But in the heat of battle, our gunners are prone to mis-measure and to spill the powder on the deck. And to have open containers of powder near active cannon is to tempt disaster. A new practice is replacing the old. Before the battle, when it is possible to work calmly, the powder is carefully measured out and placed into bags, such as that one, which are sewn shut. The bags are stockpiled in the ship’s magazine. During battle, as they are needed, they are ferried one at a time to the guns.”
“I see,” Daniel said, “then the gunner need only slash the bag open and pour its contents into the bore.”
Hardly for the first time, Hooke was a bit irked by Daniel’s stupidity. “Why waste time opening it with a knife, when fire will open it for you?”
“I beg your pardon?”
“Behold, the diameter of the bag is the same as the bore of the gun. Why open it then? No, the entire bag, sewn shut, is introduced into the barrel.”
“The gunners never even see what is inside of it!”
Hooke nodded. “The only powder that the gunners need concern themselves with is the priming-powder that is poured into the touch-hole and used to communicate fire to the bag.”
“Then those gunners are trusting the ones who sew up the bags—trusting them with their lives,” Daniel said. “If the wrong sort of powder were used—” and he faltered, and went over and dipped his fingers once more into the bag before him to feel the consistency of the powder inside. The difference between it and the Comstock powder was like that between flour and sand.
“Your discourse is strangely like that of John Comstock when he delivered that bag and that keg to me,” Hooke said.
“He brought them around in person?”
Hooke nodded. “He said he no longer trusted anyone to do it for him.”
Whereat Daniel must have looked shocked, for Hooke held up a hand as if to restrain him, and continued: “I understood his state of mind too well. Some of us, Daniel, are prone to a sort of melancholy, wherein we are tormented by phant’sies that other men are secretly plotting to do us injury. It is a pernicious state for a man to fall into. I have harbored such notions from time to time about Oldenburg and others. Your friend Newton shows signs of the same affliction. Of all men in the world, I supposed John Comstock least susceptible to this disorder; but when he came here with this bag, he was very far gone with it, which grieved me more than anything else that has happened of late.”
“My lord believes,” Daniel guessed, “that some enemy of his has been salting the magazines of Navy ships with bags filled with finely milled powder, such as this one. Such a bag, sewn shut, would look the same, to a gunner, as an ordinary one; but when loaded into the bore, and fired—”
“It would burst the barrel and kill everyone nearby,” Hooke said. “Which might be blamed on a faulty cannon, or on faulty powder; but as my lord manufactures both, the blame cannot but be laid on him in the end.”
“Where did this bag come from?” Daniel asked.
“My lord said it was sent to him by his son Richard, who found it in the magazine of his ship on the eve of their sailing for Sole Bay.”
“Where Richard was killed by a Dutch broadside,” Daniel said. “So my lord desired that you would inspect this bag and render an opinion that it had been tampered with by some malicious conspirator.”
“Just so.”
“And have you done so?”
“No one has asked my opinion yet.”
“Not even Comstock?”
“Nay, not even Comstock.”
“Why would he bring you such evidence in person, and then not ask?”
“I can only guess,” Hooke said, “that in the meantime he has come to understand that it does not really matter.”
“What an odd thing to think.”
“Not really,” Hooke said. “Suppose I testified that this bag contained powder that was too fine. What would it boot him? Anglesey—for make no mistake, that’s who’s behind this—would reply that Comstock had made up this bag in his own cellar, as false evidence to exonerate himself and his faulty cannons. Comstock’s son is the only man who could testify that it came from a ship’s magazine, and he’s dead. There might be other such bags in other magazines, but they are mostly on the bottom of the sea, thanks to Admiral de Ruyter. We have lost the war, and it must be blamed on someone. Someone other than the King and the Duke of York. Comstock has now come to understand that it is being blamed on him.”
The daylight had become much more intense in the minutes Daniel had been up here. He saw that Hooke had rigged an articulated rod to the back of the piston, and connected the rod to a system of cranks. Now, by means of a tiny touch-hole in the base of the cylinder, he introduced fire to the chamber. Thump. The piston snapped up to the top of the bore much faster than Daniel could flinch away from it. This caused an instant of violent motion in the gear-train, which had the effect of winding a spring that spiraled around in a whirling hoop the size of a dinner-plate. A ratchet stopped this from unwinding. Hooke then re-arranged the gears so that the giant watch-spring was connected, by a string wound around a tapered drum, to the drive-shaft of a peculiar helical object, very light-weight, made of parchment stretched on a frame of steam-bent cane. Like a Screw of Archimedes. The spring unwound slowly, spinning the screw swiftly and steadily. Standing at one end of it, Daniel felt a palpable breeze, which continued for more than a minute—Hooke timed it with his latest watch.
“Properly wrought, and fed with gunpowder at regular intervals, it might generate enough wind to blow itself off the ground,” Hooke said.
“Supplying the gunpowder would be difficult,” Daniel said.
“I only use it because I have some,” Hooke said. “Now that Anglesey has been elected President of the Royal Society, I look forward to experimenting with combustible vapors in its stead.”
“Even if I’ve moved to Massachusetts by then,” Daniel said, “I’ll come back to London to watch you fly through the air, Mr. Hooke.”
A church-bell began ringing not far away. Daniel remarked that it was a bit early for funerals. But a few minutes later another one started up, and another. They did not simply bong a few times and then stop—they kept pealing in some kind of celebration. But the Anglican churches did not seem to be sharing in the joy. Only the queer churches of Dutchmen and Jews and Dissenters.
LATER IN THE DAY, Roger Comstock appeared at the gates of Bedlam in a coach-and-four. The previous owner’s coat of arms had been scraped off and replaced with that of the Golden Comstocks. “Daniel, do me the honor of allowing me to escort you to Whitehall,” Roger said, “the King wants you there for the signing.”
“Signing of what?” Daniel could imagine several possibilities—Daniel’s death warrant for sedition, Roger’s for sabotage, or an instrument of surrender to the Dutch Republic, being three of the more plausible.
“Why, the Declaration! Haven’t you heard? Freedom of conscience for Dissenters of all stripes—almost—just as Wilkins wanted it.”
“That is very good news, if true—but why should His Majesty want me there?”
“Why, next to Bolstrood you are the leading Dissenter!”
“That is not true.”
“It doesn’t matter,” Roger said cheerfully. “He thinks it’s true—and after today, it will be.”
“Why does he think it’s true?” Daniel asked, though he already suspected why.
The Baroque Cycle: Quicksilver, the Confusion, and the System of the World Page 41