As roberto, incredulous, demanded to know what, and how useless, the various methods to find longitudes had been, Father Caspar replied that while all were erroneous when taken one by one, if taken together the various results could achieve a balance and compensate for the individual defects: “And this est mathematical”
To be sure, a clock after traveling thousands of miles could no longer tell accurately the time of its place of origin. But how many and various clocks, some of special and careful construction, had Roberto seen on board the Daphne] You compare their inexact times, study daily the responses of one against the assertions of the others, and you arrive at a kind of certitude.
What of the loch or the navicella, or whatever you choose to call it? The usual ones do not work, but here is what Father Caspar had constructed: a box with two vertical poles, one that wound as the other unwound a cord of fixed length equivalent to a fixed number of miles; and the winding pole was surmounted by many little blades, which as in a mill turned under the force of the same winds that swelled the sails: their movement accelerated or slowed—and therefore wound or unwound the cord—according to the strength and direction, straight or oblique, of the wind, recording meanwhile also the deviations due to tacking, or sailing against the wind. A method not much more sure than all the others, but excellent if someone compared its results with those of other soundings.
Lunar eclipses? To be sure, observing them during a voyage resulted in endless misunderstandings. But what about those observed on land?
“We must have many observers and in many places of the world, and well disposed to collaborate in the major glory of God, and not exchange insults or spitefulness or scorn. Listen: in 1612, the eighth of November, at Macao, the most reverend pater lulius de Alessis records an eclipse at eight-thirty that evening until eleven-thirty. He informs the most reverend pater Carolus Spinola, who at Nangasaki, in laponia, the same eclipse at nine-thirty of the same evening was observing. And the pater Christophorus Schnaidaa had the same eclipse seen at Ingolstadt at five in the afternoon. The differentia of one hora makes fifteen degrees of meridian, and therefore this is the distance between Macao and Nangasaki, not sixteen degrees and twenty, as says Blaeu. Verstanden? Naturally with these records you must guard against drink and smoke, have correct horologii, not lose the initium totalis immersionis, and maintain correct medium between initium and finis eclipsis, observe the intermediary moments in which the spots are dark, et cetera. If the places are distant, a very little error makes no gross differentia, but if the places are proximi, an error of a few minutes makes gross differentia.”
Apart from the fact that in the matter of Macao and Nagasaki it seems to me that Blaeu is closer to the truth than Father Caspar (which proves how complicated longitudes were at that time), this is how the Jesuits, after collecting and collating the observations of their missionary brethren, established a Horologium Catholicum, which—despite the name—was not a clock devoted to the Roman pope but a universal clock. It was in effect a kind of planisphere on which were marked all the headquarters of the Society, from Rome to the borders of the known world, and for each place the local time was marked. Thus, Father Caspar explained, he had not had to bear in mind the hour at the beginning of the voyage but only at the last outpost of the Christian world, whose longitude was beyond debate. Then the margins for error were greatly reduced, and between one station and the next they could also use methods that, in the absolute sense, offered no guarantee, such as the variation of the needle or calculation from lunar spots.
Fortunately he had brethren just about everywhere, from Pernambuco to Goa, from Mindanao to Porto Sancti Thomae, and if winds prevented the Daphne from mooring in one port, there would soon be another. For example, at Macao ... ah, Macao! At the very thought of that adventure, Father Caspar glowered. It was a Portuguese possession; the Chinese called the Europeans men of long noses precisely because the first to land on their shores were the Portuguese, who truly do have long noses, and also the Jesuits, who came with them. So the city was a single garland of blue and white fortresses on the hill, controlled by the fathers of the Society, who had to concern themselves also with military matters, since the city was threatened by the Dutch heretics.
Father Caspar had decided to head for Macao, where he knew a fellow Jesuit very learned in the astronomical sciences, but he had forgotten that he was sailing on a fluyt.
What did the good fathers of Macao do? Sighting a Dutch ship, they manned their cannons and colubrines. In vain Father Caspar waved his arms at the prow and immediately had the Society’s standard run up; those cursed long-noses, his Portuguese brothers in the Society, wrapped in the warrior smoke that invited them to a holy massacre, did not even notice, and they rained balls around the Daphne. It was the pure grace of God that the ship was barely able to strike its sails, come about, and escape to sea while the captain in his Lutheran language hurled anathema at those fathers of scant consideration. And this time he was right: sinking the Dutch is all very well, but not when there is a Jesuit on board.
Luckily it was fairly easy to reach other missions not far away, and they turned their bowsprit towards the more hospitable Mindanao. And so, from one port to the next, they kept watch over their longitude (and God help them, I add, considering that, having ended up practically in Australia, they must have lost track of every point of reference).
“Et hora we must novissima experimenta make, ut claris-sime et evidenter demonstrate that we are on meridian one hundred eighty. Otherwise the fratres of the Collegium Ro-manum will think I am a Mamelukke.”
“New experiments?” Roberto asked. “Did you not just tell me that the Specula gave you the utmost assurance of being on the one-hundred-eightieth meridian, off the Island of Solomon?”
Yes, the Jesuit replied, he was certain: he had set in competition the various imperfect methods found by others, and the accord of all these weak methods supplied a very strong certitude, as happens in the proof of God’s existence by consensus gentium, for while it is true that many men inclined to err also believe in God, it is impossible that all should be mistaken, from the forests of Africa to the deserts of China. So it happens that we believe in the movement of the sun and the moon and of the other planets, or in the hidden power of Chelidonium, or that at the center of the earth there is a fire; for thousands and thousands of years men have believed these things, and while believing them, they have been able to live on this planet and achieve many useful results from their reading of the great book of Nature. But an important discovery like this had to be confirmed by further proof, so that even the sceptics would surrender to the evidence.
Besides, science must be pursued not only for the love of learning but in the desire to share it with our brothers. So, since it had cost him such an effort to find the correct longitude, he now had to seek confirmation through other, easier methods, so that this knowledge could become the patrimony of all our brothers, “or at least of the Christian ones, or, rather, the Catholic brothers, because, as for the Dutch or English heretics—or worse, the Moravians—it would be far better if they never came to learn of these secrets.”
Now, of all the methods of taking longitude, two seemed sure to him. One, good for terra firma, was that treasure of all methods, namely the Specula Melitensis; the other, appropriate for observation at sea, was the Instrumentum Arcetri-cum, which lay below but had not yet been set up, because he first had to obtain through the Specula the certitude of their position, then see if the Instrumentum confirmed it, which was the most reliable way to proceed.
Father Caspar would have carried out this experiment long before if what happened had not happened. But the moment now had come, and it would be on that very night: the sky and the ephemerides said that now was the right occasion.
What was the Instrumentum Arcetricum? A device envisioned many years earlier by Galilei—but, mind you, envisioned, narrated, promised, never achieved, until Father Caspar set to work. When Roberto asked him if that Galilei was the same who had advanced a severely condemned hypothesis about the motion of the earth, Father Caspar replied yes, when that Galilei had stuck his nose into metaphysics and the Sacred Scriptures, he had said dreadful things, but as a mechanical he was a man of genius and very great. Asked whether it was not wrong to use the ideas of a man the Church had censured, the Jesuit answered that to the greater glory of God the ideas of a heretic also could contribute, provided they in themselves were not heretical. And we might have known that Father Caspar, who welcomed all existing methods, not swearing by any one of them but exploiting their quarrelsome conference, would exploit also the method of Galilei.
Indeed, it was highly useful both for science and for the faith to develop as soon as possible that idea of Galilei; the Florentine himself had tried to sell it to the Dutch, but fortunately, like the Spaniards a few decades earlier, they did not trust him.
Galilei had drawn some odd conclusions from a premiss that in itself was quite right, namely that of stealing the idea of the spyglass from the Flemings (who used it only to look at ships in port) and training that instrument on the heavens. And there, among the many things that Father Caspar would not dream of doubting, Galilei had discovered that Jupiter, or Jove, as he called it, had four satellites, that is to say four moons, never seen from the beginning of the world until that moment. Four little stars that revolved around it while it revolved around the sun—and we will see that for Father Caspar the idea that Jove revolved around the sun was admissible, provided the earth was left alone.
Now, it is a well-known fact that our moon, when it passes in the shadow of the earth, is eclipsed. Astronomers have long known when lunar eclipses would occur, and the ephemerides were authoritative. It was not surprising, then, that the moons of Jove also had their eclipses. Indeed, for us at least, they had two, one actual eclipse and one occultation.
In fact, the moon disappears from our sight when the earth comes between it and the sun, but the satellites of Jove disappear from our sight twice, when they pass behind it and when they pass in front, becoming united with its light; through a good spyglass you can easily follow their appearances and their disappearances. With the inestimable advantage that while the eclipses of the moon occur only very rarely and take a long time, those of the Jovian satellites occur frequently and are rapid.
Now let us suppose that the hour and the minutes of the eclipses of each satellite (each traveling in an orbit of different breadth) have been precisely established on a known meridian, and the ephemerides bear this out; at which point it is enough to be able to fix the hour and the minute when the eclipse is visible on the (unknown) meridian, and the calculation is quickly made, and the longitude of the point of observation can be deduced.
True, there were minor drawbacks, not worth discussing with a layman, but the enterprise would succeed for a good calculator who had at his disposal a measurer of time, namely a perpendiculum or pendulum, or Horologium Oscillatorium as might be, capable of measuring with absolute precision even to the second. Similarly, he would need two normal clocks that told him faithfully the hour of the beginning and the end of the phenomenon both on the meridian of observation and on that of the Isla de Hierro; and, using the table of sines, he could measure the quantity of the angle made in the eye by the bodies under examination—the angle that, if thought of as the hands of a clock, expressed in minutes and seconds the distance between the two bodies and its progressive variation.
Provided, it is well to repeat, he also had those good ephemerides that Galilei, by then old and infirm, had not been able to complete, but that the brethren of Father Caspar, already so good at calculating eclipses of the moon, had now perfected.
What were the chief flaws, over which Galilei’s adversaries had waxed so bitter? That these observations could not be made with the naked eye and the observer needed a strong spyglass, or telescope, as it was now more properly called? And Father Caspar had some of excellent facture such as not even Galilei had dreamed of. That the measuring and the calculating were not within the skill of sailors? Why, all the other methods for determining longitude, except perhaps the log, required the presence of an astronomer! And if captains had learned to use the astrolabe, which itself was not something within the grasp of any layman, they could also learn to use the glass.
But, the pedants said, such exact observations requiring great precision could perhaps be made on land, but not on a ship in motion, where no one could hold a glass fixed on a celestial body invisible to the naked eye.... Well, Father Caspar was here to demonstrate that, with a bit of skill, observations could be made also on a moving ship.
Finally, some Spaniards had objected that satellites in eclipse did not appear during the day, nor on stormy nights. “Perhaps these complainers believe that a man claps his hands and there, illico et immediate, lunar eclipses are at his disposal?” Father Caspar was irritated. Who ever said that observations had to be made at every instant? Anyone who has voyaged from one Indies to the other knows that taking the longitude cannot require a greater frequency than what is required for observing the latitude, and this, too, whether with astrolabe or Jacob’s cross, cannot be done in moments of great tumult of the sea. To measure it properly, this longitude, even only once every two or three days suffices; then, between one observation and the next it is possible to keep account of the time and the space covered, as was done in the past, using the astrolabe. But until now that was all they could use for months and months. “They seem to me,” the good father said, more indignant than ever, “like Huomo that in gross famine you assist with a basket of bread, and instead of saying gratia he is disturbed that also a roasted schweine or a fat rabbit you do not put on the table for him. Oh, Holy Wood! Would you perhaps throw into the sea the cannons of this ship only because, ninety times out of a hundred, the balls fall plop into the aqua?”
So then Father Caspar engaged Roberto in the preparation of an experiment that was to be performed on an evening like the one now ahead of them, astronomically opportune, with clear sky and with the sea in slight motion. If the experiment were done on an evening of calm, Father Caspar explained, it would be like doing it on land, and there—as was already known—it was bound to succeed. The experiment had to provide the observer with the semblance of calm on a hull moving from stern to prow and from side to side.
First of all they had to recover, from among the clocks so maltreated over the past few days, one still in proper working order. Only one, in this fortunate case, and not two: they would set it to the local hour after taking good diurnal bearings (which they did) and, as they were certain of being on the antipodal meridian, there was no reason to have another clock telling the time of the Isla de Hierro. It was enough to know that the difference was exactly twelve hours. Midnight here; noon there.
On sober reflection, however, this decision seems based on a vicious circle. Their position on the antipodal meridian was something the experiment was to prove, not something to take as a given. But Father Caspar was so sure of his previous observations that he desired only to confirm them, and then—
probably—after all the confusion on the ship there was no longer a single clock that still told the time at the other side of the globe, and they had to overcome that obstacle. Actually, Roberto was not so punctilious as to point out the flaw in this argument.
“When I say go, you look at the hour and write. And immediately strike the perpendiculum.”
The perpendiculum was supported by a little metal armature which acted as a gallows for a copper wand ending in a circular pendulum. At the lowest point of the pendulum’s course there was a horizontal wheel in which teeth were set, but shaped so that one side of the tooth was square and jutted above the level of the wheel, and the other oblique. Alternately moving in this direction and that, the pendulum struck with a protruding spike, a bristle, which in turn touched a tooth on its jutted side and moved the wheel; but when the pendulum returned, the little bristle just grazed the oblique side of the tooth, and the wheel remained still. If the teeth were numbered, it was possible, when the pendulum stopped, to count the number of teeth shifted, and thus calculate the number of particles of time that had passed.
“So you are not obliged to count every time one, two, three, et cetera, but in the end when I say sufficit, you stop the perpendiculum and count the teeth, verstanden? And write how many teeth. Then you look at the horologium and write this or that hora. And when I again say go, you a very strong push give it, and it begins again its oscillatio. Simple, even a parvulus can do.”
To be sure, this was not a great perpendiculum, as Father Caspar well knew, but debate on that mechanism was just beginning, and only at some future time would it be possible to construct perfected ones.
“Very difficult, and we must yet much learn, but if God
did not forbid die Wette—how do you say?—the pari...”
“Ah. If God did not forbid, I would bet that in the future all will go to seek longitudes and all other phenomena with the perpendiculum. But is very difficult on a ship, and you must make gross attention.”
Caspar told Roberto to arrange the devices, together with writing materials, on the quarterdeck, which was the highest observation point on the Daphne: there they would set up the Instrumentum Arcetricum. From the soda they had carried up the instruments Roberto had glimpsed while he was still pursuing the Intruder. These were easily transported, except for the metal basin, which the two men hoisted up on the deck with curses and ruinous failures, for it would not pass through the hatches. But Father Caspar, wiry as he was, now that he saw the imminent realization of his plan, revealed a physical energy equal to his will.
Almost alone, with an implement of his that tightened bolts, he mounted the armature of semicircles and little bars of iron, which turned out to be a round frame, and to this a circular canvas was fixed with some rings, so that in the end they had a kind of great basin in the form of half a spherical orb with a diameter of about two meters. It was necessary to tar it so it would retain the malodorous oil with which Roberto filled it, emptying keg after keg, complaining of the stench. Father Caspar reminded him, seraphic as a Capuchin, that they were not using the oil to fry onions.
“What is the use of it, then?”
“On this little sea we try an even more little vessel to put,” he said, and made Roberto help him place in the great canvas basin a metallic pan, almost flat, with a diameter only slightly less than that of its container. “You never heard say the sea smooth like oil? There, look, the deck tilts left and oil of the big basin tilts right, and vice versa, or, rather, so to you it seems; truly the oil in equilibrium stays, never up or down, and to the horizon parallel. It would happen also with water, but on oil the pan floats like on a calm sea. And I have already in Rome a little experiment done, with two little bowls, the bigger full of water and the little of sand, and in the sand I stuck a stylus, and I set the little afloat in the big, and I moved the big, and you could see the stylus erect like campanile, not bent like the towers of Bolonia!”
“Hora we take the pan, where we must in it a whole machine put.”
The bottom of the metal pan had some little springs on the outside so that, the Jesuit explained, once it was afloat with its cargo in the larger tub, it would remain separated by at least one finger from the bottom of the container; and if the excessive movement of its guest drove it too far down (What guest? Roberto asked; Now you will see, Caspar replied), those springs should cause it to rise to the surface again without shocks. To the inner pan they affixed a seat with a sloping back, which allowed a man to sit or, rather, recline, looking up, his feet on an iron bar that acted as a counterweight.
Having set up the basin on the deck, and having made it stable with some wedges, Father Caspar sat on the seat and explained to Roberto how to place on his back and fasten to his waist a harness of straps and bandoleers of canvas and leather, to which also a helmet with a vizor should be tied. The vizor had a hole for one eye, while at the level of the nose a rod protruded, surmounted by a small hoop. Through the hoop was inserted the spyglass, from which a little staff hung, ending in a hook. The Hyperbole of the Eyes could be moved freely until a given star was identified; but, once the star was in the center of the lens, the rigid staff was fixed to the pectoral bandoleers, and after that a steady view was assured, fixed against any possible movements of that Cyclops.
“Perfecto!” the Jesuit rejoiced. When the pan was set afloat on the becalmed oil, even the most elusive celestial bodies could be studied and no commotion of the sea in tumult could cause the horoscopant eye to be deflected from the chosen star. “This your Signer Galilei described, and I have made!”
“Very beautiful,” Roberto said, “but who will put all this in the tub of oil?”
“Now I untie myself and get down, then we put the empty pan in the oil, then I climb on again.”
“I cannot believe that will be easy.”
“Much more easier than moving the pan with me in it seated.”
Though with some effort, the pan with its chair was hoisted up and set afloat on the oil. Then Father Caspar, in helmet and harness, and the spyglass mounted on the vizor, tried to climb onto the scaffolding while Roberto held him, one hand clutching his hand and the other pushing his bottom. The attempt was repeated several times, but with no success.
It was not that the metal frame supporting the larger tub could not support also an occupant, but it denied him reasonable footholds. And if Father Caspar tried, as he did many times, to set only one foot on the rim, immediately placing the other inside the minor circle, this latter, in the disturbance of the embarkation, tended to glide over the oil towards the opposite side of the basin, making the priest’s legs part like a compass as he emitted cries of alarm until Roberto seized him by the waist and drew him closer, that is to say onto the relative terra firma of the Daphne—cursing meanwhile the memory of Galilei and extolling his persecutors and killers. At that point Father Caspar sank into the arms of his savior, assuring him with a groan that those persecutors were not killers but most worthy men of the Church, bent only on the preservation of the truth, and that with Galilei they had been paternal and merciful. Then, still cuirassed and immobilized, his gaze towards the sky and the spyglass perpendicular to his face, like a Pulcinella with a mechanical nose, he reminded Roberto that Galilei, at least with this invention, had not erred, and it was just a matter of trying and trying again. "Und so mein lieber Robertus," he then said, "perhaps you have me forgotten and believe me a tortoise, captured with belly oben? Come, push me again, there, help me touch that rim, there now, for man is proper the statura erecta."
Through these several unhappy operations the oil did not remain smooth as oil, and after a while both experimenters found themselves oleate and, what was worse, oleabund—if the context allows the chronicler this coinage without imputation of the source.
When Father Caspar had begun to despair of ever occupying that seat, Roberto observed that perhaps it was necessary first to empty the container of oil, then install the pan, then have the priest climb onto it, and finally pour in the oil again, which, as its level rose, would raise also the pan and, with it, the observer, all floating together.
So it was done, amid praise from the master lavished on his acute pupil, as midnight was approaching. Not that the apparatus gave a great impression of stability, but if Father Caspar took care not to move unduly, they could hope.
At a certain moment Father Caspar triumphed: "I see them!" The cry caused him to move his nose, and the glass, rather heavy, began to slip out of the circle: he moved his arm to arrest it, the movement of the arm jerked his shoulder, and the pan was on the point of capsizing. Roberto abandoned paper and clocks, supported Caspar, re-established the equilibrium of the whole and bade the astronomer remain motionless, allowing only his eyepiece to make very prudent shifts, and above all without expressing emotions.
The next announcement was made in a whisper which, magnified by the great vizor, seemed to resound as hoarse as a Tartar trumpet: “I see them again,” and with a measured gesture he fixed the spyglass to the pectoral. “Oh, wunderbar! Three little stars east of Jupiter, one alone west... The closest seems smallest and is ... wait... yes, at zero minutes and thirty seconds from Jupiter. Write. Now it is about to touch Jupiter, soon it will disappear. Careful and write exactly the time it disappears....”
Roberto, who had left his place to assist his master, again picked up the tablet on which he was to mark the times, but sitting, he had the clocks behind him. He turned abruptly, knocking over the pendulum. The wand slipped from its notch. Roberto seized it and tried to replace it, but he failed. Father Caspar was already shouting orders to note the time, Roberto turned towards the clock and, in moving, he struck the inkwell with his pen. Not thinking, he set the well upright, to save some of the liquid, but he knocked over the clock. “Did you take the hour? Go! The perpendiculum!” Caspar was shouting, and Roberto replied, “I cannot, I cannot!”
“How can you not, dumbhead?” And hearing no reply, he kept on shouting, “How can you not, foolish? Have you written, have you made note, did you push? It is disappearing. Go!”
“I have lost, no, not lost, I have broken everything,” Roberto said.
Father Caspar moved the spyglass away from the vizor, peered sideways, saw the pendulum in pieces, the clock overturned, Roberto’s hands stained with ink. Beside himself, he
exploded with a “Himmelpotzblitzherrgottsakrament!” that shook his whole body. In that unfortunate movement, he caused the pan to tilt too far, and he slid into the oil of the basin, the spyglass slipping from his hand and his hauberk; then, as the ship pitched, the glass rolled across the quarterdeck, bounced down the ladder, and struck the main deck before it was flung against the breech of a cannon.
Roberto did not know whether to succor first the man or the instrument. The man, flailing in that rancidity, shouted magnanimously to save the spyglass, Roberto rushed down to the elusive Hyperbole, and found it, dented, both lenses broken.
When Roberto finally removed Father Caspar from the oil, the Jesuit, who looked like a piglet ready for the oven, simply said with heroic stubbornness that not all was lost. There was another telescope, equally powerful, mounted on the Specula Melitensis. They had only to go and fetch it from the Island.
“How?” Roberto asked.
“But you told me you cannot swim, nor should you, at your age....”