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…”
“Betting.”
“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
