Monday, 28th December 1676

The sky had remained clear and the breeze fair through Sunday as Zeelandia beat into the wind across the North Sea toward Hispaniola. Monday morning's sight on Polaris had placed us at seventeen degrees, six minutes. With only twenty-four miles remaining to the landfall latitude, Charles had decided to fall off four points to place the wind abaft the beam, increasing our speed and giving us a more comfortable course.

He had explained that cutting the angle should take us to the latitude by midday and that the sun's meridian passage will confirm. As noon approached, I stood at the rail up top, enjoying the gentle breeze across the starboard quarter. Such a difference between beating into the wind and running with it.

With me stood Mid Edwards, and after he had sighted the sun again with his quadrant, he said, "It continues to rise, but now much slowed, My Lady." After examining the reading, he continued, "Measuring the altitude is the easy part. Doing the reduction still confuses me."

"What is your confusion?"

"Knowing whether to add or to subtract."

"Picture it in your mind, Mid. Imagine you are at the centre of the earth, the Equator straight ahead and the North Pole directly overhead, a right-angle between them. With the winter, the sun is now across the Equator from here, adding its declination to the ninety degrees from the pole. So to correct, we must subtract today's tabulated declination from ninety. Then from that, we subtract the quadrant's measure of the sun's altitude above the horizon to give our latitude."

"But in the book, it says sometimes we need to add."

"Indeed, but that is only when the sun is between us and the Equator. And since that will not happen until the beginning of Spring, you may ignore it until then."

A few minutes later, Edwards said, "It has stopped rising, My Lady."

"Indeed, as I see with mine." I had barely finished saying this when eight bells pealed. "There, now! Mister Cogswell's sight agrees with ours, and he has ordered noon."

Edwards grinned and nodded. "That encourages. I do hope my rendering agrees with his, as well."

"It should – it is a simple calculation." I watched as he chalked the altitude reading onto the slate, then as he sought the declination from the tables, I said, "It would be better to have done that before – while you waited for the sun. And also subtract it from ninety, so only one step remains when the shot is made."

He nodded and reddened. "Mister Cogswell had told me that, but I forgot."

While he found the declination and made his calculations, I watched Mister Cogswell, Master Hawkins and Charles conferring. Then as Edwards passed me his slate, Cogswell ordered the wheel a half turn to port, and Master's loud barks fast roused the crew on deck to adjust the sails as Zeelandia altered. "There, you see how fast it can be."

"Aye, My Lady."

I checked his figures and read his latitude. "Speed was not necessary now; we are well safe. But at times, a fast rendering is needed, such as being not where we reckoned. Possibly sailing into danger."

He nodded. "How do you know all this, My Lady?"

"Years of having my tutors instruct me in all things nautical, so I could better understand my father's stories." I nodded toward Charles. "And recently, refreshing it through discussions with Captain."

He nodded again, and I handed the slate back to him. "When Mister Cogswell is unoccupied, show him this, that he knows you have done it correctly."

A few minutes later, when Zeelandia had settled onto her westerly course, Charles led me down into the great cabin, saying as we descended, "We should raise land anytime from now to five hours hence."

"So precise with latitude, but such inaccuracy with longitude."

"Aye, how to determine our eastings and westings is the last great navigational problem."

"We know the sun's progression is regular and measured. Would a clock not assist?"

"Were they more accurate than sandglasses."

"We had one at home, which kept fine time with the one in the church tower."

"Indeed, modern clocks ashore now have a pendulum to regulate the movement, but this is impossible with the motion of a ship at sea." He pointed to the chart table. "Captain Angus left his table clock, but I have long since stopped using it."

"Oh! Why have you stopped?"

"It requires rewinding at least twice each day, and it runs fast with the spring wound tight, gaining several seconds the hour. Then as the tension eases, it slows."

"Could you not wind it more frequently? Every half hour as they do with turning the sandglasses."

"And through the night?"

"Have the sandglass keepers do it."

"The salt air is not kind to them. Captain Angus warned me against taking it outside; its works are already impaired by rust." Charles shrugged. "Besides, with the sun progressing westward at fifteen degrees each hour, which at the Equator is fifteen miles each minute, an error of ten seconds the hour would in the course of a day amount to sixty miles."

I nodded. "Half again as much as from reckoning with the sandglasses."

"Indeed. Even one second on the hour would amount to six miles per day. Using the sun to determine longitude requires a precision of seconds per day, not seconds per hour."

Tilting my head toward Olivia laying the table, I said, "But the clock would be sufficient to measure the timing of events such as meals."

"Aye, and we might bring it out to time our mornings, that we not be surprised by seven bells."

"And be again late to breakfast." I chuckled. "But now, we should refresh and clean for dinner."