Did we have a reliable time system in the 1600s and 1700s?

Summarised by Bryson; feel free to look up more detailed accounts.

*"For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man ... early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismayingly large margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigour to navigation, and to that end he determined to calculate the length of a degree.*

Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York **at the same time of day and on the same day of the year as he had made his first measurement in London**. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc."

The exercise was repeated in two other locations by the French in the 1700s.

The whole method is based around calculating the angle related to the arc that Norwood paced out on the surface, and this only has relevance on a globe. The method has no meaning on a flat earth.