In the late 18th century, ships leaving Europe for other continents routinely brought with them books such as trigonometrical tables and [*astronomical almanacs*](https://aa.usno.navy.mil/publications/asa_history).

These almanacs included *ephemerides*, that is predicted positions of various astronomical bodies (sun, moon, planets, stars), which would have been available, but certainly much less accurate and reliable without calculus.  These predicted positions greatly improved the ability of contemporary navigation officers to accurately compute the current positions of their ships.

On a broader perspective, astronomical navigation benefited from 3 major improvements during the 18th century:
  1. invention of [the sextant](https://en.wikipedia.org/wiki/Sextant)
  2. greatly improved astronomical predictions (calculus with perturbation theory)
  3. invention of [the marine chronometer](https://en.wikipedia.org/wiki/Marine_chronometer)

However, the availability of marine chronometers was, for decades after their invention, limited by their very high cost, and many ships persisted in using the [lunar method](https://en.wikipedia.org/wiki/Lunar_distance_(navigation)) instead.

It is possible to claim that improved ephemerides made the lives of sailors better (or at least longer...), as they increased the probability of not getting lost at sea and surviving the trip. The fact that naval powers of the time such as England and France were willing to fund [costly and sophisticated astronomical observatories](https://www.the-observatory.org/rgohistory) had a lot to do with seafaring applications of astronomy.

**Side note**:
As an example of the dire consequences of being unable to compute an accurate position for a ship (or fleet for that matter), consider [the Scilly naval disaster of 1707](https://en.wikipedia.org/wiki/Scilly_naval_disaster_of_1707) with over 1,400 casualties. The lost ships belonged to one of best navies of the time and had professionally trained navigation officers on board. And still, they struck the rocks while almost in their home waters.