You'll see in Patrick O'Brian's novels that the main character owns several telescopes of varying degrees of quality and price.

The reason for this is because he chose to acquire them at his own expense because he is a career naval officer and therefore simply needs them in his work every day (later on its apparent that Jack Aubrey has an actual interest in Astronomy and optics but that doesn't come until later).

Likewise, each officer on the ship concerned with actual navigating and sailing with the means to afford it is also likely to buy themselves a telescope (usually referred to as a glass).

However this is the 18th century we're talking about and a telescope is a very expensive object, so the number of telescopes on a ship really depends on how well off the officers of that particular ship are.

As you'll see pointed out in both of those series; no two ships are alike, some are very rich and some are very poor.

In the novel Master and Commander at one point, it's mentioned that the First Lieutenant's glass is the best in the ship, despite him being subordinate to the Captain. This is probably because at the start of the novel Jack is broke while later on its established the Lieutenant is very rich:

"Look again with my glass", said Dillon, passing his telescope, the best in the sloop

So really, just like with the number of uniforms, chronometers, quantity of liquor for the officers, it really all depends on how personally well off the ships company was financially.

The royal navy (and army) at the time required its officers to provide an amount of equipment personally that seems absurd when compared to today's modern military (imagine hearing about an infantry officer in Iraq not having boots because he couldn't afford them).