The tangent sight was an adjustable rear sight. The sight was on a bar, graduated either in degrees or ranges, and fitting into a socket at the center or on the side of the breech. The name is derived from a trigonometric relationship, the required height of this rear sight is the product of the distance from the rear sight to the front sight, by the tangent of the required angle of elevation. This may seem a simple concept, but it doesn't appear to have been used on artillery until it was introduced by de Gribeauval in the late-eighteenth century. (Cummins 25). Bear in mind that its use implies setting a specific angle of elevation, rather than just sighting on an aiming point. (Ruffell).
In canon, the guns of Simpson's 1634 navy have ring-and-post sights. (1634: The Baltic War, (TBW) Chap. 38).This combines a front (post) and a rear (ring) sight.It can be advantageous for the "ring" part to have several concentric circles; these can be useful in "stadiametric ranging" (measuring the angular width of a target of known actual width). A V-or U-notch is a possible substitute for the ring.
You have to hold your head just right to keep the ring and post aligned. It's also hard to use if the target is far away; bear in mind you are trying to keep in focus the target, the rear sight and the front sight, all at different distances.
Telescopic Sights. In Cooper, "Seeing the Heavens," Grantville Gazette 16, I described the state of the telescopic art as of the RoF. In 1640-41, William Gascoigne mounted telescopic sights-essentially, a Keplerian telescope with crosshairs in the focal plane-on various scientific instruments, including a micrometer and a sextant. However, the first documented use of a telescopic sight on a firearm was in 1835, and that was for use with a percussion ignition sporting rifle. (Pegler 50). And as far as I know, the first use of a telescopic sight with artillery was in 1857. (Strauss 587).
If this long time lag from the invention of the telescope to its use in gunnery surprises you, consider this: it doesn't matter if you can see the pimple on the enemy helmsman's nose if your powder and shot are so inconsistent in character, and ship motion so erratic, so you can't even hit the enemy ship with more than one shot in ten.
In canon, the best of Krak's Shooters have been given up-time telescopic sights for their flintlock rifles. (Flint, 1633, Chapter 35).
Since telescopes provide a magnified image, they necessarily have a narrowed field of view, and the eye needs to be close to the eyepiece to get that view.If the telescope is attached to a cannon, you must move your head away quickly when you fire, lest recoil result in an unpleasant experience.
Reflector Sights. A half-silvered diagonal or curved mirror can be used to overlay a virtual image of an illuminated crosshair, harmonized with the gun bore, over the field of view. While optical tricks using partially reflective mirrors are much older, the reflector gunsight reportedly was invented in 1900. A reflector sight is easier to align with the target than is an open sight. But please note that open sights were still used four decades later.
In shooting at a distant target, you need to allow for the "drop" (from gravity) and the "lead" (to anticipate relative target motion). So you have to offset the line of aim from the line of bore so that the projectile would hit the target.
Initially, gunners had to offset manually. However, analog computers were developed to calculate this offset and manipulate the optics accordingly. On these "computing gun sights," the gunner had to estimate the size of the enemy and fit the image within a reticle so the range could be calculated stadiametrically. Anti-aircraft guns had fancier "predictors."
Gyro Sights. The gyro sight was developed during WWII for aircraft (and anti-aircraft) use. The reflector was linked to a spinning gyro and this made it possible for the sight to compensate for the aircraft's own motion by adjusting the reflector. (Jarrett 190).
Firing Mechanism
The period gun has a vent (touch hole) that connects the powder chamber to the outside world. In preparing to fire the gun, the touch hole was filled with a "priming" powder, and some powder was deposited on the barrel just behind the touch hole. A linstock (forked staff) was used to bring a lit "slow match" (a slow-burning fuse, made by impregnating a rope with a saltpeter solution) over to the surface powder, igniting it. It, in turn, ignited the powder in the touch hole proper, which ignited the powder in the chamber. (Little 145).
Unfortunately, this process tended to erode the vent. Consequently, come 1697, gunners inserted disposable metal (tin) tubes into the vent. The tubes were filled with a paste of powder, gum and water, and loose powder was sprinkled on top. In 1778 the British Navy replaced the metal tubes with goose quills. (Rufell).
After 1700, it became customary to use the slow-match just to light a "portfire," a paper tube, closed at one end, filled with a mixture of gunpowder, sulfur and saltpeter in a linseed oil base; it burned rather like a motorist's emergency flare. (Peterson 66).
I imagine that we will leapfrog portfires and proceed to mechanical ignition. The first such was the Douglas flint lock (1778), which was actuated by a lanyard that pulled its trigger. In 1842 it was replaced by the Hiddens percussion lock; a hammer struck a percussion cap. (EB11/Ordnance).For the reasons why the 1633 NUS army was armed with flintlocks, not percussion locks, see Grantville Firearm Roundtable, "Flint's Lock" (Grantville Gazette 3).
The "firing interval" is the time elapsed from when the gun captain activated the ignition mechanism to when the primer actually ignited. (There would of course be a further delay until the projectile actually left the gun barrel). With the percussion lock, the firing interval averaged 0.13 seconds. (Meigs 195).
The percussion cap contains a primer, a fairly sensitive explosive mixture that in turn sets off the explosive. The first primer developed was mercury fulminate (1807). According to canon, certain reckless souls are making it. See Offord, "Dr. Phil Zinkens A Bundle" (Grantville Gazette 7); Offord and Boatright, "The Dr. Gribbleflotz Chronicles, Part 2: Dr. Phil's Amazing Essence Of Fire Tablets" (Id.); Mackey, "The Essen Steel Chronicles, Part 2: Louis de Geer" (Grantville Gazette 8); Evans, "Thunder in the Mountains" (12); Zeek, "One Fine Day" (20); Offord, "A Change of Hart" (25); Howard, "The Baptist Basement Bar and Grill" (32).
While these stories emphasize the dangers of manufacturing mercury fulminate, there are other problems. Specifically, it was found (in 1897) that the mercury in the primer became amalgamated with the brass of nineteenth-century cartridge cases, embrittling them. These cases were a large part of the cost of a cartridge and the "brass" (couldn't resist) wanted to be able to reuse them.
Accordingly, mercury fulminate was replaced with potassium chlorate (historically, first synthesized in 1786). That, too, has appeared in canon, in the percussion caps for the French "Cardinal" rifles. (TBW Chap. 27, 45).
It's not a panacea. When a gun using a potassium chlorate primer is fired, the priming reaction generates potassium chloride, which is deposited on the bore. This salt greedily absorbs water, causing rusting. In OTL, it wasn't until 1922 that potassium chlorate was identified as the cause of the rust, but Grantville's gun buffs may already know about the problem.
A non-corrosive primer, based on lead styphnate, was patented in 1928. It's likely that gun owners in Grantville have heard of it. Condensed Chemical Dictionary reveals that this is the legal label name for lead trinitrosorcinate (311), that the latter is made from magnesium styphnate and a lead salt, the former in turn being made from magnesium oxide and styphnic acid (312), and that styphnic acid is made by nitration of resorcinol (830; cp. 759).