The addition of the quadrant to the art of artillery opened a whole new field for the mathematicians, who set about compiling long, complicated, and jealously guarded tables for the gunner's guidance. But the theory was simple: since a cannon at 45° elevation would fire ten times farther than it would when the barrel was level (at zero° elevation), the quadrant should be marked into ten equal parts; the range of the gun would therefore increase by one-tenth each time the gun was elevated to the next mark on the quadrant. In other words, the gunner could get the range he wanted simply by raising his piece to the proper mark on the instrument.
Figure 46—SEVENTEENTH CENTURY GUNNER'S QUADRANT. The long end of the quadrant was laid in the bore of the cannon. The plumb bob indicated the degree of elevation on the scale.
Collado explained how it worked in the 1590's. "We experimented with a culverin that fired a 20-pound iron ball. At point-blank the first shot ranged 200 paces. At 45-degree elevation it shot ten times farther, or 2,000 paces.... If the point-blank range is 200 paces, then elevating to the first position, or a tenth part of the quadrant, will gain 180 paces more, and advancing another point will gain so much again. It is the same with the other points up to the elevation of 45 degrees; each one gains the same 180 paces." Collado admitted that results were not always consistent with theory, but it was many years before the physicists understood the effect of air resistance on the trajectory of the projectile.
Sights on cannon were usually conspicuous by their absence in the early days. A dispart sight (an instrument similar to the modern infantry rifle sight), which compensated for the difference in diameter between the breech and the muzzle, was used in 1610, but the average artilleryman still aimed by sighting over the barrel. The Spanish gunner, however, performed an operation that put the bore parallel to the gunner's line of sight, and called it "killing the vivo" (matar el vivo). How vivo affected aiming is easily seen: with its bore level, a 4-pounder falconet ranged 250 paces. But when the top of the gun was level, the bore was slightly elevated and the range almost doubled to 440 paces.
To "kill the vivo," you first had to find it. The gunner stuck his pick into the vent down to the bottom of the bore and marked the pick to show the depth. Next he took the pick to the muzzle, stood it up in the bore, and marked the height of the muzzle. The difference between the two marks, with an adjustment for the base ring (which was higher than the vent), was the vivo. A little wedge of the proper size, placed under the breech, would then eliminate the troublesome vivo.
During the first half of the 1700's Spanish cannon of the "new invention" were made with a notch at the top of the base ring and a sighting button on the muzzle, and these features were also adopted by the French. But they soon went out of use. There was some argument, as late as the 1750's, about the desirability of casting the muzzle the same size as the base ring, so that the sighting line over the gun would always be parallel to the bore; but, since the gun usually had to be aimed higher than the objective, gunners claimed that a fat muzzle hid their target!
