_The gunner's quadrant_ (fig. 46), invented by Tartaglia about 1545, was an aiming device so basic that its principle is still in use today. The instrument looked like a carpenter's square, with a quarter-circle connecting the two arms. From the angle of the square dangled a plumb bob. The gunner laid the long arm of the quadrant in the bore of the gun, and the line of the bob against the graduated quarter-circle showed the gun's angle of elevation. 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 deg. elevation would fire _ten_ times farther than it would when the barrel was level (at zero deg. 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. [Illustration: 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.