Ranging Impliments
The Gunner’s Quadrant
The quadrant has been around for a very long time, Ptolemy's Almagest (circa 150 AD) talks of using a peg on a graduated arc of 90 degrees.
An image from William Bourne’s The arte of shooting in great ordnaunce, first published in 1578, shows how the long arm of the quadrant is placed in the barrel of the gun. The plumb bob then shows the inclination on the degree scale.


The reproduction quadrant that we use.
From Museo Galileo
Quadrant consisting of two arms of unequal length joined at a right angle and fitted with a graduated arc. At the vertex of the right angle is suspended a plumb bob that shows the degrees on the graduated arc. Was typically used to measure the elevation of artillery pieces, by inserting the longer arm into the gun mouth and reading the inclination on the degree scale with the plumb bob. A variant of this instrument, designed for measuring heights and distances, used a shadow square instead of the graduated arc. Both variants of the instrument were published by Nicolò Tartaglia (1499-1557) in Nova scientia (Venice, 1537), a treatise in which ballistics, formulated with rigorous geometrical methods, is presented as a new discipline of the mathematical sciences.


The first description of its use for artillery is probably in Nicolò Tartaglia’s Nova Scientia, a work on ballistics published in Venice in 1537.
This drawing from The Compleat Gunner in Three Parts, 1672 (which is basically a reprint or translation of stuff published earlier by Casimir Simienowicz, Henry Hexham and others) shows the information that should be on the quadrant.


The Gunner’s Rule
The gunner’s rule that we use for living history is a copy of the one that appears in Eldred’s The Gunners Glass, and he is depicted with both his gunner’s rule and his linstock in the image of him at the beginning of the book. William Eldred (1563?–1646?) was about 1600 a gunner to the Cinque Ports, he lived at Dover and in 1616 became a gunner at the Castle. In 1624 he listed as master gunner, and he remained so. In 1640 he was employed by the commissioners of Dover harbour to prepare a survey of the castle, town, and harbour


As can be seen in the diagram the rule could be used to gauge your ball, and also as a sight. The rule is placed at the breech end of the gun and the target viewed through a pinhole in the centre of the slide. The slide is adjusted, so that the target, the upper edge of the gun's muzzle and the pinhole are all in line. Rules such as this were around earlier. The Museo Galileo at Florence has a lovely example dated 1595 and made by Hans Christoph Schissler.