4, and so on to 18. The inner series begins from another mark "□" (a square symbol) at the outer end, proceeding inward to 1, 2, 3, 4, and so on also to 18. These lines were used in conjunction with the other scales for a number of complex calculations. Use The instrument can be used to graphically solve questions of proportion and relies on the principle of similar triangles. Its vital feature is a pair of jointed legs, which carry paired geometrical scales. In use, problems are set up using a pair of dividers to determine the appropriate opening of the jointed legs, and the answer is taken off directly as a dimension using the dividers. Specialised scales for area, volume and trigonometrical calculations, as well as simpler arithmetical problems, were quickly added to the basic design. Different versions of the instrument also took different forms and adopted additional features. The type publicised by Hood was intended for use as a surveying instrument and included not only sights and a mounting socket for attaching the instrument to a pole or post, but also an arc scale and an additional sliding leg. Galileo's earliest examples were intended to be used as gunner's levels, as well as calculating devices. Bibliography Galilei, Galileo, Operations of the Geometric and Military Compass, 1606. Translated with an introduction by Stillman Drake. The Burndy Library, published by The Dibner Library of the History of Science and Technology of the Smithsonian Institution and The Smithsonian Institution Press, Washington, D.C. 1978. Galilei, Galileo, Le Operazioni del Compasso Geometrico et Militare, third edition, Padua 1649. Scan available at the Internet Archive. Ralf Kern: Wissenschaftliche Instrumente in ihrer Zeit. Vom 15. – 19. Jahrhundert. Verlag der Buchhandlung Walther König 2010, References A typical sector and how to use it The Scales of the Galilean Sector quotations from: "The Geometric and Military Compass” by G. Galilei (archived 2008) Cole Military Sector at the IBM Archives Galileo Galilei Mechanical calculators Italian inventions