40 SCIENTIFIC APPARATUS. 



D. Modes of representing figures in space by means of plane 

 drawings. 



A. INSTRUMENTS USED IN GEOMETRICAL DRAWING. 



The Ruler and the Compasses the two great instruments of 

 geometrical drawing and construction are of a very remote anti- 

 quity. Probably a stretched string such as is still used by car- 

 penters was the earliest form of apparatus for obtaining a straight 

 line ; and a string attached to a peg (a contrivance still adopted 

 by gardeners in laying out a flower-bed) afforded the earliest means 

 of describing a circle. Compasses such as we now use, and 

 indeed several of very different forms, have been found in 

 the excavations of Pompeii. But it is probable that the use of 

 the compasses, which is now universal, for transferring with 

 exactness measured lengths from a scale to a drawing, or from one 

 drawing to another, was hardly practised in ancient times. Had 

 this practice prevailed, it is difficult to suppose that it would not 

 have superseded the second and third problems of the First Book of 

 Euclid, in which lengths are transferred by means of the actual 

 description of circles. 



Among more recent improvements in the construction of 

 compasses we may notice (i) the arrangements adapted for very 

 fine work, and known as hair-cornpasses, needlepoint compasses, 

 and spring-dividers ; (2) the proportional or reducing compasses, 

 by which we are enabled to reduce or augment in any given 

 ratio the distances which we transfer from one drawing to another ; 



(3) the triangular compasses, by which the position of three points 

 forming a triangle can be transferred from one drawing to another, 

 and which thus serve as an instrument for transferring angles; 



(4) 'the beam compasses, consisting of a beam or bar, along which 

 the two points of the instrument may be moved backwards and 

 forwards, the distance between them admitting of adjustment with 

 great precision, by means of a micrometer screw. 



Next in the universality of its employment in all geometrical 



