GEOMETRICAL INSTRUMENTS AND MODELS. 41 



plan drawing is the scale of equal parts. Let one pair of opposite 

 sides of a rectangle be divided, say, into ten equal parts, the 

 points of division on each being numbered i, 2, 3, . . 9, and 1-et 

 the lines n, 22, 33, . . 99, be drawn parallel to the sides of the 

 rectangle. Let the other pair of opposite sides be similarly 

 divided into ten equal parts, but let the points of division be 

 joined in a slanting direction by the parallels 01, 12, 23, 34, . . . ; 

 it will be found that the first set of parallels are divided into 

 hundredths by the second set. Such a diagonal scale is placed on 

 every so called plane scale, and serves to divide one of the primary 

 divisions into hundredth parts. With a fine pair of compasses, 

 we may succeed in taking off from the scale any required length 

 with an error perhaps not exceeding one five hundredth part of a 

 primary division of the scale. 



Besides the scale of equal parts, the plane scale usually has 

 engraved upon it a scale of chords, and a protracting scale. 

 These are the simplest known contrivances for setting off an 

 angle, given in degrees and minutes, or for approximately measur- 

 ing an angle already laid down. With a good scale of chords, an 

 angle can, it is said, be set off true to the nearest minute. But, 

 for the best and most convenient solution of the problem, "to 

 construct an angle equal to a given one," we have recourse to the 

 divided circles, or parts of circles, known as circular, or semi- 

 circular, or quadrantal, protractors. 



Less elementary in their theory than the preceding simple 

 instruments, are the arrangements called Pantographs, which 

 enable us to copy any given plane figure upon a different scale. 

 Of this instrument there are two principal forms, known as the 

 older pantograph and the Milan pantograph. In each of these 

 there is a linkage movement in which only one point is absolutely 

 fixed. The linkage is so arranged that two points on different 

 bars always remain in the same straight line with the fixed point, 

 and at distances from it which are to one another in a constant 

 ratio. It follows from this that if one of these two points be made 



