ON DRAWING, WRITING, AND MEASURING. 103 



in all other directions. The systems of lines, on which music is written, are 

 drawn at one stroke by a pen with five orifices, usually made of brass. It 

 was long since proposed to rule a whole page at once, with a more complicat- 

 ed pen of the same kind, and the greatest part of the paper, on which music 

 is written in this country, is actually ruled by such a machine, for which a 

 patent has been taken out. (Plate VI, Fig. 87, 88.) 



The pantograph is used for copying figures, and at the same time reducing 

 or enlarging them; it consists of four rulers, two of them united by a joint at 

 the extremities, and receiving at the middle the other two, which are but 

 half as long, and are also united together, so as to form with the others a 

 jointed parallelogram, of which {wo of the sides are produced beyond the 

 angles ; if holes be made in these, and in one of the shorter rulers, so situated 

 as to be in the same right line in any position of the instrument, they will 

 remain in a right line in any other position, and they will always divide this 

 line in the same proportion : so that if one of the holes be placed on a fixed 

 axis or pin, a tracing point inserted in another, and a pencil in the third, 

 any figure delineated b\ the pencil will be similar to that which is described 

 by the tracing point. And instead of holes in the rulers, they may be fur- 

 nished with sliding sockets, to receive the axis, the point, and the pencil, 

 (Plate VI. Fig. 89.) .:' ' 



Proportional compasses are also of great use, in reducing lines and figures to . "' *^ ' 

 a difterent scale. This instrument consists of two legs, pointed at each end, 

 and turning on a centre, which slides in a groove common to both legs, and is 

 furnished with an index. The divisions of the scale are so laid down, that 

 the centre may divide the length of the legs from point to point in a given 

 proportion; hence, by the properties of similar triangles, when the legs are 

 opened to any extent, the intervals between each pair of points must be to 

 each other in the same ratio as the portions of the legs. Sometimes a screw 

 is added, for the sake of adjusting the centre with greater accuracy; and it is 

 usual to lay down scales for dividing the circumference of a circle into a 

 given number of parts, and for some other purposes; but the irrstrument 

 might be much improved by inserting, in the common scale, fractional or de- 

 cimal divisions, between the whole numbers, so that the legs might be di- 



