MATHEMATICAL INSTRUMENTS. 47 



holder, tracer, and fulcrum, must in all cases be in a right 

 line, so that when they are set to any number, if a string be 

 stretched over them, and they do not coincide with it, there 

 is an error either in the setting or the graduations. The long 

 tube that carries the pencil, or crayon, moves easily up or 

 down in another tube, passing afterwards through the holes 

 in the three small knobs to the tracing point, where it may, 

 if necessary, be fastened. By pulling this string, the pencil 

 is lifted up occasionally, and thus prevented from making 

 false or improper marks upon the copy. 



To Reduce in any proportions, , |, {, etc., as marked on 

 the bars. Suppose, for example, ^ is required : place the 

 two sockets at \ on the bars B and D, place the fulcrum 

 or lead weight at B, the pencil socket with pencil at D, 

 and the tracing point at C. Fasten down upon a smooth 

 board, or table, a sheet of white paper under the pencil D, 

 and the original map, &c., under the tracing point C ; al- 

 lowing yourself room enough for the various openings of 

 the instrument. Then, with a steady hand, carefully move 

 the tracing point C over the outlines of the map, and the 

 pencil D will describe exactly the same figure as the original, 

 but half the size. In the same manner for any other propor- 

 tion, by only setting the two sockets to the number of the 

 required proportion. The pencil holder moves easily in the 

 socket to give way to any irregularity in the paper. There 

 is a cup at the top for receiving an additional weight, either 

 to keep down the pencil to the paper, or to increase the 

 strength of its mark. 



If the original should be so large, that the instrument 

 will not extend over it at any one operation, two or three 

 points must be marked on the original, and the same to cor- 

 respond on the copy. The fulcrum and copy may then be 

 removed into such situations as to admit the copying of the 

 remaining part of the original; first observing, that when 

 the tracing point is applied to the three points marked on 

 the original, the pencil falls on the three corresponding points 

 upon the copy. In this manner, by repeated shiftings, a 

 pantagraph may be made to copy an original of ever so 

 large dimensions. 



To enlarge in any of the proportions, ^, ^, j, (fee. Sup- 

 pose . You set the two sockets at J, as before, and have 

 only to change places between the pencil and tracing point, 

 viz. to place the tracing point at D, and the pencil at C. 



