432 Prof. Wallace on the Invention of the Pantograph, 



point is fixed at T, the extremity of one arm, and a black lead 

 pencil, which serves as a copying point, at P, the extremity of the 

 other arm on the opposite side of the beam. The distances of 

 these points from the centres of the wheels are in every case 

 equal to the distances of the latter from the centre of the beam, 

 whatever proportion these have to each other. By this disposi- 

 tion of the members of the instrument, a straight line joining the 

 tracing and copying points passes through the axis of motion of 

 the beam, and is there divided into two parts, which have to 

 each other the proportion of the distances between the centres 

 of the wheels and the centre of the beam. Thus the conditions 

 required by the mathematical theory are satisfied. 



Having described the instrument generally, I shall now no- 

 tice its parts, particularly, in detail. 



The beam a a, for the sake of lightness and stiffness, is hol- 

 low ; it is about thirty inches long, but may be of any required 

 length ; its cross section is a square, about nine-sixteenths of an 

 inch in the side. There is a scale of 200 equal parts engraved 

 on one of its vertical faces. The length of the scale is the exact 

 distance between the centres of the axes of the wheels, and each 

 division is -^ o-th part of this length. The division at the middle 

 of the beam is (zero), and the scale is numbered both ways ; 

 the extreme divisions would be 100, if they were numbered so 

 far, but they go only to about 70, no more being ever required. 



The socket c c, in which the beam slides, is four inches long ; 

 it has an opening on one side, through which the divisions on the 

 scale appear, ard there is an index engraved on it, against which 

 the zero division is set, when the middle of the beam is exactly 

 over the centre of the vertical axis on which the socket turns. 

 Fig. 4. is a vertical cross section, through the centre of the beam 

 socket, of half the actual size. The opening for viewing the 

 scale is at v ; c is a steel conical axis, fixed into a strong plate p, 

 screwed into the bottom of the socket, and turning in the bored 

 tube s, which is screwed to d d, the base of the instrument. 



