and Description of the Eidograph. 431 



Or, generally, and more briefly, thus : 



" If, from a given point, two straight lines be drawn, contain- 

 ing a given angle, and having to each other a given ratio ; and 

 if one of them terminate in a line of any kind given in position, 

 the other terminates in a similar line, which is also given in po- 

 sition." 



The proposition in this second form gives great latitude in 

 the construction of the instrument. I have, however, only em- 

 ployed the principle as first enunciated. 



In applying the principle, the object to be accomplished was, 

 to connect by mechanism two material points, which should 

 move with perfect freedom, subject to the specified conditions of 

 the abstract proposition ; or so that one of them, a tracing point, 

 being carried along the lines of any proposed design, the other, 

 a copying point, should trace on paper a true copy of the design 

 in any given proportion. This has been effected by the instru- 

 ment now to be described. 



Its general appearance is shewn in Plate XIV. Fig. 1, which is a 

 projection of it on the plane of the surface on which the design and 

 its copy are placed. The beam a a is a square prism of brass ; it 

 passes through a socket c c, in which it may slide either way. 

 The socket is supported by, and turns on an axis rising out of a 

 base dd, which is a brass cylinder. There are two wheels^/,' 

 having equal diameters, below the beam ; these have vertical axes 

 fixed in them, which turn in bored tubes attached to its extremi- 

 ties. The wheels are connected by a metallic bandfg,fg, which 

 passes round them, and is fixed at a point in the circumference 

 of each, so that it cannot slide along their edges. 



Two arms P b, T b, pass through sockets (in which they may 

 slide), under the centres of the wheels, and turn along with them 

 in a plane parallel to that on which the instrument stands. By 

 the equality of the wheels, and their connection by the band, 

 the arms when once placed parallel continue so, although the 

 wheels are turned about their centres. A tracer with a steel 



