258 ROCHESTER ACADEMY OF SCIENCE. [April 9, 



correcting it by trial until you have a satisfactory result. Practically 

 you would not do this, but would describe your circle with one sweep 

 of the tracing point of a pair of compasses. 



To accomplish the same thing in the case of a straight line had 

 long been the object of mechanicians from the days of Watts on. 

 The problem was usually spoken of as that of parallel motion. Watts 

 accomplished it partially by means of the mechanism shown in fig. 3, 

 where the line traced (dotted) is shown nearly straight on one side of 

 the figure 8, but decidedly not straight beyond certain limits. In this 

 mechanism the short arm is perpendicular to the two equal radial 

 arms when they are parallel. Later, Richard Roberts of Manchester 

 devised the linkage shown in fig. 4, in which the distances between 

 the fixed puints is twice the distance between the two movable pivots, 

 the long arms being of equal length. The fixed pivots are designated 

 by D and the movable pivots by o . Within limits, as shown, 

 the line is nearly straight. Other methods have been devised but 

 they either mereh^ approximate, or else depend upon straight line 

 guides, as in the parallel motion of Scott Russell shown in fig. 5, 

 where the point A slides in guides, as shown, and the point B 

 describes the straight line. 



Finally, in 1864, Peaucellier, a French officer of Engineers, 

 devised the mechanism shown in skeleton in fig. 6, in which 

 /* 7"- 7^/= constant, 7" and /being opposite vertices of a rhombus. 

 To show that this product is constant, consider that 



U" = p"" -^ {P T ^ d)\ and a' =/ + ^^ whence 

 ^—0"= (FT+ dy — d' 



= {PT+ 2d) ■{PT) = FrFT=cons\.^nl, 

 since the arms a and b are invariable in length. 



Now if T be constrained to move on a circumference through P, 

 J will, as we have just seen, describe a straight line. A radial arm 

 connecting T with a fixed point equidistant from P and T would 

 accomplish this. 



In this machine we have the famous Peaucellier cell. If you 

 wonder at the word cell, I must refer you to the International 

 Dictionary where you will find — Cell : The space between the ribs of 

 a vaulted roof ; or to Murray's New English Dictionary — One of the 

 number of spaces into which a surface is divided by linear partitions; 

 one of the compartments into which anything is divided. 



As a modification of this, take any point /', fig. 7, by constructing 

 the rhombus P T, similar to 77, and connect the point P as shown. 



