l894-] BAKER CIRCULAR INVERSION. 259 



Then just as in the previous figure, b" .= />--j- d"^, a" = (</ — PTY^ p"^, 

 3.ndb'—a^ = d^-—{d—FTy ' 



= {2d—FT) FT=FI'-I'r= constant. 

 Hence /' will describe a straight line. 



The point /' is evidentl)' connected with the former cell by 

 enlarging or diminishing, even through evanescence, the rhombus TI. 



Several tracing points can be had in the same cell, as shown in 

 fig. 8, where the points/, /', /", /'" all describe straight lines, as 

 shown. The points /', /", etc., are evidently found by increasing or 

 diminishing, even through evanescence, the tetragram FI. 



From this we get a rule for constructing a Peaucellier cell. 



Construct a double isosceles tetragram [not a rhombus) luith one vertex 

 fixed {the pivot) and the other vertex constrained {by a radial arm) to move 

 on a circle through the pivot. On the pivot legs construct another tetra- 

 gram forming a rhombus with the other pair of legs. The vertex of this 

 second tetragram will describe a straight line. This second tetragram 

 can be enlarged or diminished, even through evanescence. 



In fig. 9 I have drawn the cells resulting from the application of 

 of this rule. □ indicates the pivot /*, and o the point 7" traveling on 

 the arc of a circle through the pivot. 



If to the single ceil we add another pair of arms so as to form a 

 rhombus with the pivot arms, we get the double cell of fig. lo. 

 Since /"is symmetrical with F, and F T-F I = const., FIF'T = 

 const., and F' may be taken as the pivot and either T or I as the circle 

 tracing point (see fig. ii). By taking T as the pivot and applying 

 the rule for the construction of cells we get TFTP== const, (fig. 12). 

 If we have the cell shown in fig. 13, in which FT-FI= const., and 

 remove the light arms, replacing them as shown in fig. 14, the 

 geometrical relation between the points /*, T, and / will not be 

 altered, nor will their mechanical connection be lost, and we will have 

 a cell of four arms instead of six as heretofore. From the svmmetry 

 of the figure //'-/r^ const., IF //' = const., TF- TI' = const., 

 as in the double cell. 



Various modifications of this cell or linkage as it is sometimes 

 called have been devised for different purposes, a short account of 

 which will be found in Kempe's " How to Draw a Straight Line." 



Before closing, permit me to call your attention to one phase of 

 circular inversion that will show more clearly how your early theorem 

 in Geometry is connected with the inversion diagrams that I have 

 alreadv shown vou. 



