30 



Transactions Tennessee Academy of Science 



Now turning our attention to Fig. 4, which is a skeleton drawing 

 of the Peucellier cell, we see that from the symmetry of the con- 



A 



struction of the cell, 0, C, P all lie in the same straight line, and if 

 the straight line An be drawn perpendicular to CP, Cn is equal 

 to nP. 



Now 



OA-'=On24-An2 

 AP2=Pn2+An2 

 therefore 



0A2— AP2=On2— Pn2 



= (On— Pn) . (On+Pn) 

 = OC.OP. 



Thus, since OA and AP are both constant, OC.OP is always con- 

 stant, however far or near C and P may be to 0. If then the pivot 

 be fixed to the point in Fig. 3, and the pivot C be made to de- 

 scribe the circle in the figure by being pivoted to the end of the 

 extra link, the pivot P will satisfy all the conditions necessary to 

 make it move in a straight line, and a pencil at P will draw a 

 straight line. The distance of the line from the fixed pivots will of 

 course depend on the magnitude of the quantity 0A2 — AP2, which 

 may be varied at pleasure. 



Now let us consider some modifications of the cell. The extra 

 link, the one that produces the circular motion, remains the same as 

 before, and it is only the cell that will undergo alteration. 



If I take the two linkages in Fig 5, which are known as the "kite" 

 and the "spear-head," and place one on the oilier so that the long 

 links of one coincide with those of the other, and then amalgamate 

 the coincident long links together, we shall gel the original cells of 

 Figures 2 and \. If then we keep liie angle belween ihe long links, 

 (jr ihal I)elween the short links, the same in the "kite" and "spear- 



