126 



NA TURE 



\yune 14, 1877 



P of the Peaucellier cell in Fig. 7, we see how P comfs to 

 describe a circle. 



It is hardly necessary for me to state the importance 

 of the Peaucellier compass in 

 the mechanical arts for drawing 

 ciicles of large radius. Of course 

 the various modifications of the 

 " cell " I have described may all 

 be employed for the purpose. 

 The models exhibited by the 

 Conservatoire and M. Breguet 

 are furnished with sliding pivots 

 for the purpose of varying the 

 distance between O and O, and 

 thus getting circles of any radius. 

 My attention was first called 

 to these linkworks by the lec- 

 ture of Prof. Sylvester, to which 

 I have refer reri. A passage in 

 that lecture in which it was stated that there were pro- 

 bably other forms of sevcn-liiilc parallel motions bisuJcs 



M. Peaucellier's, then the only one known, led me to in- 

 vestigate the subject, and I succeeded in obtaining some 

 new parallel motions of an entirely different chnracter 

 to that of M. Peaucellier. I shall bring two of these 

 to your notice as the investigation of them will lead us to 

 consider some other linkworks of importance. 



If I take two kites, one twice as big as the other, such 

 that the long links of each are twice the length of the 

 short ones, and make one long link of the small kite lie 

 on a short one of the large, and a short one of the small 

 on a long one of the large, and then amalgamate the coin- 

 cident links, I shall get the linkage shown in Fig. 18. 



The important property of this linkage is that, although 

 we can by moving the links about, make the points P and 

 P' approach to or recede from each other, the imaginary 

 line joining them is always perpendicular to that drawn 

 through the pivots on the bottom link L M. It follows 

 that if either of the pivots P or P' be fixed, and the link 

 L M be made to move so as always to remain parallel to 

 a fixed line, the other point will describe a straight line 

 pti jieiidicular to the fixed line. Fig. 19 shows you the 



parallel motion made by fixing P' It is unneces-ary for 



!• i o . - o . 



to 



me to point out how the parallelism of L M is preserved 



by adding the link S L, it is obvious from the figure. 

 The straight line which is described by the point P is 

 perpendicular to the line joining the two fixed pivots ; we 

 can, however, without increasing the number of links 

 make a point on the linkwork describe a straight line 

 inchned to the line S P at any angle, or rather we can, 

 by substituting for the straight link P C a plane piece, 



get a number of points on that piece mo\ing in every 

 direction. 



In Fig. 20, for simplicity, only the link C P' and the 

 new piece substituted for the link P C are shown. The 

 new piece is circular and has holes pierced in it all at 

 the same distance — the same as the lengths P C and P' C 

 — from C. Now we have seen from Fig. 19 that P moves 



