June X4, 1877] 



NATURE 



HOW TO DRAW A STRAIGHT LINE'' 

 III. 



BEFORE leaving the Peaucellier cell and its modifica- 

 tions, I must point out another important property 

 they possess besides that of furnishing us with exact recti- 

 linear motion. We have seen that our simplest linkwork 



enables us to describe a circle of any radius, and if we 

 wished to describe one often miles radius the proper course 

 would be to have a ten mile link, but as that would be, to say 

 the least, cumbrous, it is satisfactory to know that we can 

 effect our purpose with a much smaller apparatus. When 

 the Peaucellier cell is mounted for the purpose of describ- 

 ing a straight line, as I told you, the distance between 



the fij.ed pivots must be 'the same as the length of the but it may not be amiss to give here a short proof of the 

 "extra" link. If this distance be not the same we shall i proposition. 



not get straight lines described by the pencil, but circles. | In Fig. 17 let the centres Q, Q' of the two circles be at 

 If the difference be slight the circles described will be of ! distances from O proportional to the radii of the circles, 

 enormous magnitude, decreasing in size as the difference , If then O D C P S be any straight line through O, D O 



Fig. 19 



increases. If the distance Q O, Fig. 6, be made greater 

 than Q C, the convexity of the portion of the circle de- 

 scribed by the pencil (for if the circles are large it will of 



course be only a portion which is described) will be towards 

 O, if less the concavity. To a mathematician, who knows 

 that the inverse of a circle is a circle, this will be clear, 



* I-*^c*ure at South Kensington in connection with the Loan Collection of 

 Scientific A^ipar^tus, by A. li. ICempe, B.A. Continued from p. £5. 



Fig. 21. 



will be parallel to P (T, and C O to S Q', and O D will 

 bear the same proportion to O P that O O does to O Q'. 

 Now considering the proof we gave in connection with 

 Fig. 7, it will be clear that the product O D ■ O C is con- 



stant, and therefore since O P bears a constant ratio to 

 O D, O P • O C is constant. That is, if O C • O P is con- 

 stant and C describes a circle about O, P will describe 

 one about Q'. Taking then O, C, and P as the O, C, and 



H 2 



