7 6 



opens, Professor Sylvester's words :— " We are able, by this 

 machine, to bring about any mathematical relations that may 

 be desired between the distances of any two of the poles of the 

 linkage (the name of the machine) from a third, and are thus 

 potentially in possession of an universal calculating machine." 



I proceed to speak of the practical and obvious use of Peau- 

 cellier's machine as applied in mechanics. The parallel motion 

 of Watt, adopted for the purpose of giving as much directness 

 as he was able to do to the pushing of a piston by the end or 

 centre of a beam moving in the arc of a circle, is not perfect. 

 As applied in the ordinary beam engine to the cross-head proper, 

 it is so ; but as applied to the air-pump piston, the supposed 

 straight line through which its cross-head is directed is really a 

 figure of 8. Accordingly, its frequently uneven (or wabbling) 

 motion is apt to react on the head of the steam-cylinder piston, 

 and to produce a tremulous vibration ; which movement is 

 sometimes incorrectly supposed to be due to a mechanical error 

 in the parallel motion itself. The Peaucellier method has been 

 applied with admirable success to cross-heads ; in particular, 

 the steam-engine which performs the work of the Houses of 

 Parliament is so geared. There is, in fact, no common pump 

 to which the plan is not applicable. It is evident that there 

 must, in all cases, be a saving of power by substituting a direct 

 for a crooked pushing motion. 



Peaucellier has constructed linkages, or w cells," of two for- 

 mations, each of seven bars ; and a third linkage, based on the 

 same mathematical principle as Peaucellier's, has been shown by 

 a Cambridge man, consisting of only five bars — the smallest 

 possible number capable of affording a true straight line. The 

 original cell is (fig. I.) two equal bars (a), and four equal 

 ones (3), connected by two equal ones (c and d), d being 

 properly not a bar or rod, but the fixed distance equal to c. 

 The two long bars move as the radii of a circle ; the two bars 

 (b) joined to c, move from the circumference of a circle 

 whose radius is c or d ; and the further end of the rhombus 

 whose sides are b, moves, as c moves in its centre, so far as the 

 limits of the machine permit, in a straight line perpendicular to 



