WATT. 3G9 



shaking or inclining so as to press at all against the 

 sides of the cylinder any such lateral pressure occa- 

 sioning a loss of time, a jolting motion, a general de- 

 rangement of the machinery. The motion of the rod 

 and the piston must be perfectly equable, continuous, 

 and smooth : it must work, as the engineers sometimes 

 say, sweetly, at every instant, in order that the engine 

 may well perform its functions. The contrivance for 

 producing this motion of the rod so that it shall 

 be always in one line, parallel to some supposed line 

 whether vertical, as in a mine, or horizontal, or in any 

 other direction, is thence called the " Parallel Motion" 

 and it is one of Mr. Watt's most exquisite discoveries, 

 and one to which scientific principle has the most con- 

 duced. If a circle or other curve has its curvature gra- 

 dually changed, until from being concave to its axis it 

 becomes convex, it will pass through every possible 

 position or variation (whence the great refinement 

 upon fluxions, the calculus of variations, probably 

 derived its name, if not its origin), and at one point 

 it will be a straight line, or will coincide with a 

 straight line. So if a curve have two branches, one 

 concave to the axis, the other convex, as a cubic para- 

 bola for example, the point at which its concavity ends 

 and its convexity begins, is called for that reason a 

 point of contrary flexure. The contrivance of the 

 parallel motion consists in making the contrary circu- 

 lar motions of arms which bear on the rod always keep 

 to the point of contrary flexure and thus give a recti- 

 linear motion to the rod, the tendencies to disturb it 

 correcting each other. It was long ago shown by Sir 

 Isaac Newton, in the ' Principia,' that if a circle moves 



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