WATT. 39 



and finer operations than those of the miner, depends 

 essentially on the accurate position of the piston-rod, 

 with whatever velocity moving, and against whatever 

 weight contending. Its motion must be steadily main- 

 tained in the same vertical straight line, or in the same 

 horizontal line, or in the same straight line whatever 

 be its direction, without shaking or inclining so as to 

 press at all against the sides of the cylinder any 

 such lateral pressure occasioning a loss of time, a 

 jolting motion, a general derangement of the ma- 

 chinery. 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 conduced. If 

 a circle or other curve has its curvature gradually 

 changed, until from being concave to its axis it be- 

 comes 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 



