324 On Printing Presses and their Theory. 



Srbi Aa. -^- : : OB-1- AO. cos^ A : AO. cos ^ A. Divi- 



ding the second and fourth terras by — r-r-, we obtain, srb : 



° •' sinA ° 



Aa: : OB+AO. cos* A : AO. sin A. But gb represents 

 the velocity with which B moves, reduced to the direction 

 of a perpendicular to BA, and Aa denotes the cotemporane- 

 ous velocity of A. Hence the power is to either of two 

 equal resisting forces applied to A and C as AO 'sin A t 

 AO 'cos^ A+OB. — Ifthe angle BCA be not too large^ 

 we may suppose C immoveable, and the whole resistance ap- 

 plied at A. We shall then have power : resistance appHed 

 atA::2A0-sin A : : AO-cos^ A4 OB. 



Cor. When A is so small that cos* A may be consider- 

 ed as = 1, power : resistance : : 2A0 sin A : AB. When 

 the two ends B,B', are immediately applied to each other, 

 as in Prop. I. the ratio is that of 2 sin A : 1. Hence when 

 two levers act by circular cheeks, they furnish a mechanical 

 advantage greater than that of two simple levers of equal 

 length at the same angle of obliquity, in the ratio of the 

 length of the lever to the excess of this length above the ra- 

 dius of curvature of the cheek.* 



Prop. VH. Let two equal rods AB, A'B' (Fig. 7) resting 

 on the immoveable points A,A', support the circular plane 

 BEB' at two opposite points of the circumference B,B'; and 

 let this plane be capable of turning round and sliding parallel 

 to itself on the fixed line CF, which passes through its centre 

 and rises perpendicularly from C the middle of the line AA' : 

 if DE be drawn parallel to CA, the power acting at the cir- 

 cumference B, is to the weight resting on B EB which it 

 will support, as the sine of BDE to radius CA, is to CD. 



* This principle (which may be called that of excentric rollers) has llie 

 farther adA'anta^e ofeutirtly avoiding friction between the adjacent surfaces. 

 It deserves an iiiquirj' whetlier the immense power which can be thus com- 

 manded does not admit of being- advantageously introduced into certain kinds 

 of machinery. Possibly it would be an imiprovement to construct the adja- 

 ^•ewt ends of the two main levers of Mr. Wells' press in this form. 



It would be easy to assign tlie ratio of the power to the resistance for differ- 

 ent obliquities of AB and CB', when BD, B'D, are elliptic arches having 

 ABjCB' for their seraitrausverse axes. But the result would be of no prac- 

 tical importance, on account of the difficulty of grinding the surfaces BD B'D 

 to an exactly elliptical form. JVhafever be the nature of these curves, the 

 proportion given in the Cor. will be true for very small obliquities, if BO.. 

 B'O' be taken equal to the radii of curvature at the points B,B'. 



