322 On Printing Presses and their Theory. 



But, BAH= comp. BAG'; therefore power : resistance : : 

 sin ABC : sin C'AB.* 



Cor. 1. Wlien the the radii stand in opposite directions 

 as C'A, CB', ABC becomes a reflex angle of more than 

 ISO'^; but the sine of any arc is the same (except in regard 

 to its sign) as the sine of its supplement to 360° ; hence, as 

 before, the two forces applied at A and B' will be in equili- 

 brio when they are to each other as the sines of the angles 

 AB'C, CAB' to which they are respectively applied. 



Cor. 2. The same result may be extended to the case in 

 which A and B are confined to move in any lines whatever, 

 straight or curved, to which a tangent can be drawn. For 

 let AH and B6 be the tangents at the points A and B ; and 

 power : resistance : : cos ABh : cos BAH, or (drawing the 

 normals CB, C'A,) : : sin CBA : sin CAB. 



Remark. — The foregoing results will equally apply when 

 the rods CB, BA, &,c. are curved, and when in con- 

 sequence of being inserted into different parts of the same 

 roller, they are not in the same plane ; — provided that CB, 

 BA, fee. are taken as the perpendicular distances from the 

 central line of one roller to that of another. 



Prop. IV. Let there be three levers CA, CB, C'D, 

 (Fig. 3.) moveable about C, C , and C , as centres, and hav- 

 ing their other extremities connected by straight rods AD 

 and DB : ihe power applied to A will be the resistance act- 

 ing at B perpendicularly to CB, as sin CAD X sin C'DB 

 is to sin ADC" X sin DBC. 



This proposition evidently follows from the first Cor. to the 

 last, and is equally true for all possible positions of the cen- 

 tres C, C , C", and of the rods CA, CB,C'D. 



Cor. When CA and AB come into the position of a 

 straight line, sin CAB vanishes, and the power gained will H 



be infinite. If the rods be so disposed that C'D and DB 

 come into the position of a straight line at the same time, 

 the power gained at the moment of attaining this position 

 becomes infinite vpon infinite. 



Prop. V. If any number n of equal rods be connected 

 by rivets at their middle and ends as in Fig. 4, the end C >fll|| 



* This proposition determines the mechanical advantage gained at any 

 given part of the revolution of the bar, in the Stanhope press. 



