322 On Printing Presses and their Theory. 
But, a comp. BAC’; therefore power: resistance : : 
sin ABC : sin C-AB.* 
Cor. 1. When the the radii stand in opposite directions 
as C’A, CB’, ABC becomes a reflex angle of more than 
180°; 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, C AB 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 Jines whatever, 
straight or curved, to which a tangent can be drawn. for 
let AH and Bé be the tangents at the points A and B; and 
power : resistance 3: cos ABB : c AH, or (drawing the 
normals CB, C’A,) : : sin CBA : sin in C/AB. 
Remark —The ‘ar oe results will equally apply when 
the rods CB, &c. are curved, and when in con-. 
sequence of one Role d into different parts of the same 
rolier, they are not in the same plane ;—provided that CB, 
>, 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, C’B, C’D, 
(Fig. 3. * moveable about C, C’, and C”, as centres, and hav- 
ing their other extremities connected by straight rods 
an : the: power applied to A will be the resistance act- 
ing at B CBee ee ee to C’B, as sin CAD x sin C’DB 
is to sin 
is osition evidently follows from the first Cor. to the 
last, fed is equally true for all meas ositions of the cen- 
tres C, C’, C”, and of the rods C CBC 'D 
Car: When CA and AB com = into ro position of a 
straight line, sin CAB vanishes, and the power gained will 
be infinite. If the rods be so disposed that o'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 upon infinite. 
Pror. V. If any number x of equal rods be connected 
by rivets at their middle and ends as in Fig. 4, the end Cc 
| # This proposition Pitermines the. mechanical advantage pin at any 
given part of the revolution of the bar, in the Stanhope pres 
