On Printing Presses and their Theory. 321 
made by the two rods, is to the cosine of the angle, made 
by the rod to which the resistance is opposed and the direc- 
tion of the resistance. 
Cor. 1. If the power, instead of being applied at B, is ap- 
pled at any other point. be CB or CB produced,—pow- 
er: resistance: : CBrsi ABC : CX°cos BAC. 
Cor. 2. If the rods CB, BA become equal in length, 
V b2--y2 = 02-2, and the general expression is reduced to 
et That is, the power isto the resistance as twice the 
cosine of half the angle contained by the rods is to radius,— 
or as twice the distance of their point of junction from ihe 
line j joining pes outer extremities is to the length of either. 
C e power, instead of acting in a aioe 
cot paeteutar’ to CB, act in the direction of BP, it 
inferred that power : resistance : : tan BAC+tan BCA : ‘4. 
Prop. II. It is required to determine the ratio of the for- 
ces which keep each other in equilibrio when the point A 
(Fig. 2.) is confined to move in any other given line AH. 
~ From C draw Cé equal, and infinitely near to CB, and 
from & as centre with BA as radius, intersect AH in a 2 ion 
6, a, and draw the CA caret oeh arand hs. Ar is ultimate- 
equal to - =AB—rs= 
ab—rs= 
ie: easily shewn) es ek "This being an infinitesimal of 
the second pice is ultimately evanescent in respect 
rie and eon Ar—Bs=0, or Ar=Bs. It follows 
t Aa: Bb: ec BAH: sec bBs: : sec BAH : cosec 
the velocities of the points A and B; hence power: resist- 
ance : : sin ABC : cos BAH. This result includes that 
the last Prop. as a particular case. 
Prop. III. Let the extremity A, instead of moving in a 
straight line, be confined to move in a circle, by being con- 
nected with the rod AC’, moveable about the fixed point 
C’ : the power applied to B will be to the resistance an 
at A with which it is in equilibrio, as the sine of CBA is 
_ the sine of C’AB. 
For draw through A the jine AH perpendicular to AC’: 
then the initial motion of A will be in the line AH, and a 
ba last Prop. pee resistance :: sin ABC :cos BA 
Vor. Il.....No. 2 4} 
