On Printing Presses and their Theory. 3^1 



made by the two rods, is to the cosine of the angle, made 

 hy 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- 

 plied at any other point X in CB or CB produced, — pow- 

 er : resistance : : CB'sin ABC : CX-cos BAC. 



Cor. 2. If the rods CB, BA become equal in length, 

 •/62— ^a=v'ff2— 7/2, and the general expression is reduced to 



^. That is. the DOwer is to 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 the 

 line joining their outer extremities is to the length of either. 

 Cor. 3. If the power, instead of acting in a direction 

 perpendicular to CB, act in the direction of BP, it is easily 

 inferred that power: resistance : : tan BAC-f-tan BCA : 1. 



Pkop. 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 Hne AH. 



From C draw Cb equal, and infinitely near to CB, and 

 from b as centre with BA as radius, intersect AH in a. Join 

 5, a, and draw the perpendiculars or and bs. Ar is ultimate- 

 ly equal to Bs. For Ar — Bs=AB — rs = ab — rs= (as may 



be easily shewn) ■ . J^ ^ . This being an infinitesimal of 



•' '' AC-f-rs ° 



the second order, is ultimately evanescent in respect to 

 Ar, and consequently Ar — Bs=0, or Ar=Bs. It follows 

 that Aa : B6 : : sec BAH : sec 6Bs : : sec BAH : cosec 

 CBA: : sin CBA : cos BAH. But Aa and B& measure 

 the velocities of the points A and B ; hence power : resist- 

 ance : : sin ABC : cos BAH. This result includes that of 

 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 acting 

 at A with which it is in equihbrio, as the sine of CBA is to 

 the sine of CAB. 



For draw through A the line AH perpendicular to AC : 

 then the initial nwtion of A will be in the line AH, and by 

 the last Prop, power : resistance : : sin ABC : cos BAtJ> 



Vol. Ill No. 2. 41 



