PROFESSOR MOSELEY ON THE THEORY OP MACHINES. 295 



direction of a radius, that is, perpendicularly upon its bearings, and could not be made 

 to turn upon them by that pressure, or to be upon the point of turning upon them. 

 The direction of R must then be on one side of C, so as to press the axis upon its 

 bearings in a direction R L, inclined to the perpendicular C L (at the point L where 

 it intersects the circumference of the axis,) at a certain angle, R L C. Moreover, it 

 is evident (by the last article) that since this force R pressing the axis upon its bear- 

 ings at L is upon the point of causing it to slip upon them, this inclination R L C of 

 R to the perpendicular C L is equal to the limiting angle of resistance of the axis and 

 its bearings*. Now the resistance of the axis is evidently equal and opposite to the 

 resultant R of all the forces P^, Pg, &c. impressed upon the body. The resistance 

 acts, therefore, in the direction L R, and is inclined to C L at an angle equal to the 

 limiting angle of resistance. 



If the radius C L of the axis be represented by f, and the limiting angle of resist- 

 ance C L R by (p, then is the perpendicular C m upon the resistance R from the centre 

 C of the axis represented by f sin ^, so that the moment of R about that point is re- 

 presented by R f sin (p. 



9. The conditions of the equilibrium of any number of pressures in the same plane, 

 applied to a body moveable about a cylindrical axis in the state bordering upon 

 motion. 



Let Pj, Pg, P3, &c. represent these pressures, and R their resultant. Also let aj, Og, 

 flg represent the perpendiculars let fall upon them severally from the centre of the 

 axis, those perpendiculars being taken with the positive signs whose corresponding 

 pressures tend to turn the system in the same direction as the pressure Pj, and those 

 negatively which tend to turn it in the opposite direction. Also let X represent the 

 perpendicular distance of the direction of the resultant R from the centre of the axis, 

 then, since R is equal and opposite to the resistance of the axis, and that this resist- 

 ance and the pressures Pj, Pg, P3, &c. are pressures in equilibrium, we have by the 

 principle of the equality of moments, 



Pi a, + P2 «2 + P3 «3 + &c. = >. R. 

 Representing, therefore, the inclinations of the directions of the pressures Pj, Pg, P3, 

 &c. to one another by /jg? '135 '2j1'5 &c. &c., and substituting for the value of RJ, 



* The side of C on which R L falls, is manifestly determined by the direction towards which the motion is 

 about to take place. In this case it is supposed about to take place towards the left. If it had been to the 

 right, the direction of R would have been on the opposite side of C. 



t The inclination «,.a of the directions of any two pressures in the above expression, is taken Q^ 

 on the supposition that both the pressures a.ct from, or both towards the point in which they in- 

 tersect, and not one towards and the other from that point ; so that in the case represented in 

 the accompanying figure the inclination <,. 2 of the pressures P, and P^ represented by the arrows, 

 is not the angle P, I P^, but the angle P, I Q, since I Q and I P, are directions of these pres- 

 sures, both tending from their point of intersection ; whilst the directions of Pj I and I P, are 

 one of them towards that point, and the other from it. 



X PoissoN, Mecanique, Art. 33. 



