PROFESSOR MOSELEY ON THE THEORY OF 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 l5 P 2 , &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 g>, 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 § sin <p, so that the moment of R about that point is re- 
presented by R 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 P 1? P 2 , P 3 , &c. represent these pressures, and R their resultant. Also let a x , a 2 , 
ff 3 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 P l5 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 P l5 P 2 , P 3 , &c. are pressures in equilibrium, we have by the 
principle of the equality of moments, 
Pj a x + P 2 a 2 + P 3 « 3 + & c. = X R. 
Representing, therefore, the inclinations of the directions of the pressures P l5 P 2 , P 3 , 
&e. to one another by t h2 , / 13 , t 23 - f-, &c. &c., and substituting for the value of R^, 
* The side/of C on which R L falls, is manifestly determined hy 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. 
f The inclination j, „ of the directions of any two pressures in the above expression, is taken Q 
on the supposition that both the pressures act 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 j, 2 of the pressures P, and P., represented by the arrows, 
is not the angle P, I P 2 , 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 P 2 I and I P , are 
one of them towards that point, and the other from it. 
I Poisson, Mecanique, Art. 33. 
