268 APPLIED MECHANICS 
2 gl ‘ 
Hence M= -anipp |" rdr = 2rlpp m1 ; nm =alup(ri — 73). 
Ys 
The portion of the load P carried by the ring of radius 7, already 
referred to, is 
Qrr ee sin 0=2mprdr, therefore P= 2np|" 1 rdr=mp(r? — 13). 
73 
Hence dee See ig and this will be smaller, the smaller 7 is. Taking 
For a flat pivot it was shown that for uniform pressure M=2uPr, 
and for uniform wear M = weer. It would therefore appear that the 
friction of the Schiele pivot is greater than that of the flat pivot, but it 
is claimed for the Schiele pivot that the wear 
and pressure being uniform at every point, the {§ 
surfaces always fit one another, and the lubricant A” 
is not forced out. 
An approximate method of drawing the 
tractrix is shown in Fig. 410. Take points a, 
b, c, etc, on the axis YY. The distances ab, 
be, etc., may be made equal to about one-tenth 
of 7; The constant length of the tangent Y 
is taken=aA=/=r,. With centre 0 and 
radius = 2 describe an are to cut aA at HIG. GE 
B; join DB. With centre ¢ and radius=/ describe an arc to cut bB 
at C; join cC, and soon. A, B, C, etc., may be taken as points on the 
tractrix. 
It may be mentioned that a tractrix is the involute of a catenary, a 
fact which suggests a method of drawing the curve. 
A simple mechanical method of drawing the tractrix accurately is 
shown in Fig. 411. CD is an arm carrying a steel ye E with rounded 
ends, and a pencil F, the lead of which is very 
hard and sharpened to a knife edge, the edge le 
being slightly convex in the direction of its wif li 
length. The distance between the axes of the D Ci! ey 
pin E and pencil F is equal to J, the length of Fi a peaereae 
the tangent of the tractrix to be drawn. The 
edge of the pencil point lies in the plane of the 
axes of the pin and pencil. The arm CD carries 
a weight W as shown; this weight may weigh 
about one pound. A straight-edge HK is placed 
with one edge parallel to the axis YY, and at a 
distance from it equal to the radius of the pin E. 
Holding the straight-edge HK firmly with one 
hand, the pin E, held loosely between the thumb 
and fore-finger of the other hand, is drawn Fie 4 
along the edge of the straight-edge, the pin 
being kept vertical. The pencil F traces out the tractrix AB. It is 
essential that the drawing edge of the pencil shall be so sharp that it - 
