252 
ME. W. SPOTTIS W 0 ODE ON MULTIPLE CONTACT OF SUEFACES. 
Similarly from the two equations in 023 we obtain 
- ([O', 2, 3]2" -1 0 -f-(0” _1 2) 2 2" -1 3 . 0 ,l - 1 3)2”- 1 33 
+ ([0, 2', 3]0” _1 2 + (2 m ~ 1 0) 2 2 7 ‘ -1 3 . O»- 1 3)O’*- 1 30 2 +O' l - 1 2 . 2"- 1 OP 0 J 3 =0; 
and from the two equations in 013 
- ([O', 1, 3] l n ~ l 0 + (0 n_1 l) 2 0 n " 1 3 . l»- 1 3)l»- 1 30 ] 
+ ([0, r, 3] 0 n-1 l +(1” _1 0) 2 0" _1 3 . l n_1 3) 0’ 1 ~ 1 35 1 + 0 n-1 l .l-H)Po,^=O.J 
If we now put 
[1, 2', 3]l' t - 1 2+(2 n - 1 l) 2 2»- 1 3 . 1 W_1 3=B, "i 
[1, 2, 3']l- 1 3 + (3 , - 1 l) 8 3*- 1 2 . 1”- 1 2=B', 
[1, 2, 3']2»- 1 3 + (3»- 1 2) 2 3"- 1 l . 2”- 1 l=C, . 
[1', 2, 3]2»- 1 l+(l»- 1 2) 2 l™- 1 3 . 2” _1 3=C', 
[1', 2, 3]3”- 1 l + (l™- 1 3) 2 l“- 1 2 . 3 m_1 2=D, 
[1, 2', 3]3»- 1 2 + (2’ t - 1 3) 2 2»- 1 l . 3”- 1 l=D', 
[2', 3, 0]0 ,l - 1 2+(2™- 1 0) 2 2"- 1 3 . 0»- 1 3=F, 
[2, 3', 0]0 ,l-1 3 +(3’ l-1 0) 2 3" -1 2 . 0”- 1 2=F, 
[2, 3', 0]2’ l_1 3+(3 n-1 2) 2 3“ -1 0 . 2»- 1 0=H, 
[2, 3, O'J^O+CO-^O-^ . 2"~ 1 3=H', 
[2, 3, 0 , ]3»- 1 0+(0 n - 1 3) 2 0 re - 1 2 . 3”- 1 2=K, 
[2', 3, 0]3” -1 2 + (2 n-1 3) 2 2“ -1 0 . 3-^K', i 
[3, 0, B]0- 1 1 + (1»- 1 0) 2 1”- 1 3 . 0 n-1 3=L, [ 
[3', 0, l]0 ft_1 3+(3’ l_1 0) 2 3 n ~ 1 l . 0 W - 1 1=L', 
[3', 0, l]l w - 1 3 + (3“- 1 l) 2 3 ,l - 1 0 . l n_1 0=M, 
[3, O', l]F- 1 0 + (0»- 1 l) 2 0 w - 1 3 . 1™- 1 3=M', 
[3, O', l]3” -1 0+(0 m_1 3) 2 0”- 1 l . 3»- 1 l=0, 
[3, 0, 1 , ]3- 1 1 + (1*- 1 3) 3 1- 1 0 . 3 re-1 0=O', 
[0, 1', 2]0“- I l + (l»- 1 0) 2 F- 1 2 . 0” _1 2=P, 
[0, 1, 2']0 Jl “ I 2 + (2 n-1 0) 2 2 n_1 l . 0»- 1 l=F, 
[0, 1, 2 , ]l w_1 2 + (2“~ 1 1) 2 2”“ 1 0 . 1 B-1 0=Q, 
[O', 1, 2]l"- , 0+(0”- 1 l) 2 0»- , 2 . l m_1 2=Q', 
[O', 1, 2]2 ,,-1 0+(0 n-1 2) 2 0’ 1-1 l . 2 n_1 l=B, 
[0, 1', 2]2*- 1 l + (l- 1 2) s l*- 1 0 . 2 n-1 0=R'. J 
Substituting these values in the equations (7) . . (10) for determining 0, 0 lf 
shall obtain the following expressions : — 
